A fast algorithm for denoising magnitude diffusion-weighted images with rank and edge constraints.

PURPOSE: To accelerate denoising of magnitude diffusion-weighted images subject to joint rank and edge constraints.

METHODS: We extend a previously proposed majorize-minimize method for statistical estimation that involves noncentral χ distributions to incorporate joint rank and edge constraints. A new algorithm is derived which decomposes the constrained noncentral χ denoising problem into a series of constrained Gaussian denoising problems each of which is then solved using an efficient alternating minimization scheme.

RESULTS: The performance of the proposed algorithm has been evaluated using both simulated and experimental data. Results from simulations based on ex vivo data show that the new algorithm achieves about a factor of 10 speed up over the original Quasi-Newton-based algorithm. This improvement in computational efficiency enabled denoising of large datasets containing many diffusion-encoding directions. The denoising performance of the new efficient algorithm is found to be comparable to or even better than that of the original slow algorithm. For an in vivo high-resolution Q-ball acquisition, comparison of fiber tracking results around hippocampus region before and after denoising will also be shown to demonstrate the denoising effects of the new algorithm.

CONCLUSION: The optimization problem associated with denoising noncentral χ distributed diffusion-weighted images subject to joint rank and edge constraints can be solved efficiently using a majorize-minimize-based algorithm.