A New 4-D Nonlocal Transform-Domain Filter for 3-D Magnetic Resonance Images Denoising

The simultaneous removal of noise and preservation of the integrity of 3-D magnetic resonance (MR) images is a difficult and important task. In this paper, we consider characterizing MR images with 3-D operators, and present a novel 4-D transform-domain method termed 'modified nonlocal tensor-SVD (MNL-tSVD)' for MR image denoising. The proposed method is based on the grouping, hard-thresholding and aggregation paradigms, and can be viewed as a generalized nonlocal extension of tensor-SVD (t-SVD). By keeping MR images in its natural three-dimensional form, and collaboratively filtering similar patches, MNL-tSVD utilizes both the self-similarity property and 3-D structure of MR images to preserve more actual details and minimize the introduction of new artifacts. We show the adaptability of MNL-tSVD by incorporating it into a two-stage denoising strategy with a few adjustments. In addition, analysis of the relationship between MNL-tSVD and current the state-of-the-art 4-D transforms is given. Experimental comparisons over simulated and real brain data sets at different Rician noise levels show that MNL-tSVD can produce competitive performance compared with related approaches.