Deconvolution of optical spectra distorted by random noise using an artificial immune system

D.I. Galiakhmetova^a*, M.E. Sibgatullin^a,b**, D.Z. Galimullin^c***, D.I. Kamalova^a****

^aKazan Federal University, Kazan, 420008 Russia

^bTatarstan Academy of Sciences, Institute of Applied Research, Kazan, 420111 Russia

^cV.G. Timiryasov Kazan Innovative University (IEML), Kazan, 420111 Russia

 E-mail: *galiakhmetova.di@gmail.com, **sibmans@mail.ru,

***galimullin_d.z@mail.ru,  ****Dina.Kamalova@kpfu.ru

Received November 28, 2017

Full text PDF

Abstract

The deconvolution of a complex spectral contour into components by the algorithm of artificial immune system has been considered. It is the optimization method which is based on the behavior of the immune system. The random fractal noise has been used as a noise model which allows one to employ different noises, such as the high- and low-frequency noises. The results of the decomposition of the model contour consisting of three Gaussian components have been represented. The dependence of the efficiency of decomposition of spectral contours on the relative level of noise and the spectral structure of noise has been investigated.

Keywords: optical spectroscopy, deconvolution of complex spectra, artificial immune system, random noise

Figure Captions

Fig. 1. Deconvolution of the model contour, H = 0.1, relative noise level 1%.

Fig. 2. Deconvolution of the model contour, H = 0.1, relative noise level 5%.

Fig. 3. Deconvolution of the model contour, H = 0.5, relative noise level 5%.

Fig. 4. Deconvolution of the model contour, H = 0.9, relative noise level 5%.

Fig. 5. Assessment of the quality of recovery of the first contour depending on the Hurst exponent. Relative noise level 1%, 5%, and 10%.

Fig. 6. Assessment of the quality of recovery of the second contour depending on the Hurst exponent. Relative noise level 1%, 5%, and 10%.

Fig. 7. Assessment of the quality of recovery of the third contour depending on the Hurst exponent. Relative noise level 1%, 5%, and 10%.

References

1. Karpenko A.P.  Sovremennye algoritmy poiskovoi optimizatsii [Modern Algorithms of Search Optimization]. Moscow, Izd. MGTU im. N. E. Baumana, 2014. 446 p. (In Russian)

2. Galiakhmetova D.I., Sibgatullin M.E., Galimullin D.Z., Kamalova D.I. The deconvolution of complex spectra by artificial immune system.  J. Phys.: Conf. Ser., 2017, vol. 917, art.  042007, pp. 1–5. doi: 10.1088/1742-6596/917/4/042007.

3. Kamalova D.I., Galimullin D.Z., Sibgatullin M.E., Shaimukhametova E.R., Salakhov M.Kh. Separation of closely located IR Fourier absorption bands using the genetic algorithm.  Opt. Spectrosc., vol. 114, no. 1, pp. 41–46. doi: 10.1134/S0030400X1301013X.

4. Kureichik V.V., Kureichik V.M., Rodzin S.I.  Teoriya evolyutsionnykh vychislenii  [Theory of Evolutionary Calculations]. Moscow, FIZMATLIT, 2012. 260 p. (In Russian)

5. Kushnir N.V., Kushnir A.V., Anatskaya E.V., Katysheva P.A., Ustinov K.G. Artificial immune systems: Review and current state.  Nauchn. Tr. KubGTU, 2015, no. 12, pp. 1–10. (In Russian)

6. Karpenko A.P., Shurov D.L. A global optimization hybrid algorithm based on the algorithm of artificial immune system and swarm of particles.  Nauch. Izd. MGTU im. N.E. Baumana. Nauka Obraz., 2012, no. 8, pp. 339–378. doi: 10.7463/0812.0433381. (In Russian)

7. Salakhov M.Kh., Kharintsev S.S.  Matematicheskaya obrabotka i interpretatsiya spektroskopicheskogo eksperimenta  [Mathematical Processing and Interpretation of Spectroscopic Experiment]. Kazan, Kazan. Gos. Univ., 2001. 238 p. (In Russian)

For  citation: Galiakhmetova D.I., Sibgatullin M.E., Galimullin D.Z., Kamalova D.I. Deconvolution of optical spectra distorted by random noise using an artificial immune system. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 1, pp. 72–80. (In Russian)

The content is available under the license Creative Commons Attribution 4.0 License.