Signal reconstruction by the method of regularization

The problem on reconstruction of signals with noise is considered as that of calculating the values of an unbounded operator by Tikhonov's method of regularization. Several techniques (theoretically or pragmatically justified) for choosing the regularization parameter are discussed. The formulation and usage of a priori knowledge on a structure of the sought-for useful signal in time and frequency regions are allowed. The conceptions of functional analysis are used; this permits us to strictly justify our theoretical conclusions as well as to provide the breadth of possible applications in various fields of science related to the processing of experimental data. The problem statement considered in this paper corresponds to the case of direct measurements. The influence of high-level noise is studied.