Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Alternating direction method for image inpainting in wavelet domain

Language

English

Abstract

Image inpainting in wavelet domains refers to the recovery of an image from incomplete and/or inaccurate wavelet coefficients. To reconstruct the image, total variation (TV) models have been widely used in the literature, and they produce high-quality reconstructed images. In this paper, we consider an unconstrained, TV-regularized, ℓ2-data-fitting model to recover the image. The model is solved by the alternating direction method (ADM). At each iteration, the ADM needs to solve three subproblems, all of which have closed-form solutions. The per-iteration computational cost of the ADM is dominated by two Fourier transforms and two wavelet transforms, all of which admit fast computation. Convergence of the ADM iterative scheme is readily obtained. We also discuss extensions of this ADM scheme to solving two closely related constrained models. We present numerical results to show the efficiency and stability of the ADM for solving wavelet domain image inpainting problems. Numerical results comparing the ADM with some recent algorithms are also reported. © 2011 Society for Industrial and Applied Mathematics.

Keywords

Alternating direction method, Augmented lagrangian method, Fast fourier transform, Fast wavelet transform, Inpainting, Total variation, Wavelet

Publication Date

2011

Source Publication Title

SIAM Journal on Imaging Sciences

Volume

4

Issue

3

Start Page

807

End Page

826

Publisher

Society for Industrial and Applied Mathematics

DOI

10.1137/100807247

Link to Publisher's Edition

http://dx.doi.org/10.1137/100807247

ISSN (electronic)

19364954

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