A Probabilistic Model-Based Method With Nonlocal Filtering for Robust Magnetic Resonance Imaging Reconstruction

Existing model-based or data-driven methods have achieved a high-quality reconstruction in compressive sensing magnetic resonance imaging (CS-MRI). However, most methods are designed for a specific type of sampling mask or sampling rate while ignoring the existence of external noise, resulting in poor robustness. In this work, we propose a probabilistic model-based method based on Laplacian scale mixture (LSM) modeling and denoising based approximate message passing (D-AMP) algorithm to address this issue. Sparse coefficients of similar packed patches are modeled with LSM distribution to exploit the nonlocal self-similarity prior of MR image, and a maximum a posterior estimation problem for sparse coding is formulated. It is shown that both hidden scale parameters i.e. variances of sparse coefficients and location parameters can be jointly estimated along with the unknown sparse coefficients via the method of alternating optimization. Moreover, the variance of noise is also iteratively updated based on maximum likelihood estimation. With plug-and-play prior method, the above structured sparse coding procedure can be regarded as a nonlocal filtering operation and be incorporated into D-AMP for MR image reconstruction. Owing to the power of our nonlocal filtering which takes both signal and noise estimation into account, the proposed method not only outperforms many state-of-the-art methods for most situations of observation, but also delivers the best qualitative reconstruction results with finer details and less artifacts in experiments.