Orthogonal Matched Wavelets with Vanishing Moments: A Sparsity Design Approach

Joël Karel*, Ralf Peeters

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Web of Science)

Abstract

This paper presents a novel approach to design orthogonal wavelets matched to a signal with compact support and vanishing moments. It provides a systematic and versatile framework for matching an orthogonal wavelet to a specific signal or application. The central idea is to select a wavelet by optimizing a criterion which promotes sparsity of the wavelet representation of a prototype signal. Optimization is performed over the space of orthogonal wavelet functions with compact support, coming from filter banks with a given order. Parametrizations of this space are accompanied by explicit conditions for extra vanishing moments, to be used for constrained optimization. The approach is developed first for critically sampled wavelet transforms, then for undecimated wavelet transforms. Two different optimization criteria are presented: to achieve sparsity by L1-minimization or by L4-norm maximization. Masking can be employed by introducing weighting factors. Examples are given to demonstrate and evaluate the approach.
Original languageEnglish
Pages (from-to)3487-3514
Number of pages28
JournalCircuits Systems and Signal Processing
Volume37
Issue number8
Early online date18 Nov 2017
DOIs
Publication statusPublished - Aug 2018

Keywords

  • Orthogonal wavelets
  • Sparsity
  • Wavelet design
  • Matched wavelet
  • Polyphase
  • ORTHONORMAL BASES
  • L(1) MINIMIZATION
  • SIGNAL
  • SYSTEMS
  • RECONSTRUCTION
  • REPRESENTATION
  • DECOMPOSITION
  • EQUATIONS

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