Iterative Object Reconstruction from the Limited Spectrum Based on Soft Approach

In this paper we use a priori information in the object domain to reconstruct the object from the partly available spectrum. Basically, when a priori information consists of the support constraints only, this is a well known problem where an iterative IFFT/FFT is more or less efficient depending on the amount of the a prior information and relative share of the available part of the spectrum. Conceptually we use the same approach, however, we use a prior information in a more complete way by using the object distribution function and not only the constrains in the object domain. This soft approach, compared with a classical (hard) approach, contributes both in the increased speed of the convergence as well as in the total gain obtained at the end of iterations. Total gain and convergence speed in the soft approach depend on the preliminary object and generally increase with amount of the a priori information included in the initial step that defines an initial object