Sathish Ramani1, Jeffrey A. Fessler1
Based on the augmented Lagrangian (AL) formalism, we present a new method for MR image reconstruction from undersampled sensitivity encoded data using a combination of total-variation and l1-regularization. We introduce a set of constraint variables and convert the original unconstrained reconstruction problem into an equivalent constrained task. We then construct an AL function (that includes a Lagrange multiplier term and a penalty term) and iteratively minimize it (while taking care to update the Lagrange multiplier) by applying an alternating scheme that decouples the minimization process with respect to the constraint variables, leading to a simple (AL) algorithm. Numerical experiments with real MR data illustrate that the proposed AL algorithm converges faster than both general-purpose optimization methods such as the nonlinear conjugate gradient (NCG) algorithm and state-of-the-art MFISTA.