doi: 10.17586/2226-1494-2017-17-5-879-889


STUDY OF ERRORS OF SOME METHODS FOR SEPARATING OVERLAPPED SPECTRAL LINES UNDER NOISE EFFECT

V. S. Sizikov, A. V. Lavrov


Read the full article  ';
Article in Russian

For citation: Sizikov V.S., Lavrov A.V. Study of errors of some methods for separating overlapped spectral lines under noise effect. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2017, vol. 17, no. 5, pp. 879–889 (in Russian). doi: 10.17586/2226-1494-2017-17-5-879-889

Abstract

Subject of Research. We consider one of the actual problems of spectroscopy, that is, the separation of close spectral lines. Method. The problem is solved by a mathematical (computer) way, namely, by minimizing a functional of discrepancy between the meas­ured and calculated spectra. In this case, the lines (components) are modeled by Gaussians and the problem is reduced to localization of their parameters. Main Results. To minimize the functional we propose the coordinate descent method modification with the use of decremental constraintstechnique. To smooth and differentiate noisy experimental spectral data, we suggest using splines. The software on MatLab is developed and a number of spectra are processed. Practical Relevance. The developed technique can be used to restore the fine structure of spectra and, thereby, to increase the resolving power of spectrometers.


Keywords: spectrum lines separation, discrepancy functional minimization, measured and calculated spectra, Gaussians, coordinate descent method with constraints, splines, software, MatLab

Acknowledgements. This work was supported by the Russian Foundation for Basic Research (RFBR), grant No. 13-08-00442.

References
 1.     Giese A.T., French C.S. The analysis of overlapping spectral absorption bands by derivative spectrophotometry. Applied Spectroscopy, 1955, vol. 9, no. 2, pp. 78–96. doi: 10.1366/000370255774634089
2.     Kraulinya E.K., Liepa S.I., Pickalov V.V., Scudra A.I. On the Investigation of Atomic Sensibilized Fluorescence by Spectrum Line Profiles. In Ill-Posed Inverse Problems in Atomic Physics. Ed. N.G. Preobrazhensky. Novosibirsk,IPAM Publ., 1976,pp. 61–72. (In Russian)
3.     Kauppinen J.K., Moffatt D.J., Mantsch H.H., Cameron D.G. Fourier self-deconvolution: a method for resolving intrinsically overlapped bands. Applied Spectroscopy, 1981, vol. 35, no. 3, pp. 271–276. doi: 10.1366/0003702814732634
4.     Mikhailenko V.I., Mikhal’chuk V.V. Method of expanding spectra with unresolved structure. Journal of Applied Spectroscopy, 1987,vol. 46,no.4,pp. 327–335. doi: 10.1007/BF00660037
5.     Goldberg D.E. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, 1989, 412 p.
6.     Manoylov V.V., Zarutsky I.V. Capability of the algorithm on the base convolution processing signals form for the estimation of mass-spectra peak parameters in multiplets. Scientific Instrumentation, 2009,vol. 19,no.4,pp.103–108. (In Russian)
7.     Kurchatov I.S. Computer analysis of vibrational
spectra of water-alcohol solutions. genphys.phys.msu.ru/rus/diploma/diploma2010/Kurchatov.pdf (accessed 31.07.2017)
8.     Yan L., Liu H., Zhong S., Fang H. Semi-blind spectral deconvolution with adaptive Tikhonov regularization. Applied Spectroscopy, 2012, vol. 66, no. 11, pp. 1334–1346. doi: 10.1366/11-06256
9.     Tikhonov A.N., Arsenin V.Ya. Solutions of Ill-Posed Problems. New York,Wiley, 1977.
10.  Verlan’ A.F., Sizikov V.S. Integral Equations: Methods, Algorithms, Programs. Kiev,NaukovaDumka, 1986,544 p.(In Russian)
11.  Engl H., Hanke M., Neubauer A. Regularization of Inverse Problems. Dordrecht, Kluwer, 1996, 328 p.
12.  Petrov Yu.P., Sizikov V.S. Well-Posed, Ill-Posed, and Intermediate Problems with Applications. Leiden–Boston, VSP, 2005, 234p.
13.  Sizikov V.S., Krivykh A.V. Reconstruction of continuous spectra by the regularization method using model spectra. Optics and Spectroscopy, 2014, vol. 117, no. 6, pp. 1010–1017. doi: 10.1134/S0030400X14110162
14.  Sizikov V., Sidorov D. Discrete spectrum reconstruction using integral approximation algorithm. Applied Spectroscopy, 2017, vol. 71, no.7, pp. 1640–1651.doi: 10.1177/0003702817694181
15.  D’yakonov V., Abramenkova I. MATLAB. Processing of Signals and Images. St. Petersburg,Piter Publ., 2002,608 p.(In Russian)
16.  Voskoboinikov Yu.E., Preobrazhensky N.G., Sedel’nikov A.I. Mathematical Processing of Experiment in Molecular Gas Dynamics. Novosibirsk, Nauka Publ., 1984, 240 p.(In Russian)
17.  Sizikov V.S. Mathematical Methods for Processing the Results of Measurements. St. Petersburg, Polytechnika Publ., 2001, 240 p.(In Russian)
18.  Sizikov V.S. Infrared tomography of hot gas: mathematical model of active-passive diagnosis. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2013, no. 6, pp. 1–17. (In Russian)
19.  Sizikov V.S., Evseev V., Fateev A., Clausen S. Direct and inverse problems of infrared tomography. Applied Optics, 2016, vol. 55, no. 1, pp. 208–220. doi: 10.1364/AO.55.000208
20.  Nelder J.A., Mead R. A simplex method for function minimization. The Computer Journal, 1965, vol. 7, no. 4, pp. 308–313. doi: 10.1093/comjnl/7.4.308
21.  Kincaid D., Cheney W. Numerical Analysis: Mathematics of Scientific Computing. 3rd ed. Providence, AMS, 2009, 788 p.
22.  Holland J.H. Adaptation in Natural and Artificial Systems. Cambridge, MIT Press, 1992, 232 p.
23.  Bell R.J. Introductory Fourier Transform Spectroscopy. NY–London, Academic Press, 1972, 382 p.
24.  Himmelblau D.M. Applied Nonlinear Programming. NY, McGray-Hill, 1972, 416 p.
25.  D’yakonov V.P. Handbook on Algorithms and Programs in Basic Language for PC. Moscow, Nauka Publ., 1989, 240 p. (In Russian)
26.  Sizikov V., Evseev V. Bars and Spheroids in Gravimetry Problem. https://arxiv.org/abs/1604.06927, 2016
27.  Encyclopedic Dictionary of Physics.Ed. A.M. Prokhorov. Moscow, Sovetskaya Entsiklopediya Publ., 1984. 944 p.
28.  D’yakonov V.P. MATLAB 6: Training Course. St. Petersburg, Piter Publ., 2001, 592 p. (In Russian)
29.  Rautian S.G.Real spectral apparatus. Soviet Physics Uspekhi, 1958, vol. 66(1), no. 2, pp. 245–273. doi: 10.1070/PU1958v001n02ABEH003099 


Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2024 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.

Яндекс.Метрика