Regularized MR coil sensitivity estimation using augmented Lagrangian methods

Several magnetic resonance (MR) parallel imaging techniques require explicit estimates of the receive coil sensitivity profiles. These estimates must be accurate over both the object and its surrounding regions to avoid generating artifacts in the reconstructed images. Statistical estimation methods provide robust sensitivity estimates but can be computationally expensive. In this paper, we propose an augmented Lagrangian (AL) based method that estimates the coil sensitivity by minimizing a quadratic cost function. This method reformulates the finite differencing matrix to allow for exact alternating minimization steps. We also explore a variation of our algorithm that involves intermediate updating of the Lagrange multipliers. We demonstrate that our proposed algorithm converges in half the time of the traditional conjugate gradient method with a circulant preconditioner (PCG) on a real data set.