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Patch-Based Weighted SCAD Prior for Rician Noise Removal

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Abstract

The weighted nuclear norm minimization has been widely used in low-level vision tasks. To treat different singular values more flexibly, in this paper, we adopt the smoothly clipped absolute deviation (SCAD) penalty as a non-convex surrogate of the rank function. Our motivation is that SCAD shrinkage can balance the soft shrinkage and hard shrinkage well. That is, it shrinks less on large singular values but more on small singular values. The SCAD shrinkage rule is desired because large singular values contain more useful structure information, while small singular values include more noise. Then we propose a patch-based model via the weighted SCAD prior to remove Rician noise. The data fidelity term of the proposed model is obtained by maximum a posteriori estimation. The regularization term is the SCAD prior applied on the patch matrix, formulated by non-local similar patches in the image. Numerically, we utilize the alternating direction method of multipliers to solve the problem iteratively. The convergence of the proposed method is analyzed when the parameters satisfy certain conditions. Experimental results are presented to demonstrate that the proposed model outperforms some of the other existing methods in terms of quantitative measure and visual quality.

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Data Availability

All the test images are available from websites. All of them are listed in figures. Figure 1a, b are selected from IXI Dataset and can be downloaded from website http://brain-development.org/ixi-dataset/. Figure 1c, d are downloaded from website http://csrc.xmu.edu.cn/. Figure 1e, f are downloaded from website http://see.xidian.edu.cn/faculty/wsdong/NLR_Exps.htm. Figure 1g is from website https://www.math.cuhk.edu.hk/~zeng/. We will make all materials in this article available to the research community when publication.

Notes

  1. http://brain-development.org/ixi-dataset/.

  2. http://csrc.xmu.edu.cn/.

  3. http://see.xidian.edu.cn/faculty/wsdong/NLR_Exps.htm.

  4. https://www.math.cuhk.edu.hk/~zeng/

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Funding

Fang Li was supported by the National Natural Science Foundation of China (NSFC) ( No. 61731009, No. 11671002). Fang Li was supported by the Fundamental Research Funds for the Central Universities. Fang Li was supported by Science and Technology Commission of Shanghai Municipality (No. 19JC1420102, No. 18dz2271000). Xiao-Guang Lv was supported by NSF of Jiangsu Province (BK20181483). Xiao-Guang Lv was supported by Hai Yan project. Xiao-Guang Lv was supported by Lianyungang 521 project. Xiao-Guang Lv was supported by NSF of JOU (Z2017004).

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Authors and Affiliations

  1. Shanghai Key Laboratory of PMMP, and School of Mathematical Sciences, East China Normal University, Shanghai, 200062, China

    Fang Li

  2. School of Mathematical Sciences, East China Normal University, Shanghai, 200062, China

    Yamin Ru

  3. School of Science, Jiangsu Ocean University, Lianyungang, 222005, Jiangsu, China

    Xiao-Guang Lv

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  1. Fang Li
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  2. Yamin Ru
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  3. Xiao-Guang Lv
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Correspondence to Fang Li.

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This work is supported in part by the National Natural Science Foundation of China (NSFC) (No. 61731009, No. 11671002), the Fundamental Research Funds for the Central Universities, Science and Technology Commission of Shanghai Municipality (No. 19JC1420102, No. 18dz2271000), NSF of Jiangsu Province (BK20181483), Hai Yan project, Lianyungang 521 project and NSF of JOU (Z2017004)

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Li, F., Ru, Y. & Lv, XG. Patch-Based Weighted SCAD Prior for Rician Noise Removal. J Sci Comput 90, 26 (2022). https://doi.org/10.1007/s10915-021-01688-5

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