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Proceedings Paper

Semi-infinite positron emission tomography
Author(s): Bernard A. Mair; Murali Rao; J. M. M. Anderson
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Paper Abstract

In this paper, we develop a refined version of the mathematical model introduced by Shepp and Vardi for positron emission tomogrpahy. This model replaces the usual finite-dimensional linear system by a nonstandard integral equation in which the data-space is finite-dimensional, but the unknown emission intensities are represented by a mathematical measure on the region of interest. Since our measure might not be representable by a density, this is also a refinement of the integral equation model mentioned (but not analyzed) in the work of Vardi, Shepp, and Kaufman. As in the finite-dimensional model, we obtain an iteration procedure which generates a sequence of functions. Such a functional iteration has already been proposed by other researchers for solving a general class of positive linear ill-posed inverse problems. However, unlike the original finite-dimensional problem, the convergenec of this infinite- dimensional version remains an open question. This paper demonstrates examples in which these iterates are continuous functions, but does not converge to a density. We also discuss a feasible approach for settling the convergence question.

Paper Details

Date Published: 9 October 1995
PDF: 9 pages
Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); doi: 10.1117/12.224179
Show Author Affiliations
Bernard A. Mair, Univ. of Florida (United States)
Murali Rao, Univ. of Florida (United States)
J. M. M. Anderson, Univ. of Florida (United States)

Published in SPIE Proceedings Vol. 2570:
Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications
Randall Locke Barbour; Mark J. Carvlin; Michael A. Fiddy, Editor(s)

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