Clinical magnetic resonance imaging (MRI) protocols typically include multiple acquisitions of the same region of interest under different contrast settings. This paper presents an efficient algorithm to jointly reconstruct a set of undersampled images with different contrasts. The proposed method has faster reconstruction time and better quality as measured by the normalized root-mean-square error (RMSE) compared to the existing methods consisting of multi-contrast Fast Composite Splitting Algorithm (FCSA-MT), Multiple measurement vectors FOCal Underdetermined System Solver (M-FOCUSS), and total variation regularized compressed sensing (SparseMRI). To efficiently solve the £2, 1-regularized optimization problem, our proposed algorithm adopts the Split Bregman (SB) technique to divide the problem into sub-problems. We efficiently compute a closed-form solution to each of the sub-problems by implementing a 3D spatial gradient operator as element-wise multiplication in k-space. As demonstrated by the in vivo results, the proposed algorithm (SB-L21) offers 2x, 32x, and 66x faster reconstruction with lower RMSE averaged across all contrasts and slices compared to FCSA-MT, M-FOCUSS, and SparseMRI, respectively.
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