Low-rank plus sparse reconstruction using dictionary learning for 3D-MRI

This work proposes a low-rank plus sparse model using dictionary learning for 3D-MRI reconstruction from downsampling k-space data. The scheme decomposes the dynamic image signal into two parts: low-rank part L and sparse part S and then, constructing it as a constrained optimization problem. In the optimization process,a nonconvex penalty function is used to optimize the low rank part L. The sparse part S is expressed by a over-complete dictionary using blind compressed sensing and we formulate the sparsity of coffecient matrix using l1 norm. To avoid the ill-posed of the problem, the Frobenius norm is used in dictionary. We adopt an alternate optimization algorithm to solve the problem, which cycles through the minimization of five subproblems. Finally, we prove the effectiveness of proposed method in two cardiac cine data sets. Experimental results were compared with exsiting L+S, L&S and BCS schemes, which demonstrate that the proposed method behaves better in removal of artifacts and maintaining the image details.