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Choice of regularization parameter based on the regularized solution reconstruction in adaptive signal correction problem. (English. Russian original) Zbl 1467.45005

Comput. Math. Math. Phys. 61, No. 1, 43-52 (2021); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 1, 47-56 (2021).
Summary: In this paper adaptive signal correction is considered as one of possible solutions to an inverse ill-posed problem. This problem is defined to an integral equation of the convolution type, and the regularization method is used to solve it. To select the regularization parameter, it is proposed to reconstruct the regularized solution. The results of numerical experiments are presented.

MSC:

45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
65R30 Numerical methods for ill-posed problems for integral equations

Software:

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References:

[1] Eleftheriou, E.; Falconer, D., Adaptive equalization techniques for HF channels, IEEE J. Sel. Areas Commun., 5, 238-247 (1987)
[2] Santamarina, J. C.; Fratta, D., Discrete Signals and Inverse Problems (2005), New York: Wiley, New York
[3] Haykin, S., Adaptive Filter Theory (2014), Boston: Pearson, Boston · Zbl 0723.93070
[4] Maslakov, M. L., Application of two-parameter stabilizing functions in solving a convolution-type integral equation by regularization method, Comput. Math. Math. Phys., 58, 529-536 (2018) · Zbl 06909644
[5] Maslakov, M. L., Choice of regularization parameter in adaptive filtering problems, Comput. Math. Math. Phys., 59, 894-903 (2019) · Zbl 1431.65245
[6] Bauer, F.; Lukas, M. A., Comparing parameter choice methods for regularization of ill-posed problem, Math. Comput. Simul., 81, 1795-1841 (2011) · Zbl 1220.65063
[7] Hansen, P. C., Rank-Deficient and Discrete Ill-Posed Problems (1998), Philadelphia: SIAM, Philadelphia · Zbl 0890.65037
[8] Lu, S.; Pereverzev, S. V., Regularization Theory for Ill-Posed Problems (2013), Berlin: De Gruyter, Berlin · Zbl 1282.47001
[9] Hochstenbach, M. E.; Reichel, L.; Rodriguez, G., Regularization parameter determination for discrete ill-posed problems, J. Comput. Appl. Math., 273, 132-149 (2015) · Zbl 1295.65046
[10] Hamarik, U.; Palm, R.; Raus, T., A family of rules for parameter choice in Tikhonov regularization of ill-posed problems with inexact noise level, J. Comput. Appl. Math., 236, 2146-2157 (2012) · Zbl 1247.65071
[11] Goncharskii, A. V.; Leonov, A. S.; Yagola, A. G., A generalized discrepancy principle, USSR Comput. Math. Math. Phys., 13, 25-37 (1973) · Zbl 0276.65046
[12] A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Nauka, Moscow, 1990; Kluwer Academic, Dordrecht, 1995). · Zbl 0831.65059
[13] Sizikov, V. S., On discrepancy principles in solving ill-posed problems, Comput. Math. Math. Phys., 43, 1241-1259 (2003)
[14] Johnson, E. E.; Koski, E.; Furman, W. N.; Jorgenson, M.; Nieto, J., Third-Generation and Wideband HF Radio Communications (2013), Boston: Artech, Boston
[15] Xiong, F., Digital Modulation Techniques (2006), Boston: Artech, Boston · Zbl 1173.94300
[16] Proakis, J. G.; Salehi, M., Digital Communications (2008), New York: McGraw-Hill, New York
[17] Morozov, V. A., The error principle in the solution of operational equations by the regularization method, USSR Comput. Math. Math. Phys., 8, 63-87 (1968)
[18] Watteson, C. C.; Juroshek, J. R.; Bensema, W. D., Experimental confirmation of an HF channel model, IEEE Trans. Commun. Technol., 18, 792-803 (1970)
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