Abstract:
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.
Keywords:regularization methods, regularization parameter, experimental data processing, signal reconstruction, functional analysis.
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