Denoising 3 D magnitude magnetic resonance images based on weighted nuclear norm

A new denoising algorithm based on low-rank matrix approximation (LRMA) with regularization of weighted nuclear norm minimization (WNNM) is proposed to remove Rician noise of magnetic resonance (MR) images. This technique simply groups similar non-local cubic blocks from noisy 3D MR data into a patch matrix with each block lexicographically vectorizing to be as a column, calculates the singular value decomposition (SVD) on this matrix, then the closed-form solution of LRMA is achieved by hard-th