Progressive Magnetic Resonance Image Reconstruction Based on Iterative Solution of a Sparse Linear System

Kadah, Yasser M.; Fahmy, Ahmed S.; Gabr, Refaat E.; Heberlein, Keith; Hu, Xiaoping P.

doi:https://doi.org/10.1155/IJBI/2006/49378

International Journal of Biomedical Imaging

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Volume 2006 | Article ID 049378 | https://doi.org/10.1155/IJBI/2006/49378

Progressive Magnetic Resonance Image Reconstruction Based on Iterative Solution of a Sparse Linear System

Yasser M. Kadah,^1,2Ahmed S. Fahmy,^2,3Refaat E. Gabr,^2,3Keith Heberlein,¹and Xiaoping P. Hu¹

Academic Editor: Jie Tian

Received21 Aug 2005

Accepted08 Oct 2005

Published21 Feb 2006

Abstract

Image reconstruction from nonuniformly sampled spatial frequency domain data is an important problem that arises in computed imaging. Current reconstruction techniques suffer from limitations in their model and implementation. In this paper, we present a new reconstruction method that is based on solving a system of linear equations using an efficient iterative approach. Image pixel intensities are related to the measured frequency domain data through a set of linear equations. Although the system matrix is too dense and large to solve by direct inversion in practice, a simple orthogonal transformation to the rows of this matrix is applied to convert the matrix into a sparse one up to a certain chosen level of energy preservation. The transformed system is subsequently solved using the conjugate gradient method. This method is applied to reconstruct images of a numerical phantom as well as magnetic resonance images from experimental spiral imaging data. The results support the theory and demonstrate that the computational load of this method is similar to that of standard gridding, illustrating its practical utility.

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Copyright

Copyright © 2006 Yasser M. Kadah et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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