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Shrinking gradient descent algorithms for total variation regularized image denoising

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Abstract

Total variation regularization introduced by Rudin, Osher, and Fatemi (ROF) is widely used in image denoising problems for its capability to preserve repetitive textures and details of images. Many efforts have been devoted to obtain efficient gradient descent schemes for dual minimization of ROF model, such as Chambolle’s algorithm or gradient projection (GP) algorithm. In this paper, we propose a general gradient descent algorithm with a shrinking factor. Both Chambolle’s and GP algorithm can be regarded as the special cases of the proposed methods with special parameters. Global convergence analysis of the new algorithms with various step lengths and shrinking factors are present. Numerical results demonstrate their competitiveness in computational efficiency and reconstruction quality with some existing classic algorithms on a set of gray scale images.

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Notes

  1. The standard test images can be found at http://homepages.cae.wisc.edu/~ece533/images.

  2. The peak signal-to-noise ratio (PSNR) of an image u with respect to the noiseless image f is defined as PSNR = \(20\log _{10}\left( \frac{\text {MAX}}{\text {RMSE}} \right) \), where MAX is the maximum possible pixel value of the image. In our case, MAX = 255.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences (UCAS), Beijing, 100049, China

    Mingqiang Li & Ruxin Wang

  2. Key Laboratory of Big Data Mining and Knowledge Management, School of Mathematical Sciences, University of Chinese Academy of Sciences (UCAS), Beijing, 100049, China

    Congying Han & Tiande Guo

Authors
  1. Mingqiang Li
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  2. Congying Han
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  3. Ruxin Wang
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  4. Tiande Guo
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Corresponding author

Correspondence to Congying Han.

Additional information

This work was supported by the National Natural Science Foundation of China (11571014, 11331012 and 71271204).

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Li, M., Han, C., Wang, R. et al. Shrinking gradient descent algorithms for total variation regularized image denoising. Comput Optim Appl 68, 643–660 (2017). https://doi.org/10.1007/s10589-017-9931-8

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