Robust MRI reconstruction via re-weighted total variation and non-local sparse regression

Total variation (TV) based sparsity and non local self-similarity have been shown to be powerful tools for the reconstruction of magnetic resonance (MR) images. However, due to the uniform regularization of gradient sparsity, standard TV approaches often over-smooth edges in the image, resulting in the loss of important details. This paper presents a novel compressed sensing method for the reconstruction of MRI data, which uses a regularization strategy based on re-weighted TV to preserve image edges. This method also leverages the redundancy of non local image patches through the use of a sparse regression model. An efficient strategy based on the Alternating Direction Method of Multipliers (ADMM) algorithm is used to recover images with the proposed model. Experimental results on a simulated phantom and real brain MR data show our method to outperform state-of-the-art compressed sensing approaches, by better preserving edges and removing artifacts in the image.