Determination of Structure Corrections using Geodetic VLBI Observations of Fiducial Extragalactic Radio Sources

We present the further development of the mathematical technique for calculating the structure corrections using VLBI images of fiducial extragalactic radio sources entering the celestial reference frame. In contrast to techniques described in the literature, the proposed approach can be applied to arbitrary images rather than to images which can be represented by a few Gaussian or delta functions. This is especially topical in view of the appearance of new sophisticated and high-precision image-reconstruction techniques different from the conventional CLEAN procedure or model fitting. The calculation efficiency of the structure corrections is ensured by using the algorithm of fast Fourier transform. We apply the proposed method to analyze a sufficiently representative sample of 36 fiducial extragalactic sources entering the celestial reference frame and illustrate its use for four sources, 1357+769, 0229+131, 2201+315, and 2200+420, each of them belonging to one of the four structure-index classes.     

A Method for Separating the Point-Source Foreground from the Cosmic Microwave Background Maps

We propose a new technique for high-accuracy reconstruction of the cosmic microwave background (CMB) anisotropy from observations contaminated by unresolved extragalactic point sources and pixel noise. The fundamental difference of this technique from the methods suggested before consists in reconstructing the CMB temperature fluctuations in regions contaminated by point sources with allowance for a priori information on the boundedness and spherical symmetry of the spatial power spectrum of the CMB anisotropy, which obeys the Gaussian statistics. The problems of deconvolving the initial maps, localizing point sources, and interpolating the CMB values in the holes are solved by using effective modifications of the well-known maximum entropy method. The results of simulations demonstrate the possibility of achieving the highest accuracy.     

Newton-Raphson Method and Stability of Nonlinear Information Image-Recovery Techniques

We consider the Newton-Raphson method as a method for the numerical implementation of nonlinear information image-recovery techniques. The classical and generalized maximum-entropy methods (MEM) are compared from the viewpoint of their sensitivity to input-data errors. A comparison of the spectral condition values of the Jacobi matrices shows that the generalized method is much more stable to noise than the conventional method, which is in good agreement with the empirical results. Unlike the generalized method, the conventional procedure requires that regularizing terms be added to the minimized functional to improve the stability of the numerical algorithms.