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

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 &#34;smoothness&#34; 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.