Motion compensated compressed sensing dynamic MRI with low-rank patch-based residual reconstruction

One of the technical challenges of the predication/residual encoding in motion estimated and compensated k-t FOCUSS is that after the prediction, the energy of the residual measurement is significantly reduced compared to the original measurement. This implies that the residual measurement should be judiciously used to recover important geometric features rather than background noise during residual encoding stage. To address this, this paper proposes a novel patch-based residual encoding scheme to exploit geometric similarity in the residual images. In particular, this paper is interested in patch-based low rank constraint from similarity patches [1] since rank structures are relatively less sensitive to global intensity changes but easier to capture edges and etc. To address the nonconvexity and non-smoothess of the rank penalty, a concave-convex procedure is proposed. Experimental results show that the proposed algorithm clearly reconstructs important anatomic structures in cardiac cine image and provides significant performance improvement compared to the existing motion compensated k-t FOCUSS.