Statistical synthesis of algorithms for optimal processing of a Poisson image distorted by the atmosphere

The quantum effects and recording noise are allowed for in an analysis of statistical optimization of the algorithms for the processing of images distorted by the atmospheric turbulence. The Poisson statistics of the recorded images and the Gaussian statistics of atmospheric distortions are assumed in the derivation of the equations for the maximum likelihood of a spatial spectrum of one short-exposure image. An analytic solution of the equations of maximum likelihood for low and high values of the signal/noise ratio is utilized in the synthesis of the optimal processing algorithms and the physical meaning of these algorithms is discussed.