Reconstruction of signals by standard Tikhonov method

Abstract

In this work we propose a standard Tikhonov regularization approach for obtaining the signal f from the observed signal ye. The observed signal is distorted by an additive noise or error e. Deviating from the usual assumption on the bound on

e

, we assume that the available noise is e? with

e-e?

? ? 5 and prove that the error

x??-f?

between the regularized approximation x?? and the solution f? of the noise free equation Kf = y is of optimal order. The regularization parameter ? is chosen using a balancing principle considered in [10]. The computational results provided endorses the reliability and effectiveness of our method.