MRI reconstruction via enhanced group sparsity and nonconvex regularization

In this paper, a new approach to perform compressed sensing MRI (CS-MRI) reconstruction based on enhanced group sparsity and nonconvex regularization (GSNR) is presented. A new framework is developed at attempt to improve the group sparsity and the accuracy of estimated coefficients. To that end, first, we establish a generalized reordering model to train the optimal permutation, which reveals the inner structure of group and benefits to promote the sparsity of group for an arbitrarily fixed transform. Second, with the nonconvex log-sum regularization, a fast shrinkage operator to solve the corresponding nonconvex optimization problem is developed in which the optimal solution is accurately and quickly obtained. The effectiveness of GSNR is demonstrated for both noiseless and noisy real MR images. In both cases, the proposed algorithm generates high-quality images that are superior in terms of visual inspection and objective evaluations to the state-of-the-art approaches. In addition, the effects of reordering and nonconvex regularization are verified by simulations, respectively, to illustrate the superior performance of GSNR because of the proposed framework.