Informatics and Applications
2016, Volume 10, Issue 3, pp 46-54
PRECISION ANALYSIS OF WAVELET PROCESSING OF AERODYNAMIC FLOW PATTERNS
- T. V. Zakharova
- O.V. Shestakov
Abstract
This paper is devoted to a new method of aerodynamic flow pattern processing based on the wavelet analysis. Wavelet thresholding techniques are widely used in signal and image processing. These methods are easily implemented through fast algorithms; so, they are very appealing in practical situations. Besides, they adapt to function classes with different amounts of smoothness in different locations more effectively than the usual linear methods. Wavelet thresholding risk analysis is an important practical task, because it allows determining the quality of the techniques themselves and the equipment which is being used. Comparative analysis using the discriminant method was carried out to verify the new method. The empirical estimated error of processing is consistent with theoretical results for this estimate.
[+] References (15)
- Holder, D. W, and R. J. North. 1963. Schlieren methods. National Physics Laboratory. Notes on applied science No. 31. London: H.M.S.O. 106 p.
- Krasnov, N. F. 2010. Aerodinamika. T. 2: Metody aerodinamicheskogo rascheta [Aerodynamics. Vol. 2: The aero-dynamic calculation methods]. 4th ed. Moscow: Vysshaya Shkola. 416 p.
- Smolentsev, N. K. 2008. Osnovy teorii veyvletov Veyvlety v Matlab [Foundations of the theory of wavelets. Wavelets in Matlab]. Moscow: DMK Press. 448 p.
- Zakharova, T V., and O. V. Shestakov. 2012. Veyvlet-analiz i ego prilozheniya [Wavelet analysis and its applications]. 2nded. Moscow: INFRA-M. 157 p.
- Boggess, A., and F A. Narkovich. 2001. A first course in wavelets with Fourier analysis. Prentice Hall. 293 p.
- Mallat, S. 1999. Wavelet tour of signal processing. Elsevier. 661 p.
- Donoho, D., and I. Johnstone. 1994. Ideal spatial adaptation via wavelet shrinkage. Biometrika 81:425-455.
- Donoho, D., and I. Johnstone. 1995. Adapting to unknown smoothness via wavelet shrinkage. J. Am. Statist. Assoc. 90:1200-1224.
- Markin, A. V. 2009. Predel'noe raspredelenie otsenki riska pri porogovoy obrabotke veyvlet-koeffitsientov [Limit dis-tribution of risk estimate of wavelet coefficient thresh-olding]. Informatika i ee Primeneniya - Inform. Appl. 3(4):57-63.
- Markin, A. V., and O. V. Shestakov. 2010. O sostoyatel'nosti otsenki riska pri porogovoy obrabotke veyvlet-
koefficientov [Consistency of risk estimation with thresholding of wavelet coefficients]. Vestn. Mosk. un-ta. Ser. 15. Vychisl. matem. i kibern. [Moscow University Computa-tional Mathematics and Cybernetics] 1:26-34.
- Zakharova, T.V., and M.V. Berezentsev. 2004. About a method of supervision classification in the decision of aerodinamic problems. 24th Seminar (International) on Stability Problems for Stochastic Models Transactions. Riga: TTI. 353-356.
- Zakharova, TV. 2005. Metod raspoznavaniya dlya vosstanovleniya izobrazheniy tsvetnykh tenevykh kartin [Recognition method for recovery of nonferrous shadow paintings images]. Obozrenie Prikladnoy i Promyshlennoy Matematiki [Review of Applied and Industrial Mathemat-ics] 12(4):967-968.
- Zakharova, TV, and E.A. Shagirov. 2013. Oprede- lenie plotnosti aerodinamicheskogo potoka obtekaniya metodom tsvetovoy fil'tratsii [Density determination of aerodynamic flow color flow filtration method]. Matematicheskoe modelirovanie [Mathematical Modeling] 25(12):103-109.
- Zakharova, T. V, and E.A. Shagirov. 2013. Optimizatsiya metoda tsvetovoy fil'tratsii dlya resheniya zadach aero- dinamiki [Optimization of the color filter method for solving the problems of aerodynamics]. Obozrenie Prikladnoy i Promyshlennoy Matematiki [Review of Applied and Industrial Mathematics] 20(4):545-548.
- Zakharova, TV, and O.V Shestakov. Appendix to the paper "Precision analysis of wavelet processing of aerodynamic flow patterns." Available at: http://www.ipiran.ru/publications/pictures.pdf (accessed August 29, 2016).
[+] About this article
Title
PRECISION ANALYSIS OF WAVELET PROCESSING OF AERODYNAMIC FLOW PATTERNS
Journal
Informatics and Applications
2016, Volume 10, Issue 3, pp 46-54
Cover Date
2016-08-30
DOI
10.14357/19922264160307
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelet analysis; thresholding; unbiased risk estimate; aerodynamic flow
Authors
T. V. Zakharova  ,  and O.V. Shestakov ,
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center “Computer Sciences and Control” of the Russian
Academy of Sciences, 44-2 Vavilov Str.,Moscow 119333, Russian Federation
|