Huisu Yoon1, Daniel Kim2, Kyung Sang Kim1, Jong Chul Ye1
1KAIST, Daejeon, Korea; 2The University of Utah, Salt Lake City, UT, United States
Recently, many compressed sensing (CS) based algorithms have been developed for dynamic MR imaging applications by exploiting sparsity in temporal transform domain. For example, in k-t FOCUSS with motion estimation and compensation (ME/MC), when a high resolution reference frame is available, ME/MC is shown a quite effective sparsifying transforms. However, one of the limitations of ME/MC is that the energy of the residual measurement after motion compensation is significantly reduced compared to the original k-space measurement. Hence, a new reconstruction algorithm for motion residual is required that judiciously reconstructs geometrically meaningful features. One of main contributions of this paper is a novel patch-based signal processing algorithm for motion residual reconstruction that overcomes the limitation of the existing k-t FOCUSS with ME/MC. More specifically, we impose a non-convex patch-based low-rank penalty that exploits self-similarities within the residual images. This penalty is shown to favor capturing geometric features such as edges rather than reconstructing the background noises. To solve the resulting non-convex optimization problem, we propose a globally convergent concave-convex procedure (CCCP)2 using convex conjugate, which has closed form solution at each sub-iteration.