Computer Science › Computer Vision and Pattern Recognition

Image and Signal Denoising Methods

Works Count: 82519

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Description

This cluster of papers encompasses a wide range of techniques and algorithms for image denoising, including sparse representations, wavelet transform, deep learning with convolutional neural networks, non-local means, and methods specific to handling different types of noise such as Gaussian, Poisson, and salt-and-pepper noise. The applications also extend to hyperspectral imaging and the use of anisotropic diffusion for speckle reduction.

Keywords

Image Denoising; Sparse Representations; Wavelet Transform; Deep Learning; Non-Local Means; Hyperspectral Imaging; Gaussian Noise; Anisotropic Diffusion; Poisson Noise; Convolutional Neural Networks

Wavelet methods for time series analysis

2001-04-01

Donald B. Percival , Andrew T. Walden

1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. … 1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. The discrete wavelet packet transform 7. Random variables and stochastic processes 8. The wavelet variance 9. Analysis and synthesis of long memory processes 10. Wavelet-based signal estimation 11. Wavelet analysis of finite energy signals Appendix. Answers to embedded exercises References Author index Subject index.

Wavelets and signal processing

1991-10-01

Olivier Rioul , Martin Vetterli

A simple, nonrigorous, synthetic view of wavelet theory is presented for both review and tutorial purposes. The discussion includes nonstationary signal analysis, scale versus frequency, wavelet analysis and synthesis, scalograms, … A simple, nonrigorous, synthetic view of wavelet theory is presented for both review and tutorial purposes. The discussion includes nonstationary signal analysis, scale versus frequency, wavelet analysis and synthesis, scalograms, wavelet frames and orthonormal bases, the discrete-time case, and applications of wavelets in signal processing. The main definitions and properties of wavelet transforms are covered, and connections among the various fields where results have been developed are shown.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

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Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures

2009-01-01

Zhou Wang , Alan C. Bovik

In this article, we have reviewed the reasons why we (collectively) want to love or leave the venerable (but perhaps hoary) MSE. We have also reviewed emerging alternative signal fidelity … In this article, we have reviewed the reasons why we (collectively) want to love or leave the venerable (but perhaps hoary) MSE. We have also reviewed emerging alternative signal fidelity measures and discussed their potential application to a wide variety of problems. The message we are trying to send here is not that one should abandon use of the MSE nor to blindly switch to any other particular signal fidelity measure. Rather, we hope to make the point that there are powerful, easy-to-use, and easy-to-understand alternatives that might be deployed depending on the application environment and needs. While we expect (and indeed, hope) that the MSE will continue to be widely used as a signal fidelity measure, it is our greater desire to see more advanced signal fidelity measures being used, especially in applications where perceptual criteria might be relevant. Ideally, the performance of a new signal processing algorithm might be compared to other algorithms using several fidelity criteria. Lastly, we hope that we have given further motivation to the community to consider recent advanced signal fidelity measures as design criteria for optimizing signal processing algorithms and systems. It is in this direction that we believe that the greatest benefit eventually lies.

Localization of the complex spectrum: the S transform

1996-04-01

R. G. Stockwell , L. Mansinha , R. P. Lowe

The S transform, which is introduced in the present correspondence, is an extension of the ideas of the continuous wavelet transform (CWT) and is based on a moving and scalable … The S transform, which is introduced in the present correspondence, is an extension of the ideas of the continuous wavelet transform (CWT) and is based on a moving and scalable localizing Gaussian window. It is shown to have some desirable characteristics that are absent in the continuous wavelet transform. The S transform is unique in that it provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. These advantages of the S transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis, whereas the localizing scalable Gaussian window dilates and translates.

Atomic Decomposition by Basis Pursuit

1998-01-01

Scott Shaobing Chen , David L. Donoho , Michael A. Saunders

The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries --- stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition … The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries --- stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for decomposition have been proposed, including the method of frames (MOF), Matching pursuit (MP), and, for special dictionaries, the best orthogonal basis (BOB). Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions. We give examples exhibiting several advantages over MOF, MP, and BOB, including better sparsity and superresolution. BP has interesting relations to ideas in areas as diverse as ill-posed problems, in abstract harmonic analysis, total variation denoising, and multiscale edge denoising. BP in highly overcomplete dictionaries leads to large-scale optimization problems. With signals of length 8192 and a wavelet packet dictionary, one gets an equivalent linear program of size 8192 by 212,992. Such problems can be attacked successfully only because of recent advances in linear programming by interior-point methods. We obtain reasonable success with a primal-dual logarithmic barrier method and conjugate-gradient solver.

The wavelet transform, time-frequency localization and signal analysis

1990-01-01

Ingrid Daubechies

Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied. The first procedure is the short-time or windowed Fourier transform; the second is … Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied. The first procedure is the short-time or windowed Fourier transform; the second is the wavelet transform, in which high-frequency components are studied with sharper time resolution than low-frequency components. The similarities and the differences between these two methods are discussed. For both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time-frequency density. Finally, the notion of time-frequency localization is made precise, within this framework, by two localization theorems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

A Global Geometric Framework for Nonlinear Dimensionality Reduction

2000-12-22

Joshua B. Tenenbaum , Vin de Silva , John Langford

Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures … Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs—30,000 auditory nerve fibers or 106 optic nerve fibers—a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.

The dual-tree complex wavelet transform

2005-11-01

Ivan Selesnick , Richard G. Baraniuk , NG Kingsbury

The paper discusses the theory behind the dual-tree transform, shows how complex wavelets with good properties can be designed, and illustrates a range of applications in signal and image processing. … The paper discusses the theory behind the dual-tree transform, shows how complex wavelets with good properties can be designed, and illustrates a range of applications in signal and image processing. The authors use the complex number symbol C in CWT to avoid confusion with the often-used acronym CWT for the (different) continuous wavelet transform. The four fundamentals, intertwined shortcomings of wavelet transform and some solutions are also discussed. Several methods for filter design are described for dual-tree CWT that demonstrates with relatively short filters, an effective invertible approximately analytic wavelet transform can indeed be implemented using the dual-tree approach.

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Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images

1984-11-01

Stuart Geman , Donald Geman

We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a … We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (``annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ``relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.

The structure of images

1984-08-01

Jan J. Koenderink

A Practical Guide to Wavelet Analysis

1998-01-01

Christopher Torrence , Gilbert P. Compo

A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Niño–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier … A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Niño–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmöller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of changes in ENSO variance on interdecadal timescales. Using new datasets that extend back to 1871, the Niño3 sea surface temperature and the Southern Oscillation index show significantly higher power during 1880–1920 and 1960–90, and lower power during 1920–60, as well as a possible 15-yr modulation of variance. The power Hovmöller of sea level pressure shows significant variations in 2–8-yr wavelet power in both longitude and time.

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Embedded image coding using zerotrees of wavelet coefficients

1993-01-01

J.M. Shapiro

The embedded zerotree wavelet algorithm (EZW) is a simple, yet remarkably effective, image compression algorithm, having the property that the bits in the bit stream are generated in order of … The embedded zerotree wavelet algorithm (EZW) is a simple, yet remarkably effective, image compression algorithm, having the property that the bits in the bit stream are generated in order of importance, yielding a fully embedded code. The embedded code represents a sequence of binary decisions that distinguish an image from the "null" image. Using an embedded coding algorithm, an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly. Also, given a bit stream, the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream. In addition to producing a fully embedded bit stream, the EZW consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images. Yet this performance is achieved with a technique that requires absolutely no training, no pre-stored tables or codebooks, and requires no prior knowledge of the image source. The EZW algorithm is based on four key concepts: (1) a discrete wavelet transform or hierarchical subband decomposition, (2) prediction of the absence of significant information across scales by exploiting the self-similarity inherent in images, (3) entropy-coded successive-approximation quantization, and (4) universal lossless data compression which is achieved via adaptive arithmetic coding.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering

2007-08-01

Kostadin Dabov , Alessandro Foi , Vladimir Katkovnik +1 more

We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2D image fragments (e.g., … We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2D image fragments (e.g., blocks) into 3D data arrays which we call "groups." Collaborative Altering is a special procedure developed to deal with these 3D groups. We realize it using the three successive steps: 3D transformation of a group, shrinkage of the transform spectrum, and inverse 3D transformation. The result is a 3D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.

WAVELET TRANSFORMS AND THEIR APPLICATIONS TO TURBULENCE

1992-01-01

Marie Farge

Wavelet transforms are recent mathematical techniques, based on group theory and square integrable representations, which allows one to unfold a signal, or a field, into both space and scale, and … Wavelet transforms are recent mathematical techniques, based on group theory and square integrable representations, which allows one to unfold a signal, or a field, into both space and scale, and possibly directions. They use analyzing functions, called wavelets, which are localized in space. The scale decomposition is obtained by dilating or contracting the chosen analyzing wavelet before convolving it with the signal. The limited spatial support of wavelets is important because then the behavior of the signal at infinity does not play any role. Therefore the wavelet analysis or syn thesis can be performed locally on the signal, as opposed to the Fourier transform which is inherently nonlocal due to the space-filling nature of the trigonometric functions. Wavelet transforms have been applied mostly to signal processing, image coding, and numerical analysis, and they are still evolving. So far there are only two complete presentations of this topic, both written in French, one for engineers (Gasquet & Witomski 1 990) and the other for mathematicians (Meyer 1 990a), and two conference proceedings, the first in English (Combes et al 1 989), the second in French (Lemarie 1 990a). In preparation are a textbook (Holschneider 199 1 ), a course (Dau bee hies 1 99 1), three conference procecdings (Mcyer & Paul 199 1 , Beylkin et al 199 1b, Farge et al 1 99 1), and a special issue of IEEE Transactions

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Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I

1961-01-01

D. Slepian , H. O. Pollak

A complete set of bandlimited functions is described which possesses the curious property of being orthogonal over a given finite interval as well as over (− ∞, ∞). Properties of … A complete set of bandlimited functions is described which possesses the curious property of being orthogonal over a given finite interval as well as over (− ∞, ∞). Properties of the functions are derived and several applications to the representation of signals are made.

Atomic Decomposition by Basis Pursuit

2001-01-01

Scott Shaobing Chen , David L. Donoho , Michael A. Saunders

The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries---stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete … The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries---stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for decomposition have been proposed, including the method of frames (MOF), matching pursuit (MP), and, for special dictionaries, the best orthogonal basis (BOB). Basis pursuit (BP) is a principle for decomposing a signal into an "optimal"' superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions. We give examples exhibiting several advantages over MOF, MP, and BOB, including better sparsity and superresolution. BP has interesting relations to ideas in areas as diverse as ill-posed problems, abstract harmonic analysis, total variation denoising, and multiscale edge denoising. BP in highly overcomplete dictionaries leads to large-scale optimization problems. With signals of length 8192 and a wavelet packet dictionary, one gets an equivalent linear program of size 8192 by 212,992. Such problems can be attacked successfully only because of recent advances in linear and quadratic programming by interior-point methods. We obtain reasonable success with a primal-dual logarithmic barrier method and conjugate-gradient solver.

Adapting to Unknown Smoothness via Wavelet Shrinkage

1995-12-01

David L. Donoho , Iain M. Johnstone

Abstract We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet coefficients. The thresholding … Abstract We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: A threshold level is assigned to each dyadic resolution level by the principle of minimizing the Stein unbiased estimate of risk (Sure) for threshold estimates. The computational effort of the overall procedure is order N · log(N) as a function of the sample size N. SureShrink is smoothness adaptive: If the unknown function contains jumps, then the reconstruction (essentially) does also; if the unknown function has a smooth piece, then the reconstruction is (essentially) as smooth as the mother wavelet will allow. The procedure is in a sense optimally smoothness adaptive: It is near minimax simultaneously over a whole interval of the Besov scale; the size of this interval depends on the choice of mother wavelet. We know from a previous paper by the authors that traditional smoothing methods—kernels, splines, and orthogonal series estimates—even with optimal choices of the smoothing parameter, would be unable to perform in a near-minimax way over many spaces in the Besov scale. Examples of SureShrink are given. The advantages of the method are particularly evident when the underlying function has jump discontinuities on a smooth background.

Orthonormal bases of compactly supported wavelets

1988-10-01

Ingrid Daubechies

Abstract We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of … Abstract We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction. The construction then follows from a synthesis of these different approaches.

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Nonlinear total variation based noise removal algorithms

1992-11-01

L. Rudin , Stanley Osher , Emad Fatemi

On the use of windows for harmonic analysis with the discrete Fourier transform

1978-01-01

F.J. Harris

This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of … This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared. Finally, an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.

The contourlet transform: an efficient directional multiresolution image representation

2005-11-15

N. Minh , Martin Vetterli

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, … The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information. The main challenge in exploring geometry in images comes from the discrete nature of the data. Thus, unlike other approaches, such as curvelets, that first develop a transform in the continuous domain and then discretize for sampled data, our approach starts with a discrete-domain construction and then studies its convergence to an expansion in the continuous domain. Specifically, we construct a discrete-domain multiresolution and multidirection expansion using nonseparable filter banks, in much the same way that wavelets were derived from filter banks. This construction results in a flexible multiresolution, local, and directional image expansion using contour segments, and, thus, it is named the contourlet transform. The discrete contourlet transform has a fast iterated filter bank algorithm that requires an order N operations for N-pixel images. Furthermore, we establish a precise link between the developed filter bank and the associated continuous-domain contourlet expansion via a directional multiresolution analysis framework. We show that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing applications. Index Terms-Contourlets, contours, filter banks, geometric image processing, multidirection, multiresolution, sparse representation, wavelets.

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Adaptive wavelet thresholding for image denoising and compression

2000-01-01

Shih-Fu Chang , Bin Yu , Martin Vetterli

The first part of this paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresholding. The threshold is derived in a Bayesian framework, and the prior used on … The first part of this paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing applications. The proposed threshold is simple and closed-form, and it is adaptive to each subband because it depends on data-driven estimates of the parameters. Experimental results show that the proposed method, called BayesShrink, is typically within 5% of the MSE of the best soft-thresholding benchmark with the image assumed known. It also outperforms SureShrink (Donoho and Johnstone 1994, 1995; Donoho 1995) most of the time. The second part of the paper attempts to further validate claims that lossy compression can be used for denoising. The BayesShrink threshold can aid in the parameter selection of a coder designed with the intention of denoising, and thus achieving simultaneous denoising and compression. Specifically, the zero-zone in the quantization step of compression is analogous to the threshold value in the thresholding function. The remaining coder design parameters are chosen based on a criterion derived from Rissanen's minimum description length (MDL) principle. Experiments show that this compression method does indeed remove noise significantly, especially for large noise power. However, it introduces quantization noise and should be used only if bitrate were an additional concern to denoising.

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Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition

2002-12-30

Y. C. Pati , R. Rezaiifar , P. S. Krishnaprasad

We describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. affine (wavelet) frames. We propose a modification … We describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. affine (wavelet) frames. We propose a modification to the matching pursuit algorithm of Mallat and Zhang (1992) that maintains full backward orthogonality of the residual (error) at every step and thereby leads to improved convergence. We refer to this modified algorithm as orthogonal matching pursuit (OMP). It is shown that all additional computation required for the OMP algorithm may be performed recursively.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

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A theory for multiresolution signal decomposition: the wavelet representation

1989-07-01

Stéphane Mallat

Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that … Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

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A Review of Image Denoising Algorithms, with a New One

2005-01-01

Antoni Buades , B. Coll , Jean‐Michel Morel

The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, … The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding performance when the image model corresponds to the algorithm assumptions but fail in general and create artifacts or remove image fine structures. The main focus of this paper is, first, to define a general mathematical and experimental methodology to compare and classify classical image denoising algorithms and, second, to propose a nonlocal means (NL-means) algorithm addressing the preservation of structure in a digital image. The mathematical analysis is based on the analysis of the "method noise," defined as the difference between a digital image and its denoised version. The NL-means algorithm is proven to be asymptotically optimal under a generic statistical image model. The denoising performance of all considered methods are compared in four ways; mathematical: asymptotic order of magnitude of the method noise under regularity assumptions; perceptual-mathematical: the algorithms artifacts and their explanation as a violation of the image model; quantitative experimental: by tables of L2 distances of the denoised version to the original image. The most powerful evaluation method seems, however, to be the visualization of the method noise on natural images. The more this method noise looks like a real white noise, the better the method.

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Stacked Denoising Autoencoders: Learning Useful Representations in a Deep Network with a Local Denoising Criterion

2010-03-01

Pascal Vincent , Hugo Larochelle , Isabelle Lajoie +2 more

We explore an original strategy for building deep networks, based on stacking layers of denoising autoencoders which are trained locally to denoise corrupted versions of their inputs. The resulting algorithm … We explore an original strategy for building deep networks, based on stacking layers of denoising autoencoders which are trained locally to denoise corrupted versions of their inputs. The resulting algorithm is a straightforward variation on the stacking of ordinary autoencoders. It is however shown on a benchmark of classification problems to yield significantly lower classification error, thus bridging the performance gap with deep belief networks (DBN), and in several cases surpassing it. Higher level representations learnt in this purely unsupervised fashion also help boost the performance of subsequent SVM classifiers. Qualitative experiments show that, contrary to ordinary autoencoders, denoising autoencoders are able to learn Gabor-like edge detectors from natural image patches and larger stroke detectors from digit images. This work clearly establishes the value of using a denoising criterion as a tractable unsupervised objective to guide the learning of useful higher level representations.

De-noising by soft-thresholding

1995-05-01

David L. Donoho

Donoho and Johnstone (1994) proposed a method for reconstructing an unknown function f on [0,1] from noisy data d/sub i/=f(t/sub i/)+/spl sigma/z/sub i/, i=0, ..., n-1,t/sub i/=i/n, where the z/sub … Donoho and Johnstone (1994) proposed a method for reconstructing an unknown function f on [0,1] from noisy data d/sub i/=f(t/sub i/)+/spl sigma/z/sub i/, i=0, ..., n-1,t/sub i/=i/n, where the z/sub i/ are independent and identically distributed standard Gaussian random variables. The reconstruction f/spl circ/*/sub n/ is defined in the wavelet domain by translating all the empirical wavelet coefficients of d toward 0 by an amount /spl sigma//spl middot//spl radic/(2log (n)/n). The authors prove two results about this type of estimator. [Smooth]: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures. [Adapt]: the estimator comes nearly as close in mean square to f as any measurable estimator can come, uniformly over balls in each of two broad scales of smoothness classes. These two properties are unprecedented in several ways. The present proof of these results develops new facts about abstract statistical inference and its connection with an optimal recovery model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

A two-dimensional interpolation function for irregularly-spaced data

1968-01-01

Donald S. Shepard

In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface. These irregularly-spaced locations, hence referred to as “data points,” … In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface. These irregularly-spaced locations, hence referred to as “data points,” may have diverse meanings: in meterology, weather observation stations; in geography, surveyed locations; in city and regional planning, centers of data-collection zones; in biology, observation locations. It is assumed that a unique number (such as rainfall in meteorology, or altitude in geography) is associated with each data point.

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Transformed Up-Down Methods in Psychoacoustics

1971-02-01

Harry Levitt

During the past decade a number of variations in the simple up-down procedure have been used in psychoacoustic testing. A broad class of these methods is described with due emphasis … During the past decade a number of variations in the simple up-down procedure have been used in psychoacoustic testing. A broad class of these methods is described with due emphasis on the related problems of parameter estimation and the efficient placing of observations. The advantages of up-down methods are many, including simplicity, high efficiency, robustness, small-sample reliability, and relative freedom from restrictive assumptions. Several applications of these procedures in psychoacoustics are described, including examples where conventional techniques are inapplicable.

Image coding using wavelet transform

1992-04-01

Marc Antonini , Michel Barlaud , Pierre-Philippe Mathieu +1 more

A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. This method involves two steps. First, a wavelet transform used … A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. This method involves two steps. First, a wavelet transform used in order to obtain a set of biorthogonal subclasses of images: the original image is decomposed at different scales using a pyramidal algorithm architecture. The decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image. Second, according to Shannon's rate distortion theory, the wavelet coefficients are vector quantized using a multiresolution codebook. To encode the wavelet coefficients, a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed. In order to allow the receiver to recognize a picture as quickly as possible at minimum cost, a progressive transmission scheme is presented. It is shown that the wavelet transform is particularly well adapted to progressive transmission.

Singularity detection and processing with wavelets

1992-03-01

Stéphane Mallat , Wen-Liang Hwang

The mathematical characterization of singularities with Lipschitz exponents is reviewed. Theorems that estimate local Lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed. It … The mathematical characterization of singularities with Lipschitz exponents is reviewed. Theorems that estimate local Lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed. It is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their Lipschitz exponents. The wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately. The local frequency of such oscillations is measured from the wavelet transform modulus maxima. It has been shown numerically that one- and two-dimensional signals can be reconstructed, with a good approximation, from the local maxima of their wavelet transform modulus. As an application, an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales. In two dimensions, the wavelet transform maxima indicate the location of edges in images.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

2006-11-16

Michael Elad , Michal Aharon

We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and … We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and redundant representations over trained dictionaries. Using the K-SVD algorithm, we obtain a dictionary that describes the image content effectively. Two training options are considered: using the corrupted image itself, or training on a corpus of high-quality image database. Since the K-SVD is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm. This leads to a state-of-the-art denoising performance, equivalent and sometimes surpassing recently published leading alternative denoising methods.

Spectrum estimation and harmonic analysis

1982-01-01

David J. Thomson

In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," … In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," are dominant. In this paper we present a new method based on a "local" eigenexpansion to estimate the spectrum in terms of the solution of an integral equation. Computationally this method is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows (discrete prolate spheroidal sequences) to treat both the bias and smoothing problems. Some of the attractive features of this estimate are: there are no arbitrary windows; it is a small sample theory; it is consistent; it provides an analysis-of-variance test for line components; and it has high resolution. We also show relations of this estimate to maximum-likelihood estimates, show that the estimation capacity of the estimate is high, and show applications to coherence and polyspectrum estimates.

Entropy-based algorithms for best basis selection

1992-03-01

Ronald R. Coifman , Mladen Victor Wickerhauser

Adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals. It permits efficient compression of … Adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals. It permits efficient compression of a variety of signals, such as sound and images. The predefined libraries of modulated waveforms include orthogonal wavelet-packets and localized trigonometric functions, and have reasonably well-controlled time-frequency localization properties. The idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost. The method relies heavily on the remarkable orthogonality properties of the new libraries: all expansions in a given library conserve energy and are thus comparable. Several cost functionals are useful; one of the most attractive is Shannon entropy, which has a geometric interpretation in this context.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

A Wavelet Tour of Signal Processing : The Sparse Way

2008-01-01

Stéphane Mallat , Gabriel Peyré

Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising

2017-02-01

Kai Zhang , Wangmeng Zuo , Yunjin Chen +2 more

Discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction … Discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction of feed-forward denoising convolutional neural networks (DnCNNs) to embrace the progress in very deep architecture, learning algorithm, and regularization method into image denoising. Specifically, residual learning and batch normalization are utilized to speed up the training process as well as boost the denoising performance. Different from the existing discriminative denoising models which usually train a specific model for additive white Gaussian noise (AWGN) at a certain noise level, our DnCNN model is able to handle Gaussian denoising with unknown noise level (i.e., blind Gaussian denoising). With the residual learning strategy, DnCNN implicitly removes the latent clean image in the hidden layers. This property motivates us to train a single DnCNN model to tackle with several general image denoising tasks such as Gaussian denoising, single image super-resolution and JPEG image deblocking. Our extensive experiments demonstrate that our DnCNN model can not only exhibit high effectiveness in several general image denoising tasks, but also be efficiently implemented by benefiting from GPU computing.

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Adaptive filter theory

1987-06-01

Maurice Bellanger

Characterization of signals from multiscale edges

1992-07-01

Stéphane Mallat , Saishang Zhong

A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. The authors study the properties of multiscale edges through the wavelet theory. For pattern … A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. The authors study the properties of multiscale edges through the wavelet theory. For pattern recognition, one often needs to discriminate different types of edges. They show that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures. Numerical descriptors of edge types are derived. The completeness of a multiscale edge representation is also studied. The authors describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges. For images, the reconstruction errors are below visual sensitivity. As an application, a compact image coding algorithm that selects important edges and compresses the image data by factors over 30 has been implemented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

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Ideal Spatial Adaptation by Wavelet Shrinkage

1994-08-01

David L. Donoho , Iain M. Johnstone

Journal Article Ideal spatial adaptation by wavelet shrinkage Get access David L Donoho, David L Donoho Department of Statistics, Stanford University, Stanford, California, U.S.A Search for other works by this … Journal Article Ideal spatial adaptation by wavelet shrinkage Get access David L Donoho, David L Donoho Department of Statistics, Stanford University, Stanford, California, U.S.A Search for other works by this author on: Oxford Academic Google Scholar Iain M Johnstone Iain M Johnstone Department of Statistics, Stanford University, Stanford, California, U.S.A Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 81, Issue 3, September 1994, Pages 425–455, https://doi.org/10.1093/biomet/81.3.425 Published: 01 September 1994 Article history Received: 01 August 1992 Revision received: 01 June 1993 Published: 01 September 1994

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Digital Image Processing

2007-01-01

L ROSENTHALER

Digital Image Processing

2009-01-01

Mario A. Gomarasca

New approximation inversion formulas using Weinstein-Gabor transform

2025-06-24

Fethi Soltani | Open Journal of Mathematical Analysis

In this paper, we extend the one-dimensional Gabor transform discussed to the Weinstein harmonic analysis setting. We obtain the expected properties of extended Gabor transform such as inversion formula and … In this paper, we extend the one-dimensional Gabor transform discussed to the Weinstein harmonic analysis setting. We obtain the expected properties of extended Gabor transform such as inversion formula and Calderon’s reproducing formula.

Adaptive undermatched systematic error mitigation algorithm considering spatial continuity in digital image correlation

2025-06-24

Jicen Hu , Hong Miao , Jingchao Xu +3 more | Surface Topography Metrology and Properties

Abstract In the measurement of inhomogeneous complex deformations using the digital image correlation (DIC) method, systematic errors arising from undermatched shape functions are a significant source of inaccuracy, often surpassing … Abstract In the measurement of inhomogeneous complex deformations using the digital image correlation (DIC) method, systematic errors arising from undermatched shape functions are a significant source of inaccuracy, often surpassing the effects of other errors like random noise and grey-level interpolation errors. This study focuses primarily on mitigating these undermatched systematic errors. In this work, the traditional model corresponding to such errors is extended to analyse the entire subset region comprehensively. Based on this model, a novel mitigation method is proposed, which incorporates spatial continuity considerations. By averaging the recalculated displacement results for each pixel, this approach significantly minimizes potential errors introduced during calculation and achieves more accurate estimations of actual displacements when dealing with complex deformation characterization.

Radial basis function neural network (rbf-nn) for solving transient probability density function under composite stochastic noise

2025-06-24

NULL AUTHOR_ID | Physical review. E

Enhancing Galaxy Classification with U-Net Variational Autoencoders for Image Denoising

2025-06-24

S. Mirzoyan | Research in Astronomy and Astrophysics

Abstract AI-enhanced approaches are becoming common in astronomical data analysis, including&#xD;in the galaxy morphological classification. In this study, we develop an approach&#xD;that enhances galaxy classification by incorporating an image denoising … Abstract AI-enhanced approaches are becoming common in astronomical data analysis, including&#xD;in the galaxy morphological classification. In this study, we develop an approach&#xD;that enhances galaxy classification by incorporating an image denoising pre-processing step,&#xD;utilizing the U-Net Variational Autoencoder (VAE) architecture and effectively mitigating&#xD;noise in galaxy images and leading to improved classification performance. Our methodology&#xD;involves training U-Net VAEs on the EFIGI dataset. To simulate realistic observational&#xD;conditions, we introduce artifacts such as projected stars, satellite trails, and diffraction patterns&#xD;into clean galaxy images. The denoised images generated are evaluated using Peak&#xD;Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), to quantify the quality&#xD;improvements. We utilize the denoised images for galaxy classification tasks using models&#xD;such as DenseNet-201, ResNet50, VGG16 and GCNN. Simulations do reveal that, the&#xD;models trained on denoised images consistently outperform those trained on noisy images,&#xD;thus demonstrating the efficiency of the used denoising procedure. The developed approach&#xD;can be used for other astronomical datasets, via refining the VAE architecture and integrating&#xD;additional pre-processing strategies, e.g. in revealing of gravitational lenses, cosmic web&#xD;structures.

A spatially variable coupled PDE-based model for image denoising using a split Bregman algorithm

2025-06-23

A. Mohssine , Lekbir Afraites , Amine Laghrib +1 more | Zeitschrift für angewandte Mathematik und Physik

Fractional non-isotropic n-dimensional modified Stockwell transform: properties and inequalities

2025-06-23

Khaled Hleili , Youssef El Haoui | Journal of Pseudo-Differential Operators and Applications

On the approximation of sum of lognormal for correlated variates and implementation

2025-06-23

Asyraf Nadia Mohd Yunus , Nora Muda , Abdul Rahman Othman +1 more | PLoS ONE

In probabilistic modeling across engineering, finance, and telecommunications, sums of lognormal random variables frequently occur, yet no closed-form expression exists for their distribution. This study systematically evaluates three approximation methods-Wilkinson … In probabilistic modeling across engineering, finance, and telecommunications, sums of lognormal random variables frequently occur, yet no closed-form expression exists for their distribution. This study systematically evaluates three approximation methods-Wilkinson (W), Schwartz & Yeh (SY), and Inverse (I)-for correlated lognormal variates across varying sample sizes and correlation structures. Using Monte Carlo simulations with 5, 15, 25, and 30 samples and correlation coefficients of 0.3, 0.6, and 0.9, we compared Type I error rates through Anderson-Darling goodness-of-fit tests. Our findings demonstrate that the Wilkinson approximation consistently outperforms the other methods for correlated variates, exhibiting the lowest Type I error rates across all tested scenarios. This contradicts some previous findings in telecommunications literature where SY was preferred. We validated these results using real-world datasets from engineering (fatigue life of ball bearings) and finance (stock price correlations), confirming the Wilkinson approximation's superior performance through probability density function comparisons. This research provides practical guidance for selecting appropriate approximation methods when modeling correlated lognormal sums in diverse applications.

Multi-objective optimal log-Gabor filtering and threshold denoising for phase-based vibration measurement from noisy video

2025-06-23

Wendi Zhang , Shitao Sun , Jian Huang +3 more | Mechanical Systems and Signal Processing

The Multistage Filtering Method of Cavity Sonar Signal

2025-06-21

Xin Zeng , Xueshen Cao , Chao Li +3 more | Applied Geophysics

A New Class of Short‐Time Linear Canonical Transform: Theory and Applications

2025-06-20

Waseem Z. Lone , M. R. Chauhan , Amit K. Verma | Mathematical Methods in the Applied Sciences

ABSTRACT To localize the linear canonical spectrum of the time‐dependent signals, we propose a novel short‐time linear canonical transform that leverages the convolution structure of the linear canonical transform (LCT). … ABSTRACT To localize the linear canonical spectrum of the time‐dependent signals, we propose a novel short‐time linear canonical transform that leverages the convolution structure of the linear canonical transform (LCT). Unlike the traditional approach, which replaces the Fourier kernel with the LCT kernel, this method employs convolution to capture the linear canonical spectrum over limited temporal intervals, constrained by a window function. This approach not only reduces computational complexity but also holds significant potential for applications in various scientific and engineering fields. We begin our investigation by examining fundamental properties of the proposed transform, such as the orthogonality relation, inversion formula, and characterization of the range, using tools from LCT and convolution theory. Further, we explore the time‐frequency resolution and the uncertainty principles associated with the proposed transform. Additionally, we present several potential applications, including the Poisson summation formula, Paley‐Wiener criterion, and a sampling formula. To support our theoretical findings, clear examples are provided throughout the paper.

Detection of breast cancer using fractional discrete sinc transform based on empirical Fourier decomposition

2025-06-20

Mohamed Moustafa Azmy | Bio-Medical Materials and Engineering

Breast cancer is the most common cause of death among women worldwide. Early detection of breast cancer is important; for saving patients’ lives. Ultrasound and mammography are the most common … Breast cancer is the most common cause of death among women worldwide. Early detection of breast cancer is important; for saving patients’ lives. Ultrasound and mammography are the most common noninvasive methods for detecting breast cancer. Computer techniques are used to help physicians diagnose cancer. In most of the previous studies, the classification parameter rates were not high enough to achieve the correct diagnosis. In this study, new approaches were applied to detect breast cancer images from three databases. The programming software used to extract features from the images was MATLAB R2022a. Novel approaches were obtained using new fractional transforms. These fractional transforms were deduced from the fraction Fourier transform and novel discrete transforms. The novel discrete transforms were derived from discrete sine and cosine transforms. The steps of the approaches were described below. First, fractional transforms were applied to the breast images. Then, the empirical Fourier decomposition (EFD) was obtained. The mean, variance, kurtosis, and skewness were subsequently calculated. Finally, RNN-BILSTM (recurrent neural network-bidirectional-long short-term memory) was used as a classification phase. The proposed approaches were compared to obtain the highest accuracy rate during the classification phase based on different fractional transforms. The highest accuracy rate was obtained when the fractional discrete sinc transform of approach 4 was applied. The area under the receiver operating characteristic curve (AUC) was 1. The accuracy, sensitivity, specificity, precision, G-mean, and F-measure rates were 100%. If traditional machine learning methods, such as support vector machines (SVMs) and artificial neural networks (ANNs), were used, the classification parameter rates would be low. Therefore, the fourth approach used RNN-BILSTM to extract the features of breast images perfectly. This approach can be programed on a computer to help physicians correctly classify breast images.

Identification of Gaussian and poisson noise through non-convex optimization with a non-local PDE constraint of r[u]-laplace type

2025-06-20

Z. Zaabouli , Lekbir Afraites , Amine Laghrib +1 more | Numerical Algorithms

The Weinstein wavelet transform of tempered distributions

2025-06-20

Santosh Kumar Upadhyay , Amit Yadav | Asian-European Journal of Mathematics

Comparison of Gaussian and Wavelet Based Denoising Methods on fMRI Data

2025-06-20

Zhexuan Zhou | Theoretical and Natural Science

This study investigates the effectiveness of Gaussian and wavelet-based denoising methods in preprocessing functional Magnetic Resonance Imaging (fMRI) data. Through a comparative analysis, we evaluate these techniques based on their … This study investigates the effectiveness of Gaussian and wavelet-based denoising methods in preprocessing functional Magnetic Resonance Imaging (fMRI) data. Through a comparative analysis, we evaluate these techniques based on their ability to retain critical image information, influence the spatial extent of activation maps, and affect the accuracy of time series fitting. The 3D wavelet transform is shown to excel in preserving fine image details, albeit at the cost of producing smaller activation maps and poorer time series fitting. In contrast, Gaussian smoothing, while resulting in a loss of image information, generates larger activation maps with superior time series fitting. These findings highlight the trade-offs between the two methods, providing valuable insights for researchers in selecting the most appropriate denoising technique based on the specific objectives of their fMRI studies.

Multi-dimensional data interpretation for defective filter identification

2025-06-20

Pengkun Liu , Jinghua Xiao , Pingbo Tang | Deleted Journal

Robust graph-based denoising for cardiac acceleration signals

2025-06-19

Salman Almuhammad Alali , Amar Kachenoura , Lotfi Senhadji +4 more | Computers in Biology and Medicine

Deep generative models for Bayesian inference on high-rate sensor data: applications in automotive radar and medical imaging.

2025-06-19

Tristan S.W. Stevens , Jeroen Overdevest , Oisín Nolan +3 more | PubMed

Deep generative models (DGMs) have been studied and developed primarily in the context of natural images and computer vision. This has spurred the development of (Bayesian) methods that use these … Deep generative models (DGMs) have been studied and developed primarily in the context of natural images and computer vision. This has spurred the development of (Bayesian) methods that use these generative models for inverse problems in image restoration, such as denoising, inpainting and super-resolution. In recent years, generative modelling for Bayesian inference on sensory data has also gained traction. Nevertheless, the direct application of generative modelling techniques initially designed for natural images on raw sensory data is not straightforward, requiring solutions that deal with high dynamic range signals (HDR) acquired from multiple sensors or arrays of sensors that interfere with each other, and that typically acquire data at a very high rate. Moreover, the exact physical data-generating process is often complex or unknown. As a consequence, approximate models are used, resulting in discrepancies between model predictions and observations that are non-Gaussian, in turn complicating the Bayesian inverse problem. Finally, sensor data are often used in real-time processing or decision-making systems, imposing stringent requirements on, e.g. latency and throughput. In this article, we discuss some of these challenges and offer approaches to address them, all in the context of high-rate real-time sensing applications in automotive radar and medical imaging.This article is part of the theme issue 'Generative modelling meets Bayesian inference: a new paradigm for inverse problems'.

Denoising: a powerful building block for imaging, inverse problems and machine learning.

2025-06-19

Peyman Milanfar , Mauricio Delbracio | PubMed

Denoising, the process of reducing random fluctuations in a signal to emphasize essential patterns, has been a fundamental problem of interest since the dawn of modern scientific inquiry. Recent denoising … Denoising, the process of reducing random fluctuations in a signal to emphasize essential patterns, has been a fundamental problem of interest since the dawn of modern scientific inquiry. Recent denoising techniques, particularly in imaging, have achieved remarkable success, nearing theoretical limits by some measures. Yet, despite tens of thousands of research papers, the wide-ranging applications of denoising beyond noise removal have not been fully recognized. This is partly due to the vast and diverse literature, making a clear overview challenging. This article aims to address this gap. We present a clarifying perspective on denoisers, their structure and their desired properties. We emphasize the increasing importance of denoising and showcase its evolution into an essential building block for complex tasks in imaging, inverse problems and machine learning. Despite its long history, the community continues to uncover unexpected and groundbreaking uses for denoising, further solidifying its place as a cornerstone of scientific and engineering practice.This article is part of the theme issue 'Generative modelling meets Bayesian inference: a new paradigm for inverse problems'.

GCOANet: A gradient consistency constraints semi-supervised network for optical image-assisted SAR despeckling

2025-06-19

Yang Yang , Jun Pan , Jiangong Xu +3 more | International Journal of Applied Earth Observation and Geoinformation

Kernel-Diffeomorphism Bayesian Bootstrap Filter to reduce speckle noise on SAR images

2025-06-18

Mourad Zribi , Ibrahim Sadok , Bassel Marhaba | Computational Statistics

SC-BSN: Shifted Convolutions Based Blind-Spot Network for self-supervised image denoising

2025-06-18

Guo‐Yu Yang , Chengyun Song , Minglong Xue +1 more | Neurocomputing

DBFE-Net: A dual-branch feature extraction network for Gaussian blind denoising

2025-06-18

Sanzai Liu , Lihua Cao , Yunfeng Zhang +1 more | Displays

Dual‐scan self‐learning denoising for application in ultralow‐field <scp>MRI</scp>

2025-06-18

Yuxiang Zhang , Wei He , Jiamin Wu +1 more | Magnetic Resonance in Medicine

Abstract Purpose This study develops a self‐learning method to denoise MR images for use in ultralow field (ULF) applications. Methods We propose use of a self‐learning neural network for denoising … Abstract Purpose This study develops a self‐learning method to denoise MR images for use in ultralow field (ULF) applications. Methods We propose use of a self‐learning neural network for denoising 3D MRI obtained from two acquisitions (dual scan), which are utilized as training pairs. Based on the self‐learning method Noise2Noise, an effective data augmentation method and integrated learning strategy for enhancing model performance are proposed. Results Experimental results demonstrate that (1) the proposed model can produce exceptional denoising results and outperform the traditional Noise2Noise method subjectively and objectively; (2) magnitude images can be effectively denoised comparing with several state‐of‐the‐art methods on synthetic and real ULF data; and (3) the proposed method can yield better results on phase images and quantitative imaging applications than other denoisers due to the self‐learning framework. Conclusions Theoretical and experimental implementations show that the proposed self‐learning model achieves improved performance on magnitude image denoising with synthetic and real‐world data at ULF. Additionally, we test our method on calculated phase and quantification images, demonstrating its superior performance over several contrastive methods.

GNSS signal processing based on improved lifting wavelet transform with prior constraint

2025-06-18

Chen Jiang , Wenbo Yang , Y. H. Wang +1 more | Scientific Reports

A regularization-free approach for high-resolution spectral imaging based on the Lucy–Richardson–Rosen method

2025-06-17

Lianhui Zheng , Xie Yun , Zhongjian Gao | Journal of Modern Optics

2D affine transform parameters by Gaussian elimination with pivoting

2025-06-17

Tariq N. Ataiwe , Israa Mohammed , Hisham M. Jawad Al Sharaa | Archives of Civil Engineering

In many geomatics, computer vision, and computer-aided applications, coordinate transformations are needed to transform from one coordinate system to another, especially in geodesy and photogrammetry. In photogrammetry one of the … In many geomatics, computer vision, and computer-aided applications, coordinate transformations are needed to transform from one coordinate system to another, especially in geodesy and photogrammetry. In photogrammetry one of the important coordinates transformation methods used to transform photo coordinates is the 2D affine transformation which takes into consideration the change in the differences in scale factor in the x and y directions. In this paper, a new method for computing the 2D affine transform parameters will be introduced, the problem of the 2D affine transform method has been solved by Gaussian elimination with pivoting.We have derived equations by which to find transformation parameters. Geometric transformation is a technique used to define the properties of common features between different images using the same coordinates basis, This method can be effectively used in image processing and computer vision to facilitate the computation process throughout eliminating the need for solving the inverse of the matrix.

Enhancing Perception Quality in Remote Sensing Image Compression via Invertible Neural Network

2025-06-17

Junhui Li , Xingsong Hou | Remote Sensing

Despite the impressive performance of existing image compression algorithms, they struggle to balance perceptual quality and high image fidelity. To address this issue, we propose a novel invertible neural network-based … Despite the impressive performance of existing image compression algorithms, they struggle to balance perceptual quality and high image fidelity. To address this issue, we propose a novel invertible neural network-based remote sensing image compression (INN-RSIC) method. Our approach captures the compression distortion from an existing image compression algorithm and encodes it as Gaussian-distributed latent variables using an INN, ensuring that the distortion in the decoded image remains independent of the ground truth. By using the inverse mapping of the INN, we input the decoded image with randomly resampled Gaussian variables, generating enhanced images with improved perceptual quality. We incorporate channel expansion, Haar transformation, and invertible blocks into the INN to accurately represent compression distortion. Additionally, a quantization module (QM) is introduced to mitigate format conversion impact, enhancing generalization and perceptual quality. Extensive experiments show that INN-RSIC achieves superior perceptual quality and fidelity compared to existing algorithms. As a lightweight plug-and-play (PnP) method, the proposed INN-based enhancer can be easily integrated into existing high-fidelity compression algorithms, enabling flexible and simultaneous decoding of images with enhanced perceptual quality.

Non-Subsampled Contourlet Transform-Based Domain Feedback Information Distillation Network for Suppressing Noise in Seismic Data

2025-06-16

Kang Chen , Guangzhi Zhang , Cong Tang +5 more | Applied Sciences

Seismic signal processing often relies on general convolutional neural network (CNN)-based models, which typically focus on features in the time domain while neglecting frequency characteristics. Moreover, down-sampling operations in these … Seismic signal processing often relies on general convolutional neural network (CNN)-based models, which typically focus on features in the time domain while neglecting frequency characteristics. Moreover, down-sampling operations in these models tend to cause the loss of critical high-frequency details. To this end, we propose a feedback information distillation network (FID-N) in the non-subsampled contourlet transform (NSCT) domain to remarkably suppress seismic noise. The method aims to enhance denoising performance by preserving the fine-grained details and frequency characteristics of seismic data. The FID-N mainly consists of a two-path information distillation block used in a recurrent manner to form a feedback mechanism, carrying an output to correct previous states, which fully exploits competitive features from seismic signals and effectively realizes the signal restoration step by step across time. Additionally, the NSCT has an excellent high-frequency response and powerful curve and surface description capabilities. We suggest converting the noise suppression problem into NSCT coefficient prediction, which maintains more detailed high-frequency information and promotes the FID-N to further suppress noise. Extensive experiments on both synthetic and real seismic datasets demonstrated that our method significantly outperformed the SOTA methods, particularly in scenarios with low signal-to-noise ratios and in recovering high-frequency components.

Coordinate gradient descent algorithm in adaptive LASSO for pure ARCH and pure GARCH models

2025-06-16

Muhammad Jaffri Mohd Nasir , R. Nazim Khan , Gopalan Nair +1 more | Computational Statistics

RESTORE-DiT: Reliable satellite image time series reconstruction by multimodal sequential diffusion transformer

2025-06-16

Qidi Shu , Xiaolin Zhu , Shuai Xu +2 more | Remote Sensing of Environment

Morphologically reconstructed 2-D histogram with opposition learning based optimization approach for multi-level thresholding

2025-06-16

Krishna Gopal Dhal , Arunita Das , Swarnajit Ray | Cluster Computing

3D GNLM: Efficient 3D Non-Local Means Kernel with Nested Reuse Strategies for Embedded GPUs

2025-06-16

Xiang Li , Qiong Chang , Yun Li +1 more | ACM Transactions on Architecture and Code Optimization

The 3D Non-Local Means (NLM) algorithm has become a crucial preprocessing technique for 3D image data sets due to its effectiveness in denoising while preserving fine details. This method has … The 3D Non-Local Means (NLM) algorithm has become a crucial preprocessing technique for 3D image data sets due to its effectiveness in denoising while preserving fine details. This method has been proven to be highly efficient in high-demand tasks within industrial applications such as medical imaging and remote sensing. The 3D NLM algorithm computes the filtered value for each voxel by calculating the weighted average of all voxels within a 3D search window, where the weights are determined by the similarity between pairs of 3D template windows. Therefore, the computational burden becomes significant, especially in embedded GPUs with limited computational power and memory resources. To address this issue, we propose an efficient GPU parallel kernel to minimize redundant computations and memory accesses. The kernel integrates three nested reuse strategies to handle redundant computations in three dimensions: for columns, we leverage the fast data exchange mechanism to reuse column computation results via on-chip registers; for rows, we use a sliding window strategy, utilizing GPU global memory as an intermediary to store and reuse similarity values between filtered rows; and for channels, we introduce a zigzag scanning strategy that enables simultaneous computation across multiple channels and employs on-chip registers to facilitate channel computation reuse. Experimental results demonstrate that our kernel achieves an average speedup of 7.7x on the embedded Jetson AGX Xavier platform across a range of 3D image data sets compared to existing methods, showcasing exceptional performance.

Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group

2025-06-16

NULL AUTHOR_ID | Physical Review Research

High-Fidelity Image Upscaling via Convolutional Neural Networks

2025-06-15

Mayanka Chandrashekar | INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT

Abstract—This project uses Convolutional Neural Networks (CNNs) to improve image quality by making blurry or noisy images clearer. It focuses on tasks like sharpening images, removing noise, and fixing distortions. … Abstract—This project uses Convolutional Neural Networks (CNNs) to improve image quality by making blurry or noisy images clearer. It focuses on tasks like sharpening images, removing noise, and fixing distortions. Using models like SRCNN and U-Net, the system learns how to turn low-quality images into high-quality ones. The results show that CNNs work better than traditional methods for enhancing images.This work studies how Convolutional Neural Networks (CNNs) effectively improve image quality in a large variety of tasks including noise reduction, deblurring, and detail restoration. Utilizing and training models such as SRCNN and U-Net, this project assesses the performance on benchmark datasets. The results demonstrate that CNN has higher potential in low level complex transformation learning for high quality image restoration than conventional image processing approaches. Keywords:super-resolution, feature extraction, residual learning, and evaluation metrics like PSNR and SSIM.

An Improved Wavelet Soft-Threshold Function Integrated with SVMD Dual-Parameter Joint Denoising for Ancient Building Deformation Monitoring

2025-06-14

Jiaxing Zhao , Houzeng Han , Yang Deng +3 more | Remote Sensing

In deformation monitoring, complex environments, such as seismic excitation, often lead to noise during signal acquisition and transmission processing. This study integrates sequential variational mode decomposition (SVMD), a dual-parameter (DP) … In deformation monitoring, complex environments, such as seismic excitation, often lead to noise during signal acquisition and transmission processing. This study integrates sequential variational mode decomposition (SVMD), a dual-parameter (DP) model, and an improved wavelet threshold function (IWT), presenting a denoising method termed SVMD-DP-IWT. Initially, SVMD decomposes the signal to obtain intrinsic mode functions (IMFs). Subsequently, the DP parameters are determined using fuzzy entropy. Finally, the noisy IMFs denoised by IWT and the signal IMFs are used for signal reconstruction. Both simulated and engineering measurements validate the performance of the proposed method in mitigating noise. In simulation experiments, compared to wavelet soft-threshold function (WST) with the sqtwolog threshold, the root-mean-square error (RMSE) of SVMD-Dual-CC-WST (sqtwolog threshold), SVMD-DP-IWT (sqtwolog threshold), and SVMD-DP-IWT (minimaxi threshold) improved by 51.44%, 52.13%, and 52.49%, respectively. Global navigation satellite system (GNSS) vibration monitoring was conducted outdoors, and the accelerometer vibration monitoring experiment was performed on a pseudo-classical building in a multi-functional shaking table laboratory. GNSS displacement data and acceleration data were collected, and analyses of the acceleration signal characteristics were performed. SVMD-DP-IWT (sqtwolog) and SVMD-DP-IWT (minimaxi) effectively retain key vibration signal features during the denoising process. The proposed method significantly preserves vibration features during noise reduction of an ancient building in deformation monitoring, which is crucial for damage assessment.

Enhancing sonar image quality for underwater object recognition in marine environments: A review

2025-06-14

Chi Zhang , Yingqian Chai , Xiaoyang Wang +1 more | Ocean Engineering

Implementation of Fast Fourier Transform and Least Mean Square Algorithms in The Denoising Process of Audio Signal

2025-06-13

Putri Rahmasari Rayes , Nuzla Af'idatur Robbaniyyah , Syamsul Bahri | EIGEN MATHEMATICS JOURNAL

Audio signals play an important role as a medium for storing information, such as lecture materials, interview results, and other archives. However, audio signals are often contaminated by noise, which … Audio signals play an important role as a medium for storing information, such as lecture materials, interview results, and other archives. However, audio signals are often contaminated by noise, which is unwanted interference that can affect their quality. Therefore, a denoising process is needed to reduce or eliminate noise components in the signal. The Fast Fourier Transform (FFT) and Least Mean Square (LMS) algorithms are frequently used in the denoising process due to their simple and easy-to-implement steps. This research uses primary data, specifically audio signals recorded under two noise conditions: rain noise as Audio Signal 1 and guitar instrument noise as Audio Signal 2, both stored in WAV format. The denoising process was performed using MATLAB software and evaluated based on Signal-to-Noise Ratio (SNR) and Mean Squared Error (MSE) metrics. Higher SNR values and lower MSE values indicate the success of the denoising process in improving audio signal quality. The results of this study demonstrate the effectiveness of the applied algorithms, where the SNR value reached 38.2596 dB with an MSE of 0.0000028211 for Audio Signal 1, and an SNR value of 38.6881 dB with an MSE of 0.0000014988 for Audio Signal 2. An SNR value between 25 dB and 40 dB is categorized as a very good signal, indicating that the quality of the processed audio signals falls into the very good signal category.

An Effective Image Denoising Model Using Improved Deep Learning Techniques with Optimization Algorithm

2025-06-13

S. Mythili , S. S. Sivaraju , T. Anuradha +1 more | International Journal of Pattern Recognition and Artificial Intelligence

Compressed sensing transformer unfolding network for high resolution image denoising

2025-06-13

Jie Zhang , Wenxiao Huang , Miaoxin Lu +4 more | Complex & Intelligent Systems

Enhancing blind image deblurring robustness against impulse noise via adaptive noise detection and graph regularization

2025-06-13

Xin Liu , Zhe Li , Libo Cheng +1 more | Signal Image and Video Processing

An enhanced wavelet-based numerical scheme with higher convergence order for a class of high-order boundary value problems

2025-06-12

Zhang Rui-min , Lei Yang , Hui Zhu +2 more | Applied Mathematics and Computation

Broadband Measurement Algorithm Based on Smooth Linear Segmented Threshold Wavelet Denoising and Improved VMD-Prony

2025-06-12

Feng Gao , Xutao Li , Hongqiang Li | Electronics

Accurate measurement of broadband signals is fundamental to the broadband oscillation analysis of power grids. However, the measurement process of broadband signals generally suffers from noise interference and insufficient measurement … Accurate measurement of broadband signals is fundamental to the broadband oscillation analysis of power grids. However, the measurement process of broadband signals generally suffers from noise interference and insufficient measurement accuracy. To address these issues, this study introduces a novel broadband measurement algorithm that integrates smooth linear segmented threshold (SLST) wavelet denoising with a fusion of the improved variational mode decomposition (VMD) and Prony methods. Initially, noise reduction preprocessing is designed for broadband signals based on the smooth linear segmented threshold wavelet denoising method to reduce the interference of noise on the measurement process, and two evaluation indices are established based on Pearson’s correlation coefficient and the signal-to-noise ratio (SNR) to assess the effectiveness of noise reduction. Subsequently, mutual information entropy and energy entropy are employed to optimize the parameters of VMD to enhance measurement precision. The denoised signal is decomposed into several modes with distinct center frequencies using the parameter-optimized VMD, thereby simplifying the signal processing complexity. Concurrently, the Prony algorithm is integrated to accurately identify the parameters of each mode, extracting frequency, amplitude, and phase information to achieve precise broadband signal measurement. The simulation results confirm that the proposed algorithm effectively reduces noise interference and enhances the measurement accuracy of broadband signals.

Burst denoising transformer with multi-task optical flow estimation

2025-06-01

Sicheng Pan , Yingming Li | Neural Networks