Denoising diffusion-weighted images using grouped iterative hard thresholding of multi-channel framelets

Noise in diffusion-weighted (DW) images increases the complexity of quantitative analysis and decreases the reliability of inferences. Hence, to improve analysis, it is often desirable to remove noise and at the same time preserve relevant image features. In this paper, we propose a tight wavelet frame based approach for edge-preserving denoising of DW images. Our approach (1) employs the unitary extension principle (UEP) to generate frames that are discrete analogues to differential operators of various orders; (2) introduces a very efficient method for solving an ₀ denoising problem that involves only thresholding and solving a trivial inverse problem; and (3) groups DW images acquired with neighboring gradient directions for collaborative denoising. Experiments using synthetic data with noncentral chi noise and real data with repeated scans confirm that our method yields superior performance compared with denoising using state-of-the-art methods such as non-local means.