Multiple regularization based MRI reconstruction

• This paper proposes MRI reconstruction based on multiple regularizers.
• Nonlocal total variation and wavelet are the regularizers used in this work.
• The Split Bregman method is used to solve the hybrid L1-regularizer.
• The Split Bregman algorithm makes use of Gauss–Seidel and Fourier transform methods, it is easily parallelizable and easily coded.
• The proposed method performs better in terms of reconstruction quality and computational complexity.

This paper introduces an efficient algorithm for magnetic resonance (MR) image reconstruction. The proposed method minimizes a linear combination of nonlocal total variation, least square data fitting term and wavelet sparsity terms to reconstruct the MR image from undersampled k  -space data. The nonlocal total variation and wavelet sparsity are taken as the hybrid L1-regularizationL1-regularization functional and solving it using a Split Bregman algorithm. The proposed algorithm is compared with previous methods in terms of the reconstruction accuracy and computational complexity. The comparison results demonstrate the superiority of the proposed algorithm for compressed MR image reconstruction.