RECOVERY OF EDGES FROM SPECTRAL DATA WITH NOISE—A NEW PERSPECTIVE
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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 √η, and the O(1) scale of the jump discontinuities. We use concentration factors which are adjusted to the standard deviation of the noise √η ≫ 1/N in order to detect the underlying O(1)-edges, which are separated from the noise scale √η ≪ 1.