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

Xueying Zeng, Lixin Shen, Yuesheng Xu

Research output: Contribution to journalConference article

1 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)
Pages (from-to)27-45
Number of pages19
JournalMathematics and Visualization
Issue number221219
DOIs
StatePublished - Jan 1 2018
EventInternational conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016 - Bergen, Norway
Duration: Aug 29 2016Sep 2 2016

ASJC Scopus subject areas

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

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