FA-SART: A Frequency-Adaptive Algorithm in Pinhole SPECT Tomography

As a solution to the frequently reported problem of the high frequencies reconstructed sometimes many iterations after the low frequencies in tomography, we proposed in a recent paper [V. Israel-Jost, Ph. Choquet, and A. Constantinesco, Int. J. Biomed. Imaging, 2006, paper 34043.] a general adaptati...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2008-01, Vol.30 (2), p.819-836
Main Author: Israel-Jost, Vincent
Format: Article
Language:English
Subjects:
Algorithms
Iterative methods
Projectors
Radon
Sensors
Tomography
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Summary:As a solution to the frequently reported problem of the high frequencies reconstructed sometimes many iterations after the low frequencies in tomography, we proposed in a recent paper [V. Israel-Jost, Ph. Choquet, and A. Constantinesco, Int. J. Biomed. Imaging, 2006, paper 34043.] a general adaptation that can apply to many algorithms: the incomplete backprojection. We stressed the fact that this type of frequency adapted (FA) algorithm works only when the linear problem of tomography to be solved involves deblurring, i.e., when the point spread functions (PSFs) associated with each voxel are large. Thus, depending on the desired level of detail, a parameter is set to achieve the reconstruction within a small number of iterations. The aim of this paper is to give a mathematical analysis of both the acceleration obtained and the convergence of an FA algorithm derived from the simultaneous algebraic reconstruction technique (SART) algorithm of Andersen and Kak, the so-called FA-SART algorithm.
ISSN:1064-8275
1095-7197
DOI:10.1137/060668341