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A Two-Step Regularization Framework for Non-Local Means

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Abstract

As an effective patch-based denoising method, non-local means (NLM) method achieves favorable denoising performance over its local counterparts and has drawn wide attention in image processing community. The implementation of NLM can formally be decomposed into two sequential steps, i.e., computing the weights and using the weights to compute the weighted means. In the first step, the weights can be obtained by solving a regularized optimization. And in the second step, the means can be obtained by solving a weighted least squares problem. Motivated by such observations, we establish a two-step regularization framework for NLM in this paper. Meanwhile, using the framework, we reinterpret several non-local filters in the unified view. Further, taking the framework as a design platform, we develop a novel non-local median filter for removing salt-pepper noise with encouraging experimental results.

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Authors and Affiliations

  1. Department of Mathematics Science, Liaocheng University, Liaocheng, 252000, China

    Zhong-Gui Sun & Li-Shan Qiao

  2. College of Computer Science and Technology, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China

    Zhong-Gui Sun & Song-Can Chen

Authors
  1. Zhong-Gui Sun
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  2. Song-Can Chen
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  3. Li-Shan Qiao
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Corresponding author

Correspondence to Song-Can Chen.

Additional information

The research was partially supported by the National Natural Science Foundation of China under Grant No. 61300154, the Natural Science Foundations of Shandong Province of China under Grant Nos. NZR2010FL011, ZR2012FQ005, Jiangsu Qing Lan Projects, the Fundamental Research Funds for the Central Universities of China under Grant No. NZ2013306, and the Natural Science Foundation of Liaocheng University under Grant No. 318011408.

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Sun, ZG., Chen, SC. & Qiao, LS. A Two-Step Regularization Framework for Non-Local Means. J. Comput. Sci. Technol. 29, 1026–1037 (2014). https://doi.org/10.1007/s11390-014-1487-9

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  • DOI: https://doi.org/10.1007/s11390-014-1487-9

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