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Application of polynomial cellular neural networks in diagnosis of astrometric chromaticity. (English) Zbl 1201.85005
Summary: Minimization of the chromatic error in the data reduction pipeline of the Gaia mission is presented by applying polynomial cellular neural networks (PCNN). We introduce generalized PCNN model which enables us to solve the nonlinear approximation task. The advantage of the newly proposed method is in solving large-size image processing problem of diagnosis of astrometric chromaticity in real time. Rigorous stability analysis of the PCNN is presented by using the method of Lyapunov’s finite majorizing equations. The simulation results show a linear relation between the output of the proposed PCNN model and the chromaticity values as the target data.

MSC:
85A04 General questions in astronomy and astrophysics
34A33 Ordinary lattice differential equations
34D20 Stability of solutions to ordinary differential equations
68T05 Learning and adaptive systems in artificial intelligence
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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[1] D. Pourbaix, Chromatic effects in Hipparcos parallaxes and implications for distance scale, in: IAU Colloqium 196: D.W. Kurtz (Ed.), Transits of Venus: New Views of the Solar System and Galaxy, 2005, pp. 377-385.
[2] Bazarghan, M.; Gupta, R., Automated classification of sloan digital sky survey (SDSS) stellar spectra using artificial neural networks, Astrophys. space sci., 315, 201-210, (2008)
[3] Gai, M.; Cancelliere, R., Neural network correction of astrometric chromaticity, Mon. not. R. astron. soc., 362, 4, 1483-1488, (2005)
[4] M.A.C. Perryman et al., GAIA - composition, formation and evolution of the galaxy, Concept and technology study, Report and Execution, Summary, ESA-SCI ,vol. 4, European Space Agency, Munich, Germany, 2000.
[5] Loyd-Hart, M.; Wizinowich, P.; McLeod, B.; Wittman, D.; Colucci, D.; Dekany, R.; McCarthy, D.; Angel, J.R.P.; Sandler, D., First results of an on-line adaptive optics system with atmospheric wavefront sensing by an artificial neural network, Astrophys. J., 390, L41-44, (1992)
[6] Wizinowich, P.; Loyd-Hart, M.; Angel, R., Adaptive optics for array telescopes using neural networks techniques on transputers, (), 170-183
[7] Chua, L.O.; Yang, L., CNN: theory, IEEE trans. circuits syst., 35, 1257-1272, (1988) · Zbl 0663.94022
[8] Chua, L.O.; Yang, L., CNN: applications, IEEE trans. circuits syst., 35, 1273-1299, (1988)
[9] Slavova, A.; Markova, M., Polynomial lotka – volterra CNN model: dynamics and complexity, C.R. acad. sci. bulg., 60, 12, 1271-1276, (2007) · Zbl 1174.34041
[10] Slavova, A.; Zecca, P., Complex behaviour of polynomial fitzhugh – nagumo CNN model, Nonlinear anal. real world appl., 8, 4, 1331-1340, (2007) · Zbl 1116.35066
[11] M.Laiho, A.Paasio, K.Halonen, Structure of a CNN with linear and second order polynomial feedback terms, in: Proceedings of IEEE CNNA’2000, Catania, 2000, pp. 401-406.
[12] R. Tetzlaff, F. Gollas, Modeling complex systems by reaction – diffusion cellular nonlinear networks with polynomial weight-functions, in: Proceedings of IEEE CNNA, 2005.
[13] Born, M.; Wolf, E., Principles of optics, (1985), Pergamon New York
[14] Gai, M.; Busonero, D.; Loreggia, D.; Gardiol, D.; Lattanzi, M.G., Chromaticity in all-reflective telescopes for astrometry, Astron. astrophys., (2004)
[15] Cancelliere, R.; Gai, M., A comparative analysis of neural network performances in astronomy imaging, Appl. numer. math., 45, 1, 87-98, (2003) · Zbl 1019.85001
[16] Cancelliere, R.; Slavova, A., Dynamics and stability of generalizded cellular neural network model, Appl. math. comp., 165, 1, 127-136, (2005) · Zbl 1062.92003
[17] Grebenikov, E.A.; Ryabov, Yu.A., Constructive methods in the analysis of nonlinear systems, (1979), Mir Publisher Moscow, English translation · Zbl 0466.65041
[18] Lyapunov, A.M., General problem about the stability of motion, (1950), Gostekhizdat Moscow, Russia · Zbl 0041.32204
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