Trust Region Methods for the Estimation of a Complex Exponential Decay Model in MRI With a Single-Shot or Multi-Shot Trajectory

Joint estimation of spin density R* 2 decay and OFF-resonance frequency maps is very useful in many magnetic resonance imaging 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...

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Bibliographic Details
Published in:IEEE transactions on image processing Vol. 24; no. 11; pp. 3694 - 3706
Main Authors: Chenxi Hu, Reeves, Stanley J.
Format: Journal Article
Language:English
Published: United States IEEE 01.11.2015
Subjects:
Algorithms
Approximation methods
Brain - anatomy & histology
Convergence
Cost function
Estimation
field map estimation
Humans
Image Processing, Computer-Assisted - methods
Image reconstruction
iterative algorithm
Magnetic resonance imaging
Magnetic Resonance Imaging - methods
Models, Statistical
Phantoms, Imaging
R 2 estimation
Trajectory
trust region method
trust region method
R_{2}^{\ast } estimation
iterative algorithm
field map estimation
ISSN:1057-7149, 1941-0042
Online Access:Get full text
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Summary:Joint estimation of spin density R* 2 decay and OFF-resonance frequency maps is very useful in many magnetic resonance imaging 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-shot 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 paper, 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 reduce the regularization gradually over the parameter maps and facilitates convergence from poor initializations. The two trust region methods are compared with the 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.
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ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2015.2442917