Exact reconstruction analysis of log-sum minimization for compressed sensing

Yanning Shen, Jun Fang, Hongbin Li

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

The fact that fewer measurements are needed by log-sum minimization for sparse signal recovery than the L1-minimization has been observed by extensive experiments. Nevertheless, such a benefit brought by the use of the log-sum penalty function has not been rigorously proved. This paper provides a theoretical justification for adopting the log-sum as an alternative sparsity-encouraging function. We prove that minimizing the log-sum penalty function subject to Az = y is able to yield the exact solution, provided that a certain condition is satisfied. Specifically, our analysis suggests that, for a properly chosen regularization parameter, exact reconstruction can be attained when the restricted isometry constant δ3k is smaller than one, which presents a less restrictive isometry condition than that required by the conventional L1-type methods.

Original languageEnglish
Article number6631489
Pages (from-to)1223-1226
Number of pages4
JournalIEEE Signal Processing Letters
Volume20
Issue number12
DOIs
StatePublished - 2013

Keywords

  • Compressed sensing
  • Iterative reweighted algorithms
  • Log-sum minimization

Fingerprint

Dive into the research topics of 'Exact reconstruction analysis of log-sum minimization for compressed sensing'. Together they form a unique fingerprint.

Cite this