Accelerated Computation of Regularized Field Map Estimates

INTRODUCTION Field inhomogeneity affects magnetic resonance (MR) imaging techniques that use long readout times (e.g., spiral pulse sequences and echo-planer imaging (EPI)). To correct for reconstruction artifacts related to the inhomogeneity, one must have an accurate estimate of the off-resonance frequency at each voxel; i.e., a field map. The conventional method to estimate the field map is to acquire two scans with different echo times, reconstruct the corresponding images, and then compute their phase difference and divide by the difference in echo times [1]. However, such estimates are highly corrupted by noise in voxels with low signal. Instead, Funai et al. [1] proposed a statistical based estimator that enforces our a priori knowledge that the field maps should be smooth. Although highly robust, this estimator has a nonconvex cost function that is complicated to minimize. To address this, a solution using the optimization transfer principle and separable quadratic surrogates was proposed [1]. However, this approach can require thousands of iterations to converge. Since field maps of a 3D volume are often estimated on a slice-by-slice basis, this cost is significant. We present a novel optimization transfer method that uses Huber’s algorithm for quadratic surrogates [2] to minimize the non-convex cost function in [1] much faster.