International Journal of Biomedical Imaging
Volume 2006 (2006), Article ID 49378, 9 pages
doi:10.1155/IJBI/2006/49378
Progressive Magnetic Resonance Image Reconstruction Based on Iterative Solution of a Sparse Linear System
1Biomedical Imaging Technology Center, Department of Biomedical Engineering, Emory University/Georgia Institute of Technology, Atlanta 30322, GA, USA
2Biomedical Engineering Department, Cairo University, Giza 12613, Egypt
3Electrical and Computer Engineering Department, The Johns Hopkins University, Baltimore 21218, MD, USA
Received 21 August 2005; Accepted 8 October 2005
Academic Editor: Jie Tian
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.
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.