Sparsity enforcing edge detection method for blurred and noisy Fourier data

W. Stefan, A. Viswanathan, Anne Gelb, Rosemary Renaut

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We present a new method for estimating the edges in a piecewise smooth function from blurred and noisy Fourier data. The proposed method is constructed by combining the so called concentration factor edge detection method, which uses a finite number of Fourier coefficients to approximate the jump function of a piecewise smooth function, with compressed sensing ideas. Due to the global nature of the concentration factor method, Gibbs oscillations feature prominently near the jump discontinuities. This can cause the misidentification of edges when simple thresholding techniques are used. In fact, the true jump function is sparse, i.e. zero almost everywhere with non-zero values only at the edge locations. Hence we adopt an idea from compressed sensing and propose a method that uses a regularized deconvolution to remove the artifacts. Our new method is fast, in the sense that it only needs the solution of a single l1 minimization. Numerical examples demonstrate the accuracy and robustness of the method in the presence of noise and blur.

Original languageEnglish (US)
Pages (from-to)536-556
Number of pages21
JournalJournal of Scientific Computing
Issue number3
StatePublished - Mar 2012


  • Compressive sensing
  • Concentration factors
  • Edge detection
  • Higher order methods
  • Partial Fourier data
  • Sparseness

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • General Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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