Joint denoising of diffusion‐weighted images via structured low‐rank patch matrix approximation

Purpose To develop a joint denoising method that effectively exploits natural information redundancy in MR DWIs via low‐rank patch matrix approximation. Methods A denoising method is introduced to jointly reduce noise in DWI dataset by exploiting nonlocal self‐similarity as well as local anatomical/structural similarity within multiple 2D DWIs acquired with the same anatomical geometry but different diffusion directions. Specifically, for each small 3D reference patch sliding within 2D DWI, nonlocal but similar patches are searched by matching image contents within entire DWI dataset and then structured into a patch matrix. The resulting patch matrices are denoised by enforcing low‐rankness via weighted nuclear norm minimization and finally are back‐distributed to DWI space. The proposed procedure was evaluated with simulated and in vivo brain diffusion tensor imaging (DTI) datasets and then compared to existing Marchenko‐Pastur principal component analysis denoising method. Results The proposed method achieved significant noise reduction while preserving structural details in all DWIs for both simulated and in vivo datasets. Quantitative evaluation of error maps demonstrated it consistently outperformed Marchenko‐Pastur principal component analysis method. Further, the denoised DWIs led to substantially improved DTI parametric maps, exhibiting significantly less noise and revealing more microstructural details. Conclusion The proposed method denoises DWI dataset by utilizing both nonlocal self‐similarity and local structural similarity within DWI dataset. This weighted nuclear norm minimization–based low‐rank patch matrix denoising approach is effective and highly applicable to various diffusion MRI applications, including DTI as a postprocessing procedure.