Motion Residual Reconstruction Using Low Rank Property of Similarity Patches in Motion Compensated Compressed Sensing Dynamic MRI

Huisu Yoon¹, Daniel Kim², Kyung Sang Kim¹, Jong Chul Ye¹

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.