Anders C. Hansen

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All published works

Action	Title	Year	Authors
+ PDF Chat	On the consistent reasoning paradox of intelligence and optimal trust in AI: The power of 'I don't know'	2024	Alexander Bastounis Paolo Campodonico Mihaela van der Schaar Ben Adcock Anders C. Hansen
+	Implicit regularization in AI meets generalized hardness of approximation in optimization -- Sharp results for diagonal linear networks	2023	Johan S. Wind Vegard Antun Anders C. Hansen
+	The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning	2023	Alexander Bastounis Alexander N. Gorban Anders C. Hansen Desmond J. Higham Danil Prokhorov Oliver J. Sutton Ivan Tyukin Qinghua Zhou
+	On the existence of optimal multi-valued decoders and their accuracy bounds for undersampled inverse problems	2023	Nina Maria Gottschling Paolo Campodonico Vegard Antun Anders C. Hansen
+	When can you trust feature selection? -- II: On the effects of random data on condition in statistics and optimisation	2023	Alexander Bastounis Felipe Cucker Anders C. Hansen
+	When can you trust feature selection? -- I: A condition-based analysis of LASSO and generalised hardness of approximation	2023	Alexander Bastounis Felipe Cucker Anders C. Hansen
+	The foundations of spectral computations via the Solvability Complexity Index hierarchy	2022	Matthew J. Colbrook Anders C. Hansen
+	The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale’s 18th problem	2022	Matthew J. Colbrook Vegard Antun Anders C. Hansen
+	Generalised hardness of approximation and the SCI hierarchy -- On determining the boundaries of training algorithms in AI	2022	Luca Eva Gazdag Anders C. Hansen
+	The extended Smale's 9th problem -- On computational barriers and paradoxes in estimation, regularisation, computer-assisted proofs and learning	2021	Alexander Bastounis Anders C. Hansen Verner Vlačić
+	The mathematics of adversarial attacks in AI - Why deep learning is unstable despite the existence of stable neural networks.	2021	Alexander Bastounis Anders C. Hansen Verner Vlačić
+	Total Variation Minimization	2021	Ben Adcock Anders C. Hansen
+	Fourier Transforms and Series	2021	Ben Adcock Anders C. Hansen
+	Local Structure and Nonuniform Recovery	2021	Ben Adcock Anders C. Hansen
+	Appendices	2021	Ben Adcock Anders C. Hansen
+	Preface	2021	Ben Adcock Anders C. Hansen
+	Linear Algebra	2021	Ben Adcock Anders C. Hansen
+	Convex Analysis and Convex Optimization	2021	Ben Adcock Anders C. Hansen
+	References	2021	Ben Adcock Anders C. Hansen
+	Properties of Walsh Functions and the Walsh Transform	2021	Ben Adcock Anders C. Hansen
+	Notation	2021	Ben Adcock Anders C. Hansen
+	Probability	2021	Ben Adcock Anders C. Hansen
+	Functional Analysis	2021	Ben Adcock Anders C. Hansen
+	Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling	2021	Ben Adcock Vegard Antun Anders C. Hansen
+	Can stable and accurate neural networks be computed? - On the barriers of deep learning and Smale's 18th problem.	2021	Vegard Antun Matthew J. Colbrook Anders C. Hansen
+	The extended Smale's 9th problem -- On computational barriers and paradoxes in estimation, regularisation, computer-assisted proofs and learning	2021	Alexander Bastounis Anders C. Hansen Verner Vlačić
+	The mathematics of adversarial attacks in AI -- Why deep learning is unstable despite the existence of stable neural networks	2021	Alexander Bastounis Anders C. Hansen Verner Vlačić
+	Computing solutions of Schrödinger equations on unbounded domains- On the brink of numerical algorithms.	2020	Simon Becker Anders C. Hansen
+ PDF Chat	On instabilities of deep learning in image reconstruction and the potential costs of AI	2020	Vegard Antun Francesco Renna Clarice Poon Ben Adcock Anders C. Hansen
+	The troublesome kernel: why deep learning for inverse problems is typically unstable.	2020	Nina Maria Gottschling Vegard Antun Ben Adcock Anders C. Hansen
+	The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems	2020	Nina Maria Gottschling Vegard Antun Ben Adcock Anders C. Hansen
+ PDF Chat	Compressed sensing MRI with variable density averaging (CS-VDA) outperforms full sampling at low SNR	2019	Jasper Schoormans Gustav J. Strijkers Anders C. Hansen Aart J. Nederveen Bram F. Coolen
+	The foundations of spectral computations via the Solvability Complexity Index hierarchy: Part II	2019	Matthew J. Colbrook Anders C. Hansen
+	Linear reconstructions and the analysis of the stable sampling rate.	2019	Laura Thesing Anders C. Hansen
+ PDF Chat	On the infinite-dimensional QR algorithm	2019	Matthew J. Colbrook Anders C. Hansen
+	What do AI algorithms actually learn? - On false structures in deep learning	2019	Laura Thesing Vegard Antun Anders C. Hansen
+	Linear reconstructions and the analysis of the stable sampling rate	2019	Laura Thesing Anders C. Hansen
+	The foundations of spectral computations via the Solvability Complexity Index hierarchy	2019	Matthew J. Colbrook Anders C. Hansen
+	On the stable sampling rate for binary measurements and wavelet reconstruction	2018	Anders C. Hansen Laura Thesing
+ PDF Chat	Linear Reconstructions and the Analysis of the Stable Sampling Rate	2018	Laura Thesing Anders C. Hansen
+ PDF Chat	Sampling from binary measurements - on reconstructions from Walsh coefficients	2017	Anders C. Hansen Laura Terhaar
+ PDF Chat	Complexity issues in computing spectra, pseudospectra and resolvents	2017	Anders C. Hansen Olavi Nevanlinna
+ PDF Chat	On the Absence of Uniform Recovery in Many Real-World Applications of Compressed Sensing and the Restricted Isometry Property and Nullspace Property in Levels	2017	Alexander Bastounis Anders C. Hansen
+ PDF Chat	BREAKING THE COHERENCE BARRIER: A NEW THEORY FOR COMPRESSED SENSING	2017	Ben Adcock Anders C. Hansen Clarice Poon Bogdan Roman
+	Complexity Issues in Computing Spectra, Pseudospectra and Resolvents	2016	Anders C. Hansen Olavi Nevanlinna
+ PDF Chat	Density Theorems for Nonuniform Sampling of Bandlimited Functions Using Derivatives or Bunched Measurements	2016	Ben Adcock Milana Gatarić Anders C. Hansen
+ PDF Chat	A Note on Compressed Sensing of Structured Sparse Wavelet Coefficients From Subsampled Fourier Measurements	2016	Ben Adcock Anders C. Hansen Bogdan Roman
+	Analyzing the structure of multidimensional compressed sensing problems through coherence	2016	Alexander Daniel Jones Ben Adcock Anders C. Hansen
+	Complexity Issues in Computing Spectra, Pseudospectra and Resolvents	2016	Anders C. Hansen Olavi Nevanlinna
+ PDF Chat	On Asymptotic Incoherence and Its Implications for Compressed Sensing of Inverse Problems	2015	Alexander Daniel Jones Ben Adcock Anders C. Hansen
+ PDF Chat	Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples	2015	Ben Adcock Milana Gatarić Anders C. Hansen
+	New barriers in complexity theory: On the solvability complexity index and the towers of algorithms	2015	Jonathan Ben-Artzi Anders C. Hansen Olavi Nevanlinna Markus Seidel
+	On the Solvability Complexity Index Hierarchy and Towers of Algorithms	2015	Jonathan Ben-Artzi Matthew J. Colbrook Anders C. Hansen Olavi Nevanlinna M. Seidel
+	Stable nonuniform sampling with weighted Fourier frames and recovery in arbitrary spaces	2015	Ben Adcock Milana Gatarić Anders C. Hansen
+	On random and deterministic compressed sensing and the Restricted Isometry Property in levels	2015	Alexander Bastounis Anders C. Hansen
+ PDF Chat	Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements	2015	Ben Adcock Anders C. Hansen Gitta Kutyniok Jackie Ma
+ PDF Chat	The Quest for Optimal Sampling: Computationally Efficient, Structure-Exploiting Measurements for Compressed Sensing	2015	Ben Adcock Anders C. Hansen Bogdan Roman
+	Continuous Compressed Sensing of Inelastic and Quasielastic Helium Atom Scattering Spectra	2015	A E Jones Anton Tamtögl Irene Calvo‐Almazán Anders C. Hansen
+ PDF Chat	Recovering Piecewise Smooth Functions from Nonuniform Fourier Measurements	2015	Ben Adcock Milana Gatarić Anders C. Hansen
+	Computing Spectra -- On the Solvability Complexity Index Hierarchy and Towers of Algorithms	2015	Jonathan Ben-Artzi Matthew J. Colbrook Anders C. Hansen Olavi Nevanlinna Markus Seidel
+	Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients	2014	Ben Adcock Anders C. Hansen
+	On Asymptotic Incoherence and its Implications for Compressed Sensing of Inverse Problems	2014	Alex D. Jones Ben Adcock Anders C. Hansen
+	On the absence of the RIP in real-world applications of compressed sensing and the RIP in levels	2014	Alexander Bastounis Anders C. Hansen
+	On asymptotic structure in compressed sensing	2014	Bogdan Roman Anders C. Hansen Ben Adcock
+	Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples	2014	Ben Adcock Milana Gatarić Anders C. Hansen
+ PDF Chat	A Stability Barrier for Reconstructions from Fourier Samples	2014	Ben Adcock Anders C. Hansen Alexei Shadrin
+	Density theorems for nonuniform sampling of bandlimited functions using derivatives or bunched measurements	2014	Ben Adcock Milana Gatarić Anders C. Hansen
+ PDF Chat	On Stable Reconstructions from Nonuniform Fourier Measurements	2014	Ben Adcock Milana Gatarić Anders C. Hansen
+	Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements	2014	Ben Adcock Anders C. Hansen Gitta Kutyniok Jackie Ma
+	A note on compressed sensing of structured sparse wavelet coefficients from subsampled Fourier measurements	2014	Ben Adcock Anders C. Hansen Bogdan Roman
+	The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing	2014	Ben Adcock Anders C. Hansen Bogdan Roman
+	On Asymptotic Incoherence and its Implications for Compressed Sensing of Inverse Problems	2014	Alex D. Jones Ben Adcock Anders C. Hansen
+	Recovering piecewise smooth functions from nonuniform Fourier measurements	2014	Ben Adcock Milana Gatarić Anders C. Hansen
+	On stable reconstructions from univariate nonuniform Fourier measurements	2013	Ben Adcock Milana Gatarić Anders C. Hansen
+	On optimal wavelet reconstructions from Fourier samples: Linearity and universality of the stable sampling rate	2013	Ben Adcock Anders C. Hansen Clarice Poon
+	Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing	2013	Ben Adcock Anders C. Hansen Clarice Poon Bogdan Roman
+	Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum	2013	Ben Adcock Anders C. Hansen Bogdan Roman Gerd Teschke
+ PDF Chat	Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem	2013	Ben Adcock Anders C. Hansen Clarice Poon
+	Breaking the coherence barrier: A new theory for compressed sensing	2013	Ben Adcock Anders C. Hansen Clarice Poon Bogdan Roman
+	On stable reconstructions from nonuniform Fourier measurements	2013	Ben Adcock Milana Gatarić Anders C. Hansen
+	Beyond consistent reconstructions: optimality and sharp bounds for generalized sampling, and application to the uniform resampling problem	2013	Ben Adcock Anders C. Hansen Clarice Poon
+	Optimal wavelet reconstructions from Fourier samples via generalized sampling	2013	Ben Adcock Anders C. Hansen Clarice Poon
+ PDF Chat	Generalized sampling: extension to frames and inverse and ill-posed problems	2012	Ben Adcock Anders C. Hansen Evelyn Herrholz Gerd Teschke
+ PDF Chat	A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases	2012	Ben Adcock Anders C. Hansen
+	On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate	2012	Ben Adcock Anders C. Hansen Clarice Poon
+	A stability barrier for reconstructions from Fourier samples	2012	Ben Adcock Anders C. Hansen Alexei Shadrin
+ PDF Chat	Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon	2011	Ben Adcock Anders C. Hansen
+	On the order of deferred correction	2011	Anders C. Hansen John Strain
+ PDF Chat	A theoretical framework for backward error analysis on manifolds	2011	Anders C. Hansen
+	On the Solvability Complexity Index, the 𝑛-pseudospectrum and approximations of spectra of operators	2010	Anders C. Hansen
+	Infinite-dimensional numerical linear algebra: theory and applications	2010	Anders C. Hansen
+	A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases	2010	Ben Adcock Anders C. Hansen
+	Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon	2010	Ben Adcock Anders C. Hansen
+	On the approximation of spectra of linear operators on Hilbert spaces	2008	Anders C. Hansen

Common Coauthors

Coauthor	Papers Together
Ben Adcock	55
Alexander Bastounis	11
Milana Gatarić	10
Vegard Antun	9
Bogdan Roman	9
Clarice Poon	9
Matthew J. Colbrook	8
Olavi Nevanlinna	6
Laura Thesing	5
Verner Vlačić	4
Nina Maria Gottschling	3
Jonathan Ben-Artzi	3
Alexander Daniel Jones	2
Gitta Kutyniok	2
Felipe Cucker	2
Paolo Campodonico	2
Markus Seidel	2
Gerd Teschke	2
Alex D. Jones	2
Alexei Shadrin	2
Jackie Ma	2
Johan S. Wind	1
A E Jones	1
Oliver J. Sutton	1
Mihaela van der Schaar	1
Anton Tamtögl	1
Luca Eva Gazdag	1
Qinghua Zhou	1
Irene Calvo‐Almazán	1
Jasper Schoormans	1
Simon Becker	1
Evelyn Herrholz	1
Ivan Tyukin	1
Francesco Renna	1
Alexander N. Gorban	1
Desmond J. Higham	1
Gustav J. Strijkers	1
Danil Prokhorov	1
Bram F. Coolen	1
Aart J. Nederveen	1
Laura Terhaar	1
John Strain	1
M. Seidel	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases	2012	Ben Adcock Anders C. Hansen	40
+	On the Solvability Complexity Index, the 𝑛-pseudospectrum and approximations of spectra of operators	2010	Anders C. Hansen	34
+ PDF Chat	Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon	2011	Ben Adcock Anders C. Hansen	34
+ PDF Chat	Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem	2013	Ben Adcock Anders C. Hansen Clarice Poon	34
+	On the approximation of spectra of linear operators on Hilbert spaces	2008	Anders C. Hansen	32
+	New tight frames of curvelets and optimal representations of objects with piecewise <i>C</i><sup>2</sup> singularities	2003	Emmanuel J. Candès David L. Donoho	31
+ PDF Chat	Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information	2006	Emmanuel J. Candès Justin Romberg Terence Tao	31
+	On optimal wavelet reconstructions from Fourier samples: Linearity and universality of the stable sampling rate	2013	Ben Adcock Anders C. Hansen Clarice Poon	29
+ PDF Chat	Pseudospectral Fourier reconstruction with the modified Inverse Polynomial Reconstruction Method	2009	Tomasz Hrycak Karlheinz Gröchenig	28
+ PDF Chat	Compressive fluorescence microscopy for biological and hyperspectral imaging	2012	Vincent Studer J. Bobin Makhlad Chahid Hamed Mousavi Emmanuel J. Candès Maxime Dahan	27
+	Wavelets on the Interval and Fast Wavelet Transforms	1993	Albert Cohen Ingrid Daubechies Pierre Vial	25
+ PDF Chat	A Probabilistic and RIPless Theory of Compressed Sensing	2011	Emmanuel J. Candès Yaniv Plan	23
+ PDF Chat	BREAKING THE COHERENCE BARRIER: A NEW THEORY FOR COMPRESSED SENSING	2017	Ben Adcock Anders C. Hansen Clarice Poon Bogdan Roman	23
+	A Wavelet Tour of Signal Processing : The Sparse Way	2008	Stéphane Mallat Gabriel Peyré	23
+	Compressed sensing	2006	David L. Donoho	22
+	GENERAL FRAMEWORK FOR CONSISTENT SAMPLING IN HILBERT SPACES	2005	Yonina C. Eldar Tobias Werther	21
+ PDF Chat	Stable and Robust Sampling Strategies for Compressive Imaging	2013	Felix Krahmer Rachel Ward	21
+	Complexity theory and numerical analysis	1997	Steve Smale	19
+ PDF Chat	A Stability Barrier for Reconstructions from Fourier Samples	2014	Ben Adcock Anders C. Hansen Alexei Shadrin	19
+	Compressed sensing and best 𝑘-term approximation	2008	Albert Cohen Wolfgang Dahmen Ronald DeVore	19
+ PDF Chat	On Stable Reconstructions from Nonuniform Fourier Measurements	2014	Ben Adcock Milana Gatarić Anders C. Hansen	19
+ PDF Chat	Spread Spectrum Magnetic Resonance Imaging	2011	Gilles Puy José P. Marques Rolf Gruetter Jean‐Philippe Thiran Dimitri Van De Ville Pierre Vandergheynst Yves Wiaux	18
+ PDF Chat	Sparsity and incoherence in compressive sampling	2007	Emmanuel J. Candès Justin Romberg	18
+ PDF Chat	Sampling-50 years after Shannon	2000	Michaël Unser	18
+ PDF Chat	Universal Adversarial Perturbations	2017	Seyed-Mohsen Moosavi-Dezfooli Alhussein Fawzi Omar Fawzi Pascal Frossard	18
+	On asymptotic structure in compressed sensing	2014	Bogdan Roman Anders C. Hansen Ben Adcock	18
+	Convergence Analysis of the Finite Section Method and Banach Algebras of Matrices	2010	Karlheinz Gröchenig Ziemowit Rzeszotnik Thomas Strohmer	18
+ PDF Chat	Image reconstruction by domain-transform manifold learning	2018	Bo Zhu Jeremiah Zhe Liu Stephen Cauley Bruce R. Rosen Matthew S. Rosen	17
+ PDF Chat	Imaging via Compressive Sampling	2008	Justin Romberg	17
+ PDF Chat	On instabilities of deep learning in image reconstruction and the potential costs of AI	2020	Vegard Antun Francesco Renna Clarice Poon Ben Adcock Anders C. Hansen	17
+	Sampling Without Input Constraints: Consistent Reconstruction in Arbitrary Spaces	2004	Yonina C. Eldar	17
+ PDF Chat	Deep Convolutional Neural Network for Inverse Problems in Imaging	2017	Kyong Hwan Jin Michael T. McCann Emmanuel Froustey Michaël Unser	17
+	Coherence estimates between Hadamard matrices and Daubechies wavelets	2016	Vegard Antun	17
+ PDF Chat	On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines	1989	Lenore Blum M. Shub Steve Smale	17
+ PDF Chat	Convolutional Neural Networks for Inverse Problems in Imaging: A Review	2017	Michael T. McCann Kyong Hwan Jin Michaël Unser	17
+	Mathematical problems for the next century	1998	Steve Smale	17
+ PDF Chat	Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?	2006	Emmanuel J. Candès Terence Tao	16
+	Nonlinear approximation	1998	Ronald DeVore	16
+	Compactly supported shearlets are optimally sparse	2011	Gitta Kutyniok Wang‐Q Lim	16
+	C* - Algebras and Numerical Analysis	2000	Ronald Hagen Steffen Roch Bernd Silbermann	16
+	Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method	2006	Marko Lindner	16
+ PDF Chat	An Analysis of Block Sampling Strategies in Compressed Sensing	2016	Jérémie Bigot Claire Boyer Pierre Weiss	16
+ PDF Chat	On the Absence of Uniform Recovery in Many Real-World Applications of Compressed Sensing and the Restricted Isometry Property and Nullspace Property in Levels	2017	Alexander Bastounis Anders C. Hansen	16
+	Biorthogonal bases of compactly supported wavelets	1992	Albert Cohen Ingrid Daubechies Jean-Christophe Feauveau	16
+ PDF Chat	Structured Compressed Sensing: From Theory to Applications	2011	Marco F. Duarte Yonina C. Eldar	16
+ PDF Chat	Interpolation via weighted ℓ1 minimization	2015	Holger Rauhut Rachel Ward	16
+ PDF Chat	Towards a Mathematical Theory of Super‐resolution	2013	Emmanuel J. Candès Carlos Fernandez‐Granda	16
+ PDF Chat	Fundamental Performance Limits for Ideal Decoders in High-Dimensional Linear Inverse Problems	2014	Anthony Bourrier Mike Davies Tomer Peleg Patrick Pérez Rémi Gribonval	16
+ PDF Chat	Compressive Imaging Using Approximate Message Passing and a Markov-Tree Prior	2012	Subhojit Som Philip Schniter	15
+ PDF Chat	The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing	2013	Andreas M. Tillmann Marc E. Pfetsch	15