RESTORATION OF ASTRONOMICAL IMAGES WITH USING HARTLEY TRANSFORM

The methods for restoration of the astronomical images, based on Tikho nov's regularization theory, are described. The linear algorithm perfo rms the minimization of the objective function (Tikhonov's functional) without any constraints and with using two-dimensional fast Hartley t ransform procedure. The nonlinear algorithm utilizes for the minimizat ion the method of gradient projection on a non-negative function set. This nonlinear constraint allows to take into account a priori informa tion about solution and leads to an improvement in results and to supe r-resolution. The calculations of the objective function and the gradi ent are carried out in the spatial frequencies domain also using the H artley transform. In comparison with using the fast Fourier transform, the advantage of necessary computer memory on factor of two and a pro cessor time saving can be achieved. The results of numerical experimen ts and the restored image of M 31 nucleus are presented.