Collaborative Filter Paradigm to Remove Noise in MRI Modality: Application to Diffusion Weighted Images

Denoising volumetric data is essential for improving data quality and facilitating accurate analysis, interpretation, and diagnostic capabilities in various fields, including medical imaging, scientific visualization, and engineering simulations. This article proposes a BM4D, an expansion of the BM3D filter designed specifically for volumetric data. This unique approach combines grouping and Collaborative Filtering (CF) principles. It entails grouping dimensionally similar patches into a (d + 1)-dimensional array, then processing them collectively in the transform domain. Unlike BM3D, where basic data patches are pixel blocks, BM4D uses voxel cubes combined into a Four-Dimensional (4-D) "Group." This 4-D transformation takes advantage of local correlations inside each voxel cube as well as non-local correlations between matching voxels from other cubes. This produces a highly sparse spectrum within this group, allowing for effective signal-to-noise distinction via coefficient reduction. Estimates for each grouped cube are received after applying the inverse transformation, which is then adaptively mixed at their original positions. The proposed algorithm's performance is assessed in the context of denoising volumetric data corrupted by Gaussian and Rician noise. Experimental results showcase BM4D's outstanding denoising capabilities, establishing its effectiveness in the domain of volumetric data denoising and positioning it as a cutting-edge solution.