Research On Magnetic Resonance Image Processing Algorithm Based On Nonlocal Self-similarity And Non-convex Regularization

The nuclear norm based convex surrogate of the rank function has been widely used in image restoration to exploit the sparsity of nonlocal similar patches in an image.However,this method treats different singular values equally,thus producing a result far from the optimum.The reason is that large singular values are used to reconstruct useful information in an image,while small ones may contain noisy information.To alleviate the limitations of the nuclear norm,different singular values should be treated differently.Non-convex regularization function plays an important role in the field of sparse optimization,in which Smoothly Clipped Absolute Deviation(SCAD)is one of representative non-convex regularization functions.SCAD can make the estimation model achieve a good balance between soft shrinkage and hard shrinkage,which is in line with the regularization function requirements in this paper.Therefore,we proposes a regularization term which combines the sparsity of nonlocal similar blocks and SCAD non-convex regularization function,and applies this regularization term to MRI reconstruction and denoising respectively.Numerically,we utilize the alternating direction method of multiplier(ADMM)to solve the problem iteratively.We further analyze the convergence of the proposed methods under mild conditions.Experimental results are presented to demonstrate that the proposed models outperform some of the other existing methods in terms of quantitative measure and visual quality.