A variable splitting based algorithm for fast multi-coil blind compressed sensing MRI reconstruction

Recent work on blind compressed sensing (BCS) has shown that exploiting sparsity in dictionaries that are learnt directly from the data at hand can outperform compressed sensing (CS) that uses fixed dictionaries. A challenge with BCS however is the large computational complexity during its optimization, which limits its practical use in several MRI applications. In this paper, we propose a novel optimization algorithm that utilize variable splitting strategies to significantly improve the convergence speed of the BCS optimization. The splitting allows us to efficiently decouple the sparse coefficient, and dictionary update steps from the data fidelity term, resulting in subproblems that take closed form analytical solutions, which otherwise require slower iterative conjugate gradient algorithms. Through experiments on multi coil parametric MRI data, we demonstrate the superior performance of BCS, while achieving convergence speed up factors of over 15 fold over the previously proposed implementation of the BCS algorithm.