Statistical Synthesis of Optimal Processing Algorithms for Series of Atmospherically Distorted “Speckle” Images of Astronomical Objects

The authors propose and investigate a statistical model of the spatial spectrum of a “speckle” image of an astronomical object. This model is used as a basis for obtaining the maximum-likelihood equation for estimating the spatial spectrum of the object on the basis of a series of speckle images. Analytic solution of the maximum-likelihood equation for the case of observation of bright and weak astronomical objects leads to synthesis of algorithms for optimal estimation of the square of the modulus and phase of the spatial spectrum of the object. The conditions are determined under which the quasioptimal Labeyrie and Knox–Thompson methods coincide with the synthesized ones and become optimal. Ways of optimally modifying quasioptimal methods are indicated.