  We propose a new approach for the accurate reconstruction of cosmic microwave
background distributions from observations containing in addition to the
primary fluctuations the radiation from unresolved extragalactic point sources
and pixel noise. The approach uses some effective realizations of the
well-known maximum entropy method and principally takes into account {\it a
priori} information about finiteness and spherical symmetry of the power
spectrum of the CMB satisfying the Gaussian statistics.
