<title>Stable solution of photon-count statistics inverse problem by means of iterated operator eigenfunctions</title>

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 diagonalize 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 application to the processing ofphoton counts statistics experimental data.