Stable solution of photon-count statistics inverse problem by means of iterated operator eigenfunctions

Vitalij N. Kurashov; Andrey V. Kurashov; Alexandr G. Chumakov

doi:10.1117/12.224173

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9 October 1995 Stable solution of photon-count statistics inverse problem by means of iterated operator eigenfunctions

Vitalij N. Kurashov, Andrey V. Kurashov, Alexandr G. Chumakov

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Proceedings Volume 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications; (1995) https://doi.org/10.1117/12.224173
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

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.

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Vitalij N. Kurashov, Andrey V. Kurashov, and Alexandr G. Chumakov "Stable solution of photon-count statistics inverse problem by means of iterated operator eigenfunctions", Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); https://doi.org/10.1117/12.224173

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