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Recovery of Edges from Spectral Data with Noise—A New Perspective

Recovery of Edges from Spectral Data with Noise—A New Perspective

We consider the problem of detecting edges—jump discontinuities in piecewise smooth functions from their N-degree spectral content, which is assumed to be corrupted by noise. There are three scales involved: the "smoothness" scale of order $1/N$, the noise scale of order $\sqrt{\eta}$, and the $\mathcal{O}(1)$ scale of the jump discontinuities. …