Trust region methods for estimation of a complex exponential decay model in MRI with a single-shot or multi-shot trajectory (in review)
Joint estimation of spin density, R2* decay and off-resonance frequency maps is very useful in many magnetic resonance imaging (MRI) applications. The standard multi-echo approach can achieve high accuracy but requires a long acquisition time for sampling multiple k-space frames. There are many approaches to accelerate the acquisition. Among them, single- or multi-shot trajectory based sampling has recently drawn attention due to its fast data acquisition. However, this sampling strategy destroys the Fourier relationship between k-space and images, leading to a great challenge for the reconstruction. In this work, we present two trust region methods based on two different linearization strategies for the nonlinear signal model. A trust region is defined as a local area in the variable space where a local linear approximation is trustable. In each iteration, the method minimizes a local approximation within a trust region so that the step size can be kept in a suitable scale. A continuation scheme is applied to gradually reduce the regularization over the parameter maps and facilitate convergence from poor initializations. The two trust region methods are compared to two other previously proposed methods---the nonlinear conjugate gradients and the gradual refinement algorithm. Experiments based on various synthetic data and real phantom data show that the two trust region methods have a clear advantage in both speed and stability.