Methods of restoration of radial brightness distribution across a stellar disk from speckle interferometric data and its application to analysis of observations of α Orionis

The methods of restoration of radial brightness distribution across a stellar disk from an anaysis of speckle interferometric data in the case of circular symmetry are proposed. These methods are based on modern numerical methods of solution of ill-posed problems. The application of these methods to an analysis of published data for α Ori allows to find the brightness distributions for the TiO absorption band and the neighbouring continuum. The results do not contradict the assumption that this star has a near-by dust envelope located inside the extended atmosphere