Semi-infinite positron emission tomography

Bernard A. Mair; Murali Rao; J. M. M. Anderson

doi:10.1117/12.224179

9 October 1995 Semi-infinite positron emission tomography

Bernard A. Mair, Murali Rao, J. M. M. Anderson

Proceedings Volume 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications; (1995) https://doi.org/10.1117/12.224179
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

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.

Citation Download Citation

Bernard A. Mair, Murali Rao, and J. M. M. Anderson "Semi-infinite positron emission tomography", Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); https://doi.org/10.1117/12.224179

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