Estimation of Optimal Parameter of Regularization of Signal Recovery

Abstract

In this paper there are researched regularizing properties of discretization in a space of output signals for some linear operator equation with noisy data. The essence of proposed method is selection of discretization level which is a parameter of the regularization in this context by the principle of equality of random and deterministic components of the input signal recovering error. It is shown the method, i.e. the solution which is discrete by input signal is stable to small inaccuracies in input signal. At that in case of definite level of output signal measurements inaccuracy the recovering error of input signal is unambiguously defined by input signal sampling increment that allows to select reasonably the regularization parameter for specific criterion, for example, for definite measurements inaccuracy. Specific calculations and examples are represented in explicit form for single-dimension case but this does not restricts generality of proposed method.