Iterative design of concentration factors for jump detection

Adityavikram Viswanathan, Anne Gelb, Douglas Cochran

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The concentration method of edge detection was developed to compute the locations and values of jump discontinuities in a piecewise-Analytic function from its first few Fourier series coefficients. The accuracy and characteristic features of the resulting jump approximation depend on Fourier space filter factors known as concentration factors. In this paper, we provide a flexible, iterative framework for the design of these factors. Previously devised concentration factors are shown to be the solutions of specific problem formulations within this new framework. We also provide sample formulations of the procedure applicable to the design of concentration factors for data with missing spectral bands. Several illustrative examples are used to demonstrate the capabilities of the method.

Original languageEnglish (US)
Pages (from-to)631-649
Number of pages19
JournalJournal of Scientific Computing
Volume51
Issue number3
DOIs
StatePublished - Jun 2012

Keywords

  • Concentration edge detection
  • Convex optimization
  • Jump detection

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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