Reconstruction of signals by standard Tikhonov method
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Date
2011
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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?<inf>?</inf>-f?
between the regularized approximation x?<inf>?</inf> 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.
e
, we assume that the available noise is e? with
e-e?
? ? 5 and prove that the error
x?<inf>?</inf>-f?
between the regularized approximation x?<inf>?</inf> 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.
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Keywords
Balancing principle, Inverse and Ill-posed problems, Signal reconstruction, Tikhonov regularization
Citation
Applied Mathematical Sciences, 2011, 5, 57-60, pp. 2819-2829