Compressed Sensing Undersampled MRI Reconstruction using Iterative Shrinkage Thresholding based on NSST

Compressed sensing (CS) has great potential for use in reducing data acquisition time in MRI. Generally sparsity is used as a prior knowledge to improve the quality of reconstructed image. In this paper, we propose an effective compressed sensing rapid MR imaging method incorporating Non-Subsampled Shearlet transform (NSST) sparsity prior information for MR image reconstruction from highly undersampled k-space data. In particular, we have implemented the more flexible decomposition with 2n directional subbands at each scale using NSST to obtain the prominent sparser representation for MR images. In addition, the mixed L1-L2 norm of the coefficients from the prior component and residual component is used to enforce joint sparsity. Numerical experiments demonstrate that the proposed method can significantly increase signal sparsity and improve the ill-conditioning of MR imaging system using NSST sparsity regularization. The evaluations on a T2-weighted brain image and a MR phantom experiment demonstrate superior performance of the proposed method in terms of reconstruction error reduction, detail preservation and aliasing, Gibbs ringing artifacts suppression compared to state-of-the-art technique. Its performance in objective evaluation indices outperforms conventional CS-MRI methods prominently.