Weighted Thresholding and Nonlinear Approximation

Emil Solsbæk Ottosen, Morten Nielsen

Research output: Working paperResearch

Abstract

We present a new method for performing nonlinear approximation with redundant dictionaries. The method constructs an m−term approximation of the signal by thresholding with respect to a weighted version of its canonical expansion coefficients, thereby accounting for dependency between the coefficients. The main result is an associated strong Jackson embedding, which provides an upper bound on the corresponding reconstruction error. To complement the theoretical results, we compare the proposed method to the pure greedy method and the Windowed-Group Lasso by denoising music signals with elements from a Gabor dictionary.
Original languageEnglish
PublisherArXiv
Number of pages22
Publication statusPublished - Nov 2017

Keywords

  • weighted thresholdin
  • nonlinear approximation
  • Time-frequency analysis
  • Gabor frames
  • modulation spaces
  • social sparcity

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