Sparse signal estimation by maximally sparse convex optimization

Ivan Selesnick, Ilker Bayram

Research output: Contribution to journalArticle

Abstract

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g., sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of non-convex penalty functions (regularizers) constrained so as to ensure the convexity of the total cost function F to be minimized. The method is based on parametric penalty functions, the parameters of which are constrained to ensure convexity of F. It is shown that optimal parameters can be obtained by semidefinite programming (SDP). This maximally sparse convex (MSC) approach yields maximally non-convex sparsity-inducing penalty functions constrained such that the total cost function F is convex. It is demonstrated that iterative MSC (IMSC) can yield solutions substantially more sparse than the standard convex sparsity-inducing approach, i.e., L1 norm minimization.

Original languageEnglish (US)
Article number6705656
Pages (from-to)1078-1092
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume62
Issue number5
DOIs
StatePublished - Mar 1 2014

Fingerprint

Convex optimization
Cost functions
Deconvolution
Signal processing

Keywords

  • basis pursuit
  • Convex optimization
  • deconvolution
  • L1 norm
  • lasso
  • non-convex optimization
  • sparse optimization
  • sparse regularization
  • threshold function

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

Cite this

Sparse signal estimation by maximally sparse convex optimization. / Selesnick, Ivan; Bayram, Ilker.

In: IEEE Transactions on Signal Processing, Vol. 62, No. 5, 6705656, 01.03.2014, p. 1078-1092.

Research output: Contribution to journalArticle

@article{0d1f8d73c2724f23abd5477adb2e65be,
title = "Sparse signal estimation by maximally sparse convex optimization",
abstract = "This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g., sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of non-convex penalty functions (regularizers) constrained so as to ensure the convexity of the total cost function F to be minimized. The method is based on parametric penalty functions, the parameters of which are constrained to ensure convexity of F. It is shown that optimal parameters can be obtained by semidefinite programming (SDP). This maximally sparse convex (MSC) approach yields maximally non-convex sparsity-inducing penalty functions constrained such that the total cost function F is convex. It is demonstrated that iterative MSC (IMSC) can yield solutions substantially more sparse than the standard convex sparsity-inducing approach, i.e., L1 norm minimization.",
keywords = "basis pursuit, Convex optimization, deconvolution, L1 norm, lasso, non-convex optimization, sparse optimization, sparse regularization, threshold function",
author = "Ivan Selesnick and Ilker Bayram",
year = "2014",
month = "3",
day = "1",
doi = "10.1109/TSP.2014.2298839",
language = "English (US)",
volume = "62",
pages = "1078--1092",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "5",

}

TY - JOUR

T1 - Sparse signal estimation by maximally sparse convex optimization

AU - Selesnick, Ivan

AU - Bayram, Ilker

PY - 2014/3/1

Y1 - 2014/3/1

N2 - This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g., sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of non-convex penalty functions (regularizers) constrained so as to ensure the convexity of the total cost function F to be minimized. The method is based on parametric penalty functions, the parameters of which are constrained to ensure convexity of F. It is shown that optimal parameters can be obtained by semidefinite programming (SDP). This maximally sparse convex (MSC) approach yields maximally non-convex sparsity-inducing penalty functions constrained such that the total cost function F is convex. It is demonstrated that iterative MSC (IMSC) can yield solutions substantially more sparse than the standard convex sparsity-inducing approach, i.e., L1 norm minimization.

AB - This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g., sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of non-convex penalty functions (regularizers) constrained so as to ensure the convexity of the total cost function F to be minimized. The method is based on parametric penalty functions, the parameters of which are constrained to ensure convexity of F. It is shown that optimal parameters can be obtained by semidefinite programming (SDP). This maximally sparse convex (MSC) approach yields maximally non-convex sparsity-inducing penalty functions constrained such that the total cost function F is convex. It is demonstrated that iterative MSC (IMSC) can yield solutions substantially more sparse than the standard convex sparsity-inducing approach, i.e., L1 norm minimization.

KW - basis pursuit

KW - Convex optimization

KW - deconvolution

KW - L1 norm

KW - lasso

KW - non-convex optimization

KW - sparse optimization

KW - sparse regularization

KW - threshold function

UR - http://www.scopus.com/inward/record.url?scp=84894593844&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894593844&partnerID=8YFLogxK

U2 - 10.1109/TSP.2014.2298839

DO - 10.1109/TSP.2014.2298839

M3 - Article

VL - 62

SP - 1078

EP - 1092

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 5

M1 - 6705656

ER -