Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Constrained total variational deblurring models and fast algorithms based on alternating direction method of multipliers

Language

English

Abstract

The total variation (TV) model is attractive in that it is able to preserve sharp attributes in images. However, the restored images from TV-based methods do not usually stay in a given dynamic range, and hence projection is required to bring them back into the dynamic range for visual presentation or for storage in digital media. This will affect the accuracy of the restoration as the projected image will no longer be the minimizer of the given TV model. In this paper, we show that one can get much more accurate solutions by imposing box constraints on the TV models and solving the resulting constrained models. Our numerical results show that for some images where there are many pixels with values lying on the boundary of the dynamic range, the gain can be as great as 10.28 decibel in the peak signal-to-noise ratio. One traditional hindrance using the constrained model is that it is difficult to solve. However, in this paper, we propose using the alternating direction method of multipliers (ADMM) to solve the constrained models. This leads to a fast and convergent algorithm that is applicable for both Gaussian and impulse noise. Numerical results show that our ADMM algorithm is better than some state-of-the-art algorithms for unconstrained models in terms of both accuracy and robustness with respect to the regularization parameter. © 2013 Society for Industrial and Applied Mathematics.

Keywords

Alternating direction method of multipliers, Box constraint, Deblurring, Total variation

Publication Date

2013

Source Publication Title

SIAM Journal on Imaging Sciences

Volume

6

Issue

1

Start Page

680

End Page

697

Publisher

Society for Industrial and Applied Mathematics

DOI

10.1137/110860185

Link to Publisher's Edition

http://dx.doi.org/10.1137/110860185

ISSN (electronic)

19364954

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