Decomposition and Regularization of the Solution of Ill-Conditioned Inverse Problems in Processing of Measurement Information. Part 1. A Theoretical Evalution of the Method

A theoretical evaluation of a method of solving ill-conditioned inverse problems that arise in mathematicostatistical processing of measurement information under conditions of unavoidable errors in measurements and a mathematical model of the study object is considered. The method is based on physical and canonical decomposition of the initial model of the object, specified in the form of a system of linear equations as well as two-sided regularization of the solution of a canonical (diagonal) system of equations. It is shown that through the use of the method it is possible to create an adaptive algorithm for recognition and stable estimation of a group of information parameters of a physically decomposed model.