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Spatially dependent regularization parameter selection for total generalized variation-based image denoising

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Abstract

We propose a novel image denoising model based on the total generalized variation (TGV) regularization. In the model, a spatially dependent regularization parameter is utilized to adaptively fit the local image features, resulting in further exploitation of the denoising potential of the TGV regularization. The proposed model is formulated under a joint optimization framework, by which the estimations of the restored image and the regularization parameter are achieved simultaneously. Furthermore, the model is general purpose that can handle various types of noise occurring in image processing. An alternating minimization-based numerical scheme is especially developed, which leads to an efficient algorithmic solution to the nonconvex optimization problem. Numerical experiments are reported to illustrate the effectiveness of our model in terms of both peak signal-to-noise ratio and visual perception.

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Notes

  1. A function \(f:\mathbb {R}^n\rightarrow \mathbb {R}\) is called quasiconcave if its domain and all its superlevel set \(\{x|f(x)\ge \alpha \}\) are convex; see Boyd and Vandenberghe (2004) for more details.

  2. http://www.uni-graz.at/imawww/ifb/sa-tv/index.html.

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Acknowledgments

The authors would like to thank the editor and the anonymous referees for their valuable suggestions and comments. This research is supported by 973 Program (2013CB329404), NSFC (61370147, 61170311), and the Fundamental Research Funds for the Central Universities (ZYGX2013Z005).

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Authors and Affiliations

  1. School of Mathematical Sciences/Research Center for Image and Vision Computing, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China

    Tian-Hui Ma, Ting-Zhu Huang & Xi-Le Zhao

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  1. Tian-Hui Ma
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  2. Ting-Zhu Huang
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  3. Xi-Le Zhao
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Correspondence to Tian-Hui Ma.

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Communicated by Joerg Fliege.

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Ma, TH., Huang, TZ. & Zhao, XL. Spatially dependent regularization parameter selection for total generalized variation-based image denoising. Comp. Appl. Math. 37, 277–296 (2018). https://doi.org/10.1007/s40314-016-0342-8

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  • DOI: https://doi.org/10.1007/s40314-016-0342-8

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