Universal Journal of Computational Mathematics(CEASE PUBLICATION) Vol. 2(1), pp. 11 - 16
DOI: 10.13189/ujcmj.2014.020103
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Regularization and Adaptation for the Approximation of Nonsmooth Solutions for Fredgolm First Kind Integral Equations

T.I. Serezhnikova ^*
Institute of Mathematics and Mechanics UrB RAS,Ural Federal University,Ekaterinburg, Russia

ABSTRACT

In the paper, we propose a new regularization algorithm based on the generalized Tikhonov regularization method. In the paper proposed technique treats problems in the form of Fredholm first kind integral equations which must be inverted. In classical regularization functionals we propose put in the specialize summand, which allows to distribution control of points of approximate solutions. The best additional summand one can get with using more information about solutions. There are six model numerical results in the paper. Numerical experiments prove, that our technique does a better job of preserving functions jumps. As result in the case of the image reconstructions problems, we obtain approximate solutions of better accuracy and images become more blur-free images.

KEYWORDS
Image Reconstruction, Nonsmooth Solutions, Ill-posed Problems, Tikhonov Regularization, Integral Equations, Adaptive Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] T.I. Serezhnikova , "Regularization and Adaptation for the Approximation of Nonsmooth Solutions for Fredgolm First Kind Integral Equations," Universal Journal of Computational Mathematics(CEASE PUBLICATION), Vol. 2, No. 1, pp. 11 - 16, 2014. DOI: 10.13189/ujcmj.2014.020103.

(b). APA Format:
T.I. Serezhnikova (2014). Regularization and Adaptation for the Approximation of Nonsmooth Solutions for Fredgolm First Kind Integral Equations. Universal Journal of Computational Mathematics(CEASE PUBLICATION), 2(1), 11 - 16. DOI: 10.13189/ujcmj.2014.020103.