Accelerated Computation of Regularized Field Map Estimates

Michael J. Allison¹, Jeffrey A. Fessler¹

Existing regularized field map estimators are highly robust, but require the minimization of a non-convex cost function. The current fastest minimization method, an optimization transfer approach with separable quadratic surrogates, requires thousands of iterations to converge. We propose a novel optimization transfer method which uses Huber's algorithm for quadratic surrogates to solve the non-convex problem. By framing the problem in this way, we are able to exploit the sparse banded structure of typical finite differencing matrices. We evaluated our algorithm on a brain image dataset finding that it converged in one hundredth of the time.