http://dx.doi.org/10.1137/100807697">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Inexact alternating direction methods for image recovery

Language

English

Abstract

In the image processing community, there have recently been many restoration and reconstruction problems that can be reformulated into linearly constrained convex programming models whose objective functions have separable structures. These favorable reformulations have promoted impressive applications of the alternating direction method (ADM) in the field of image processing. At each iteration, the computation of ADM is dominated by solving two subproblems exactly. However, in many restoration and reconstruction applications, it is either impossible or extremely expensive to obtain exact solutions of these ADM subproblems. This fact urges the development on inexact versions of ADM, which allow the generated ADM subproblems to be solved approximately subject to certain inexactness criteria. In this paper, we develop some truly implementable inexact ADMs whose inexactness criteria controlling the accuracy of the ADM subproblems are easily implementable. The convergence of the new inexact ADMs will be proved. Numerical results on several image processing problems will be given to illustrate the effectiveness of the proposed inexact ADMs. © 2011 Societ y for Industrial and Applied Mathematics.

Keywords

Alternating direction method, Compression, Convergence, Image reconstruction, Image restoration, Inexact

Publication Date

2011

Source Publication Title

SIAM Journal on Scientific Computing

Volume

33

Issue

4

Start Page

1643

End Page

1668

Publisher

Society for Industrial and Applied Mathematics

ISSN (print)

10648275

ISSN (electronic)

10957197

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