Regularized parallel mri reconstruction using an alternating direction method of multipliers

Abstract

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.