Patch-Based Weighted SCAD Prior for Rician Noise Removal

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.