## Toeplitz-based iterative image reconstruction for MRI with correction for magnetic field inhomogeneity (2005)

Venue: | IEEE Trans. Signal Process |

Citations: | 18 - 3 self |

### BibTeX

@ARTICLE{Fessler05toeplitz-basediterative,

author = {Jeffrey A. Fessler and Senior Member and Sangwoo Lee and Valur T. Olafsson and Hugo R. Shi and Student Member and Student Member and Student Member and Douglas C. Noll Member},

title = {Toeplitz-based iterative image reconstruction for MRI with correction for magnetic field inhomogeneity},

journal = {IEEE Trans. Signal Process},

year = {2005},

volume = {53},

pages = {3393--3402}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract — In some types of magnetic resonance (MR) imaging, particularly functional brain scans, the conventional Fourier model for the measurements is inaccurate. Magnetic field inhomogeneities, caused by imperfect main fields and by magnetic susceptibility variations, induce distortions in images that are reconstructed by conventional Fourier methods. These artifacts hamper the use of functional MR imaging (fMRI) in brain regions near air/tissue interfaces. Recently, iterative methods that combine the conjugate gradient (CG) algorithm with nonuniform FFT (NUFFT) operations have been shown to provide considerably improved image quality relative to the conjugatephase method. However, for non-Cartesian k-space trajectories, each CG-NUFFT iteration requires numerous k-space interpolations, operations that are computationally expensive and poorly suited to fast hardware implementations. This paper proposes a faster iterative approach to field-corrected MR image reconstruction based on the CG algorithm and certain Toeplitz matrices. This CG-Toeplitz approach requires k-space interpolations only for the initial iteration; thereafter only FFTs are required. Simulation results show that the proposed CG-Toeplitz approach produces equivalent image quality as the CG-NUFFT method with significantly reduced computation time. Index Terms — fMRI imaging, spiral trajectory, magnetic susceptibility, non-Cartesian sampling I.

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