Tkachuk O. Image signal restoring in conditions of noise interference by inversion of sample estimates of correlation matrix of observations

The object of research is the process of restoring image signals in the information system with adaptive antenna array. The subject of research is methods and algorithms for restoring image signals under conditions of arbitrary intensity noise interference in the information system with adaptive antenna array. Methods of research. The research of dissertation work was carried out using the theory of matrix calculus, mathematical analysis, complex analysis, computational linear algebra, the theory of ordinary differential equations, methods for solving incorrect problems, methods of multidimensional optimization, the theory of random processes, with the help of which mathematical models and the method for restoring image signals in noise interference conditions were developed. Statistical (simulation) modeling in the MATLAB programming environment is used to assess the adequacy of the proposed method. Theoretical and practical results: For the first time use of method based on inversion of correlation matrix of observations for restoring image signals in information system with adaptive antenna array is proposed, which allows to restore image signals against arbitrary intensity noise interference background; method of dynamic regularization of sample estimates of correlation matrix of observations with optimal parameter equal to dimension of adaptive antenna array is first proposed, which allows to obtain solution of inverse problem in real time without involvement of a priori data and additional computational costs for search of optimal parameter of regularization; method invariant to correlation of useful signals is developed, which is based only on results of spatial spectral analysis, which enables to receive an arbitrary number of both image signals and noise interference of arbitrary intensity from independent sources in the information system with adaptive antenna array.