MRI reconstruction via multi transforms learning and logarithm ratio for vectorized groups

Abstract

Compressed sensing (CS) has been demonstrated to substantially reduce the scan time of magnetic resonance imaging (MRI) by undersampling k-space data. The desirable reconstruction of MR image depends on a reasonable sparse representation model that synthesizes the prior information of image as much as possible. Since learning transform is expected to provide a sparser representation, which is associated with lower reconstruction error, in this work, a multi group transforms learning scheme is proposed, which combines the adaptive sparsifying process with the utilization of nonlocal self-similarity, to generate the highly sparse coefficients of groups composed of similar patches. In addition, a non-convex logarithm ratio function is defined to better approximate l0 norm, and thus employed as the regularizer function to enforce sparsity over image coefficients. Furthermore, based on the alternating direction method of multipliers (ADMM), an efficient numerical algorithm is deduced to optimize the proposed CS-MRI model. Within this framework, the obtained coefficients and the undersampled k-space data are incorporated in a least squares problem, which is efficiently solved to reconstruct a clear MR image. The learned multi group transforms overcome the restriction of Kronecker product structure and global transform, thus resulting in obvious performance improvement. The proposed iterative formula to calculate the proximal mapping of logarithm ratio guarantees the convergence towards the unique optimal solution, also brings a certain performance gain. Extensive experimental results reveal that the proposed method not only results in better visual quality but achieves higher PSNR and SSIM than competing methods for all sampling rates and noise intensities.