Prior information constrained alternating direction method of multipliers for longitudinal compressive sensing MR imaging

Sparsity is widely utilized for magnetic resonance imaging (MRI) to reduce k-space sampling. In many clinical MRI scenarios, existing similarity within a series of MRI images and between different contrasts in the same scan can be used to substantially shorten the acquisition time. In this study, the prior information on the pre-acquired reference image is employed in the framework of alternating direction method of multipliers (ADMM) for accurate longitudinal compressed sensing (CS) MRI (LCS-MRI) reconstruction. We propose an efficient algorithm based on the ADMM framework, by using similarity prior information for LCS-MRI. The algorithm minimizes the linear combination of three terms including a least squares data fitting and two ℓ₁ norm regularization terms. The first ℓ₁ norm regularization is utilized for measuring the sparsity of the recovered signal, and the other ℓ₁ norm regularization is employed for measuring the sparsity of the difference between the recovered MR image and the prior known MR scan. The proposed method formulates the reconstruction problem to several unconstrained minimization sub-problems, which can be solved by shrinking operators and alternating minimization algorithms. We compare the proposed algorithm with previous methods in terms of reconstruction accuracy and computation complexity. Numerous experiments demonstrate that the proposed method is more effective and robust and obtained superior performance in reconstructing longitudinal compressed MR image than the other methods.