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

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

2007-04-28

arxiv.org/abs/0704.3822v1

Mathematics

Numerical Analysis

Scientific paper

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

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