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Algebraic reconstruction for magnetic resonance imaging under B0 inhomogeneity
1Department of Radiology, Center for Magnetic Resonance Research, University of Minnesota, Minneapolis 55455, USA.
IEEE Transactions on Medical Imaging
|September 15, 1998
Summary
Magnetic resonance imaging (MRI) spatial distortions caused by B0 field inhomogeneities are corrected using an inverse problem formulation. Robust algebraic reconstruction methods, including nonlinear k-space trajectories, yield improved image quality.
Area of Science:
- Medical Imaging
- Physics
- Computational Science
Background:
- Magnetic resonance imaging (MRI) typically uses Fourier encoding for spatial localization.
- B0 field inhomogeneities disrupt the linear frequency-spatial relationship, leading to image distortions.
Purpose of the Study:
- To develop and validate a robust image reconstruction method for MRI under B0 field inhomogeneities.
- To address the ill-posed nature of image reconstruction in distorted MRI data.
Main Methods:
- Formulating the problem as an inverse problem of a linear Fredholm equation of the first kind.
- Estimating operators using field mapping and k-space trajectories.
- Employing robust solvers like singular value decomposition and the conjugate gradient method.
Main Results:
- Achieved corrected images optimal in the Frobenius norm sense.
- Demonstrated that nonlinear k-space trajectories lead to better-conditioned operators.
- Showcased effective application to distortions along one image dimension, simplifying to 1D problems.
Conclusions:
- The proposed algebraic reconstruction technique effectively corrects spatial distortions in MRI caused by B0 inhomogeneities.
- Nonlinear k-space trajectories are advantageous for improving reconstruction stability and accuracy.