Regularized parallel mri reconstruction using an alternating direction method of multipliers

Using sparsity-based regularization to improve magnetic resonance image (MRI) reconstruction quality demands computation-intensive nonlinear optimization. In this paper, we develop an iterative algorithm based on the method of multipliers-augmented Lagrangian (AL) formalism-for reconstruction from sensitivity encoded data using sparsity-based regularization. We first convert the unconstrained reconstruction problem into an equivalent constrained optimization task and attack the constrained version in an AL framework using an alternating direction minimization method-this leads to an alternating direction method of multipliers whose intermediate steps are amenable to parallelization. Numerical experiments with in-vivo human brain data illustrate that the proposed algorithm converges faster than both general-purpose optimization algorithms such as nonlinear conjugate gradient (NCG) and state-of-the-art MFISTA.