Enhanced low-rank matrix approximation

Ankit Parekh, Ivan W. Selesnick

Research output: Contribution to journalArticle

Abstract

This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with nonconvex regularization. We employ parameterized nonconvex penalty functions to estimate the nonzero singular values more accurately than the nuclear norm. A closed-form solution for the global optimum of the proposed objective function (sum of data fidelity and the nonconvex regularizer) is also derived. The solution reduces to singular value thresholding method as a special case. The proposed method is demonstrated for image denoising.

Original languageEnglish (US)
Article number7420602
Pages (from-to)493-497
Number of pages5
JournalIEEE Signal Processing Letters
Volume23
Issue number4
DOIs
StatePublished - Apr 1 2016

Fingerprint

Matrix Approximation
Low-rank Approximation
Low-rank Matrices
Singular Values
Image denoising
Convex optimization
Image Denoising
Global Optimum
Penalty Function
Thresholding
Convex Optimization
Closed-form Solution
Estimate
Fidelity
Regularization
Objective function
Optimization Problem
Norm

Keywords

  • convex
  • image denoising
  • Low-rank matrix
  • non-convex regularization
  • nuclear norm
  • optimization

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing
  • Applied Mathematics

Cite this

Enhanced low-rank matrix approximation. / Parekh, Ankit; Selesnick, Ivan W.

In: IEEE Signal Processing Letters, Vol. 23, No. 4, 7420602, 01.04.2016, p. 493-497.

Research output: Contribution to journalArticle

@article{079071caccba459b84bac449712f4f38,
title = "Enhanced low-rank matrix approximation",
abstract = "This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with nonconvex regularization. We employ parameterized nonconvex penalty functions to estimate the nonzero singular values more accurately than the nuclear norm. A closed-form solution for the global optimum of the proposed objective function (sum of data fidelity and the nonconvex regularizer) is also derived. The solution reduces to singular value thresholding method as a special case. The proposed method is demonstrated for image denoising.",
keywords = "convex, image denoising, Low-rank matrix, non-convex regularization, nuclear norm, optimization",
author = "Ankit Parekh and Selesnick, {Ivan W.}",
year = "2016",
month = "4",
day = "1",
doi = "10.1109/LSP.2016.2535227",
language = "English (US)",
volume = "23",
pages = "493--497",
journal = "IEEE Signal Processing Letters",
issn = "1070-9908",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "4",

}

TY - JOUR

T1 - Enhanced low-rank matrix approximation

AU - Parekh, Ankit

AU - Selesnick, Ivan W.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with nonconvex regularization. We employ parameterized nonconvex penalty functions to estimate the nonzero singular values more accurately than the nuclear norm. A closed-form solution for the global optimum of the proposed objective function (sum of data fidelity and the nonconvex regularizer) is also derived. The solution reduces to singular value thresholding method as a special case. The proposed method is demonstrated for image denoising.

AB - This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with nonconvex regularization. We employ parameterized nonconvex penalty functions to estimate the nonzero singular values more accurately than the nuclear norm. A closed-form solution for the global optimum of the proposed objective function (sum of data fidelity and the nonconvex regularizer) is also derived. The solution reduces to singular value thresholding method as a special case. The proposed method is demonstrated for image denoising.

KW - convex

KW - image denoising

KW - Low-rank matrix

KW - non-convex regularization

KW - nuclear norm

KW - optimization

UR - http://www.scopus.com/inward/record.url?scp=84964389876&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964389876&partnerID=8YFLogxK

U2 - 10.1109/LSP.2016.2535227

DO - 10.1109/LSP.2016.2535227

M3 - Article

AN - SCOPUS:84964389876

VL - 23

SP - 493

EP - 497

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

SN - 1070-9908

IS - 4

M1 - 7420602

ER -