Revunova E. The methods and information technology for stable recovery of signals by the results of indirect measurements

The dissertation is devoted to the development of methods and informational technology for recovery of signals obtained by indirect measurements, by the development of stable methods for solving discrete ill posed inverse problems (DIPs). The methodology for theoretical quality criteria analysis of models is developed in order to determine the patterns of model optimal complexity dependence on the level of uncertainty in the data. The method for the stable solution of DIPs based on the random projections is developed; this method uses multiplication by a random matrix for decreasing dimensionality, as well as a special model selection criterion. The method for the DIP solution based on random projection with an analytical averaging over realizations of random matrices is distinguished by eliminating the variance of the root-mean-square error of the input vector recovery that is introduced by averaging over random matrices. For the DIP solution by the method of truncated singular value decomposition it is analytically showed that the minimum position of input recovery error and output recovery error coincide. The model selection criterion is developed for determining the regularization parameter. The method for the transformation of the output of multichannel measuring system to the output of the system with a higher resolution is developed. On the base of the developed methods, the information technology for stable signal recovery by the results of indirect measurements is created, as well as software modules for a practical implementation of the technology.