A Convergent Fixed-Point Proximity Algorithm Accelerated by FISTA for the ℓ0 Sparse Recovery Problem

Xueying Zeng, Lixin Shen, Yuesheng Xu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

We propose an approximation model of the original ℓ0 minimization model arising from various sparse signal recovery problems. The objective function of the proposed model uses the Moreau envelope of the ℓ0 norm to promote the sparsity of the signal in a tight framelet system. This leads to a non-convex optimization problem involved the ℓ0 norm. We identify a local minimizer of the proposed non-convex optimization problem with a global minimizer of a related convex optimization problem. Based on this identification, we develop a two stage algorithm for solving the proposed non-convex optimization problem and study its convergence. Moreover, we show that FISTA can be employed to speed up the convergence rate of the proposed algorithm to reach the optimal convergence rate of O(1 ∕ k2). We present numerical results to confirm the theoretical estimate.

Original languageEnglish (US)
Title of host publicationMathematics and Visualization
EditorsXue-Cheng Tai, Egil Bae, Marius Lysaker
PublisherSpringer Heidelberg
Pages27-45
Number of pages19
ISBN (Electronic)9783319912745
ISBN (Print)9783319912738, 9783319912738, 9783540250326, 9783540250760, 9783540332749, 9783540886051, 9783642150135, 9783642216077, 9783642231742, 9783642273421, 9783642341403, 9783642543005
DOIs
StatePublished - 2018
EventInternational conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016 - Bergen, Norway
Duration: Aug 29 2016Sep 2 2016

Publication series

NameMathematics and Visualization
Volume0
ISSN (Print)1612-3786
ISSN (Electronic)2197-666X

Other

OtherInternational conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016
Country/TerritoryNorway
CityBergen
Period8/29/169/2/16

ASJC Scopus subject areas

  • Modeling and Simulation
  • Geometry and Topology
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

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