Wavelet inpainting by nonlocal total variation

Xiaoqun Zhang; Tony F. Chan

doi:10.3934/ipi.2010.4.191

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2010, Volume 4, Issue 1: 191-210. Doi: 10.3934/ipi.2010.4.191

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Wavelet inpainting by nonlocal total variation

Xiaoqun Zhang^1, and
Tony F. Chan^2,

1.
UCLA Mathematics Department, Box 951555, Los Angeles, CA 90095-1555
2.
The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Received: July 2009

Revised: November 2009

Published: February 2010

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Abstract

Wavelet inpainting problem consists of filling in missed data in the wavelet domain. In [17], Chan, Shen, and Zhou proposed an efficient method to recover piecewise constant or smooth images by combining total variation regularization and wavelet representations. In this paper, we extend it to nonlocal total variation regularization in order to recover textures and local geometry structures simultaneously. Moreover, we apply an efficient algorithm framework for both local and nonlocal regularizers. Extensive experimental results on a variety of loss scenarios and natural images validate the performance of this approach.

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Mathematics Subject Classification: Primary: 42C40, 65T60; Secondary: 49N45.

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