A new method for removing point radio sources and other non-Gaussian noise is proposed as a means of improving the accuracy of estimates of the angular power spectrum of the cosmic microwave background (CMB). The main idea of the method is to reconstruct fluctuations of the CMB in places contaminated by such emission, while traditional methods simply exclude these regions from consideration, leading to the appearance of "holes" in the resulting maps. The fundamental possibility of reconstructing the CMB signal in such holes follows from the analytical properties of a function with a finite spatial spectrum (the Silk damping frequency). A two-dimensional median filter is used to localize the point radio sources. Results of simulations of the method for maps of modest size are presented. The efficiency of applying the method to reconstruct the CMB from data with limited resolution and contaminated by appreciable pixel noise is investigated. The fundamental possibility of applying the method to reconstruct the CMB distribution in the region of the Galaxy is also demonstrated.
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