A MR Image Denoising Algorithm based on Dictionary Learning with Minimax Concave Penalty

Denoising for Magnetic Resonance (MR) image has become a hot research direction in the field of MR image processing. In recent years, dictionary learning methods has been widely used for MR image denoising, which are divided into two categories according to the different sparse regularizers: ℓ
₀
norm-based methods, ℓ
₁
norm-based methods. But ℓ
₀
norm will cause NP-hard problems, ℓ
₁
norm will cause problems such as weak sparsity and overpenalization. In this paper, we propose a novel MR denoising model based on dictionary learning with Minimax Concave Penalty (MCP) which is a nonconvex regularizer obtain unbiased results. To solve the problem efficiently, firstly, we apply local operations, patch-based dictionary for sparse representation. Secondly, we employ a decomposition method to transfer the whole problem to a set of subproblems, and then we employ alternating scheme for updating the dictionary and sparse coefficient alternately. To address the nonconvex subproblem with respect to the coefficient vector, we employ Difference of Convex (DC) technology and the Proximal Operator (PO) to obtain the closed-form solutions. Finally, we use the trained dictionary and the updated sparse coefficient to reconstruct the MR image, leading to an efficient denoising algorithm. In the experiment, we apply the proposed denoising algorithm to real-world data i.e. MR images of different parts of the human body to test the robustness, its denoising results are better than that of KSVD and SGK.