Two-Level Bregman Method For MRI Reconstruction With Graph Regularized Sparse Coding

In recent years, sparse representation has become the most popular in MRI reconstruction and pattern recognition. The highly undersampled mainstream research direction is to update the dictionary learning and sparse coding stage alternatively. However, most of the existing approaches only reside on a low-dimensional submanifold embedded in the high-dimensional space to sparse coding, and failing to consider the geometrical structure of the K-space data. In this paper, we propose a Two-level Bregman Method for MRI Reconstruction with Graph Regularized Sparse Coding(TBMGR) which based on graph regularized sparse coding and incorporated with two-level Bregman iterative procedure to utilize the geometrical structure of the K-space data, emphasizing local structure adaptively. Bregman iterative procedure that updates the data term in outer-level and learns dictionary in inner-level. Moreover, the graph regularized sparse coding and simple dictionary updating stages derived by the inner minimization make the proposed algorithm converge in few iterations, meanwhile achieving superior reconstruction performance. Extensive experimental results have demonstrated TBMGR can consistently recover both simulated MR images and real MR data efficiently, and outperforms the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.