Recovery of edges from spectral data with noise -- a new perspective

2007/04/28 by Shlomo Engelberg, Eitan Tadmor, Engelberg, Shlomo +1
Computer Science · Mathematics · #42A10 #42A50 #65T10 #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.0704.3822

openalex publication_date 2007/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of detecting edges 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 η and the O(1) scale of the jump discontinuities. We use concentration factors which are adjusted to the noise variance, η >> 1/N, in order to detect the underlying O(1)-edges, which are separated from the noise scale, η << 1.

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