http://dx.doi.org/10.1137/10080172X">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

On L1 data fitting and concave regularization for image recovery

Language

English

Abstract

We propose a new family of cost functions for signal and image recovery: they are composed of ℓ1 data fitting terms combined with concave regularization. We exhibit when and how to employ such cost functions. Our theoretical results show that the minimizers of these cost functions are such that each one of their entries is involved either in an exact data fitting component or in a null component of the regularization part. This is a strong and particular property that can be useful for various image recovery problems. The minimization of such cost functions presents a computational challenge. We propose a fast minimization algorithm to solve this numerical problem. The experimental results show the effectiveness of the proposed algorithm. All illustrations and numerical experiments give a flavor of the possibilities offered by the minimizers of this new family of cost functions in solving specialized image processing tasks. © 2013 Society for Industrial and Applied Mathematics.

Keywords

ℓ1 data fitting, Continuation methods, Image recovery, Inverse problems, MRI, Multidimensional shrinkage, Nonsmooth and nonconvex analysis, Nonsmooth and nonconvex minimization, Penalty methods, Properties of minimizers, Regularization, Total variation, Variable-splitting, Variational methods

Publication Date

2013

Source Publication Title

SIAM Journal on Scientific Computing

Volume

35

Issue

1

Start Page

A397

End Page

A430

Publisher

Society for Industrial and Applied Mathematics

ISSN (print)

10648275

ISSN (electronic)

10957197

This document is currently not available here.

Share

COinS