Inverse Problems and Imaging (IPI)

Wavelet inpainting by nonlocal total variation

Pages: 191 - 210, Volume 4, Issue 1, February 2010      doi:10.3934/ipi.2010.4.191

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Xiaoqun Zhang - UCLA Mathematics Department, Box 951555, Los Angeles, CA 90095-1555, United States (email)
Tony F. Chan - The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China (email)

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.

Keywords:  Inverse problems, wavelet inpainting, nonlocal total variation.
Mathematics Subject Classification:  Primary: 42C40, 65T60; Secondary: 49N45.

Received: July 2009;      Revised: November 2009;      Available Online: February 2010.