  Magnetic field inhomogeneity estimation is important in some types of
magnetic resonance imaging (MRI), including field-corrected reconstruction for
fast MRI with long readout times, and chemical shift based water-fat imaging.
Regularized field map estimation methods that account for phase wrapping and
noise involve nonconvex cost functions that require iterative algorithms. Most
existing minimization techniques were computationally or memory intensive for
3D datasets, and are designed for single-coil MRI. This paper considers 3D MRI
with optional consideration of coil sensitivity, and addresses the multi-echo
field map estimation and water-fat imaging problem. Our efficient algorithm
uses a preconditioned nonlinear conjugate gradient method based on an
incomplete Cholesky factorization of the Hessian of the cost function, along
with a monotonic line search. Numerical experiments show the computational
advantage of the proposed algorithm over state-of-the-art methods with similar
memory requirements.
