Improved dynamic MRI reconstruction by exploiting sparsity and rank-deficiency.

In this paper we address the problem of dynamic MRI reconstruction from partially sampled K-space data. Our work is motivated by previous studies in this area that proposed exploiting the spatiotemporal correlation of the dynamic MRI sequence by posing the reconstruction problem as a least squares minimization regularized by sparsity and low-rank penalties. Ideally the sparsity and low-rank penalties should be represented by the l(0)-norm and the rank of a matrix; however both are NP hard penalties. The previous studies used the convex l(1)-norm as a surrogate for the l(0)-norm and the non-convex Schatten-q norm (0<q ≤ 1) as a surrogate for the rank of matrix. Following past research in sparse recovery, we know that non-convex l(p)-norm (0<p ≤ 1) is a better substitute for the NP hard l(0)-norm than the convex l(1)-norm. Motivated by these studies, we propose improvements over the previous studies by replacing the l(1)-norm sparsity penalty by the lp-norm. Thus, we reconstruct the dynamic MRI sequence by solving a least squares minimization problem regularized by l(p)-norm as the sparsity penalty and Schatten-q norm as the low-rank penalty. There are no efficient algorithms to solve the said problems. In this paper, we derive efficient algorithms to solve them. The experiments have been carried out on Dynamic Contrast Enhanced (DCE) MRI datasets. Both quantitative and qualitative analysis indicates the superiority of our proposed improvement over the existing methods.