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. We use concentration factors which are adjusted to the standard deviation of the noise $\sqrt{\eta} \gg 1/N$ in order to detect the underlying $\mathcal{O}(1)$-edges, which are separated from the noise scale $\sqrt{\eta} \ll 1$.

• Publication year

  2007

• Venue

  SIAM Journal on Numerical Analysis

• Publication date

  2007-04-28

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1137/070689899arXiv 0704.3822
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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