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Proceedings Paper

Stable solution of photon-count statistics inverse problem by means of iterated operator eigenfunctions
Author(s): Vitalij N. Kurashov; Andrey V. Kurashov; Alexandr G. Chumakov
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Paper Abstract

Restoration of light intensity fluctuations from photon-counting data provides typical ill-posed inverse problem for non-Hermitian transforming operator. Such problems cannot be solved with the help of eigenfunction representation which diagonalizes operator and simplifies the regularization of quasi-solution. We describe an analytical method to solve this inverse problem which is based on the Poisson transform operator representation in mixed basis. The last one is determined by eigenfunctions of left and right iterated operators and diagonlize Poisson transform. On the base of proposed method we have performed the set of numerical experiments with typical intensity distributions. It has been shown that restoration procedure has necessary stability and may be used when the level of statistical errors is relatively high. In conclusion we describe the results of inversion procedure appreciation to the processing of photon counts statistics experimental data.

Paper Details

Date Published: 9 October 1995
PDF: 12 pages
Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); doi: 10.1117/12.224173
Show Author Affiliations
Vitalij N. Kurashov, Kiev Univ. (Ukraine)
Andrey V. Kurashov, Kiev Univ. (Ukraine)
Alexandr G. Chumakov, Kiev Univ. (Ukraine)

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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