Efficient computation of regularized field map estimates in 3D
Estimating the main magnetic field inhomogeneity is important for many magnetic resonance imaging (MRI) techniques. Regularized estimation methods can provide accurate estimates that intrinsically avoid phase wrapping, account for the chemical shift due to fat, and reduce noise. However, these methods require minimizing nonconvex cost functions and existing algorithms are undesirably slow or do not scale to realistic 3D datasets due to memory limitations. This paper proposes a new algorithm that overcomes these limitations. The algorithm adapts the nonlinear conjugate gradient method by incorporating an monotonic line search and efficient iteration-dependent preconditioning. Experiments on multi-echo field map estimation show that our algorithm is competitive with state-of-the-art methods in 2D, and scale successfully to 3D datasets, where current fast methods fail due to memory limitations.