L 0-norm and total variation for wavelet inpainting

Andy C. Yau; Xue-Cheng TAI; Kwok Po NG

doi:10.1007/978-3-642-02256-2_45

L ₀-norm and total variation for wavelet inpainting

Andy C. Yau, Xue-Cheng TAI, Kwok Po NG

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Conference contribution › peer-review

9 Citations (Scopus)

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.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision - Second International Conference, SSVM 2009, Proceedings
Pages	539-551
Number of pages	13
DOIs	https://doi.org/10.1007/978-3-642-02256-2_45
Publication status	Published - 2009
Event	2nd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2009 - Voss, Norway Duration: 1 Jun 2009 → 5 Jun 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5567 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	2nd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2009
Country/Territory	Norway
City	Voss
Period	1/06/09 → 5/06/09

Scopus Subject Areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-02256-2_45

Cite this

Yau, A. C., TAI, X-C., & NG, K. P. (2009). L ₀-norm and total variation for wavelet inpainting. In Scale Space and Variational Methods in Computer Vision - Second International Conference, SSVM 2009, Proceedings (pp. 539-551). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5567 LNCS). https://doi.org/10.1007/978-3-642-02256-2_45

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title = "L 0-norm and total variation for wavelet inpainting",

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.",

author = "Yau, {Andy C.} and Xue-Cheng TAI and NG, {Kwok Po}",

note = "Copyright: Copyright 2009 Elsevier B.V., All rights reserved.; 2nd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2009 ; Conference date: 01-06-2009 Through 05-06-2009",

year = "2009",

doi = "10.1007/978-3-642-02256-2_45",

language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Yau, AC, TAI, X-C & NG, KP 2009, L ₀-norm and total variation for wavelet inpainting. in Scale Space and Variational Methods in Computer Vision - Second International Conference, SSVM 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5567 LNCS, pp. 539-551, 2nd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2009, Voss, Norway, 1/06/09. https://doi.org/10.1007/978-3-642-02256-2_45

L ₀-norm and total variation for wavelet inpainting. / Yau, Andy C.; TAI, Xue-Cheng; NG, Kwok Po.

Scale Space and Variational Methods in Computer Vision - Second International Conference, SSVM 2009, Proceedings. 2009. p. 539-551 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5567 LNCS).

Research output: Chapter in book/report/conference proceeding › Conference contribution › peer-review

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AB - 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.

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Yau AC, TAI X-C, NG KP. L ₀-norm and total variation for wavelet inpainting. In Scale Space and Variational Methods in Computer Vision - Second International Conference, SSVM 2009, Proceedings. 2009. p. 539-551. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-02256-2_45