Denoising diffusion-weighted magnitude MR images using rank and edge constraints

Purpose To improve signal-to-noise ratio for diffusion-weighted magnetic resonance images. Methods A new method is proposed for denoising diffusion-weighted magnitude images. The proposed method formulates the denoising problem as an maximum a posteriori} estimation problem based on Rician/noncentral χ likelihood models, incorporating an edge prior and a low-rank model. The resulting optimization problem is solved efficiently using a half-quadratic method with an alternating minimization scheme. Results The performance of the proposed method has been validated using simulated and experimental data. Diffusion-weighted images and noisy data were simulated based on the diffusion tensor imaging model and Rician/noncentral χ distributions. The simulation study (with known gold standard) shows substantial improvements in single-to-noise ratio and diffusion tensor estimation after denoising. In vivo diffusion imaging data at different b-values were acquired. Based on the experimental data, qualitative improvement in image quality and quantitative improvement in diffusion tensor estimation were demonstrated. Additionally, the proposed method is shown to outperform one of the state-of-the-art nonlocal means-based denoising algorithms, both qualitatively and quantitatively. Conclusion The single-to-noise ratio of diffusion-weighted images can be effectively improved with rank and edge constraints, resulting in an improvement in diffusion parameter estimation accuracy.