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Proceedings Paper

Least-squares framework for projection MRI reconstruction
Author(s): Jens Gregor; Fernando Rannou
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Paper Abstract

Magnetic resonance signals that have very short relaxation times are conveniently sampled in a spherical fashion. We derive a least squares framework for reconstructing three-dimensional source distribution images from such data. Using a finite-series approach, the image is represented as a weighted sum of translated Kaiser-Bessel window functions. The Radon transform thereof establishes the connection with the projection data that one can obtain from the radial sampling trajectories. The resulting linear system of equations is sparse, but quite large. To reduce the size of the problem, we introduce focus of attention. Based on the theory of support functions, this data-driven preprocessing scheme eliminates equations and unknowns that merely represent the background. The image reconstruction and the focus of attention both require a least squares solution to be computed. We describe a projected gradient approach that facilitates a non-negativity constrained version of the powerful LSQR algorithm. In order to ensure reasonable execution times, the least squares computation can be distributed across a network of PCs and/or workstations. We discuss how to effectively parallelize the NN-LSQR algorithm. We close by presenting results from experimental work that addresses both computational issues and image quality using a mathematical phantom.

Paper Details

Date Published: 3 July 2001
PDF: 11 pages
Proc. SPIE 4322, Medical Imaging 2001: Image Processing, (3 July 2001); doi: 10.1117/12.431168
Show Author Affiliations
Jens Gregor, Univ. of Tennessee/Knoxville (United States)
Fernando Rannou, Univ. de Santiago de Chile (Chile)


Published in SPIE Proceedings Vol. 4322:
Medical Imaging 2001: Image Processing
Milan Sonka; Kenneth M. Hanson, Editor(s)

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