Volume 11, Issue 1
A Boosting Procedure for Variational-Based Image Restoration

Samad Wali, Zhifang Liu, Chunlin Wu & Huibin Chang

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 49-73.

Published online: 2018-11

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  • Abstract

Variational methods are an important class of methods for general image restoration. Boosting technique has been shown capable of improving many image denoising algorithms. This paper discusses a boosting technique for general variational image restoration methods. It broadens the applications of boosting techniques to a wide range of image restoration problems, including not only denoising but also deblurring and inpainting. In particular, we combine the recent SOS technique with dynamic parameter to variational methods. The dynamic regularization parameter is motivated by Meyer's analysis on the ROF model. In each iteration of the boosting scheme, the variational model is solved by augmented Lagrangian method. The convergence analysis of the boosting process is shown in a special case of total variation image denoising with a "disk" input data. We have implemented our boosting technique for several image restoration problems such as denoising, inpainting and deblurring. The numerical results demonstrate promising improvement over standard variational restoration models such as total variation based models and higher order variational model as total generalized variation.

  • Keywords

Variational method, image restoration, total variation, boosting, augmented Lagrangian method.

  • AMS Subject Headings

68U10, 90C25, 49M37

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-11-49, author = {}, title = {A Boosting Procedure for Variational-Based Image Restoration}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {1}, pages = {49--73}, abstract = {

Variational methods are an important class of methods for general image restoration. Boosting technique has been shown capable of improving many image denoising algorithms. This paper discusses a boosting technique for general variational image restoration methods. It broadens the applications of boosting techniques to a wide range of image restoration problems, including not only denoising but also deblurring and inpainting. In particular, we combine the recent SOS technique with dynamic parameter to variational methods. The dynamic regularization parameter is motivated by Meyer's analysis on the ROF model. In each iteration of the boosting scheme, the variational model is solved by augmented Lagrangian method. The convergence analysis of the boosting process is shown in a special case of total variation image denoising with a "disk" input data. We have implemented our boosting technique for several image restoration problems such as denoising, inpainting and deblurring. The numerical results demonstrate promising improvement over standard variational restoration models such as total variation based models and higher order variational model as total generalized variation.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0046}, url = {http://global-sci.org/intro/article_detail/nmtma/10661.html} }
TY - JOUR T1 - A Boosting Procedure for Variational-Based Image Restoration JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 49 EP - 73 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0046 UR - https://global-sci.org/intro/article_detail/nmtma/10661.html KW - Variational method, image restoration, total variation, boosting, augmented Lagrangian method. AB -

Variational methods are an important class of methods for general image restoration. Boosting technique has been shown capable of improving many image denoising algorithms. This paper discusses a boosting technique for general variational image restoration methods. It broadens the applications of boosting techniques to a wide range of image restoration problems, including not only denoising but also deblurring and inpainting. In particular, we combine the recent SOS technique with dynamic parameter to variational methods. The dynamic regularization parameter is motivated by Meyer's analysis on the ROF model. In each iteration of the boosting scheme, the variational model is solved by augmented Lagrangian method. The convergence analysis of the boosting process is shown in a special case of total variation image denoising with a "disk" input data. We have implemented our boosting technique for several image restoration problems such as denoising, inpainting and deblurring. The numerical results demonstrate promising improvement over standard variational restoration models such as total variation based models and higher order variational model as total generalized variation.

Samad Wali, Zhifang Liu, Chunlin Wu & Huibin Chang. (2020). A Boosting Procedure for Variational-Based Image Restoration. Numerical Mathematics: Theory, Methods and Applications. 11 (1). 49-73. doi:10.4208/nmtma.OA-2017-0046
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