MR image reconstruction using cosupport constraints and group sparsity regularisation

It has always been challenging to reconstruct magnetic resonance (MR) images from a limited set of k-space data due to the ill-posed nature. An effective way to compensate for the data incompleteness is through the use of the sparsity-based regularisation. Recent work in image processing suggests that exploiting structured sparsity may lead to improved results. In this study, this idea is explored in combination with additional support prior of the MR images in the analysis context. Put differently, the authors propose a highly effective regulariser constraining group sparsity of the analysis coefficients within the pre-estimated cosupport. A two-stage iterative algorithm is developed and proceeds by alternatively calling its two key components: image reconstruction and cosupport detection. The feasibility of the proposed method is demonstrated for individual and multiple T1/T2-weighted MR images. Simulation results show considerable improvement of their method compared with the methods using structured sparsity and support knowledge in the synthesis context and other related reconstruction methods.