A multilevel iterated-shrinkage approach to l1 penalized least-squares minimization

Eran Treister, Irad Yavneh

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

The area of sparse approximation of signals is drawing tremendous attention in recent years. Typically, sparse solutions of underdetermined linear systems of equations are required. Such solutions are often achieved by minimizing an l1 penalized least squares functional. Various iterative-shrinkage algorithms have recently been developed and are quite effective for handling these problems, often surpassing traditional optimization techniques. In this paper, we suggest a new iterative multilevel approach that reduces the computational cost of existing solvers for these inverse problems. Our method takes advantage of the typically sparse representation of the signal, and at each iteration it adaptively creates and processes a hierarchy of lower-dimensional problems employing well-known iterated shrinkage methods. Analytical observations suggest, and numerical results confirm, that this new approach may significantly enhance the performance of existing iterative shrinkage algorithms in cases where the matrix is given explicitly.

Original languageEnglish GB
Article number6303948
Pages (from-to)6319-6329
Number of pages11
JournalIEEE Transactions on Signal Processing
Volume60
Issue number12
DOIs
StatePublished - 1 Dec 2012
Externally publishedYes
Event2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012 - Eilat, Israel
Duration: 14 Nov 201217 Nov 2012

Keywords

  • Compressed sensing
  • Convex optimization
  • Sparse approximation

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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