L0-Norm and Total Variation for Wavelet Inpainting

Authors:
Andy C. Yau;Xue-Cheng Tai;Michael K. Ng
Affiliations:
Division of Mathematical Science, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore;Division of Mathematical Science, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore and Mathematics Institute, University of Bergen, Norway;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong,
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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Abstract

In this paper, we suggest an algorithm to recover an image whose wavelet coefficients are partially lost. We propose a wavelet inpainting model by using L 0 -norm and the total variation (TV) minimization. Traditionally, L 0 -norm is replaced by L 1 -norm or L 2 -norm due to numerical difficulties. We use an alternating minimization technique to overcome these difficulties. In order to improve the numerical efficiency, we also apply a graph cut algorithm to solve the subproblem related to TV minimization. Numerical results will be given to demonstrate our advantages of the proposed algorithm.