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Article: Alternating direction method for image inpainting in wavelet domains
Title | Alternating direction method for image inpainting in wavelet domains |
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Authors | |
Keywords | Fast wavelet transform Fast fourier transform Augmented lagrangian method Alternating direction method Inpainting Total variation Wavelet |
Issue Date | 2011 |
Publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/siims.php |
Citation | SIAM Journal on Imaging Sciences, 2011, v. 4, n. 3, p. 807-826 How to Cite? |
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, â 2 -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. |
Persistent Identifier | http://hdl.handle.net/10722/250977 |
ISSN | 2023 Impact Factor: 2.1 2023 SCImago Journal Rankings: 0.960 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chan, Raymond H. | - |
dc.contributor.author | Yang, Junfeng | - |
dc.contributor.author | Yuan, Xiaoming | - |
dc.date.accessioned | 2018-02-01T01:54:14Z | - |
dc.date.available | 2018-02-01T01:54:14Z | - |
dc.date.issued | 2011 | - |
dc.identifier.citation | SIAM Journal on Imaging Sciences, 2011, v. 4, n. 3, p. 807-826 | - |
dc.identifier.issn | 1936-4954 | - |
dc.identifier.uri | http://hdl.handle.net/10722/250977 | - |
dc.description.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, â 2 -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. | - |
dc.language | eng | - |
dc.publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/siims.php | - |
dc.relation.ispartof | SIAM Journal on Imaging Sciences | - |
dc.subject | Fast wavelet transform | - |
dc.subject | Fast fourier transform | - |
dc.subject | Augmented lagrangian method | - |
dc.subject | Alternating direction method | - |
dc.subject | Inpainting | - |
dc.subject | Total variation | - |
dc.subject | Wavelet | - |
dc.title | Alternating direction method for image inpainting in wavelet domains | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/100807247 | - |
dc.identifier.scopus | eid_2-s2.0-80052894191 | - |
dc.identifier.volume | 4 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 807 | - |
dc.identifier.epage | 826 | - |
dc.identifier.isi | WOS:000295405200002 | - |
dc.identifier.issnl | 1936-4954 | - |