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Reconstruction of the shape of echo-sounded objects

  • Acoustic Signal Processing and Computer Simulation
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Abstract

The paper considers the problem of reconstructing the shape of echo-sounded objects under conditions when the well-known methods, e.g., the Boyarskii method, are inapplicable or inefficient. A variant of the method is proposed for reconstructing the shape of an object using the function from the Gaussian curvature of the surface. As well, it is shown that the main information on this function is carried by the initial region of the echo signal and that the results of reconstructing the shape depend on the correlation duration of probing signals. When ultra-wideband probing signals are applied, this method is fundamentally suitable for reconstructing the shape of silt-covered objects. Formally, the method is applicable only for convex surfaces, but it can be expanded to more complex surfaces under certain conditions.

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References

  1. D. Colton, and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, New York, 1984; Mir, Moscow, 1987).

    Google Scholar 

  2. A. N. Tikhonov, and A. A. Samarskii, Equations of Mathematical Physics (Nauka, Moscow, 1977), [in Russian].

    Google Scholar 

  3. V. A. Burov, A. A. Goryunov, A. V. Saskovets, and T. A. Tikhonova, Akust. Zh. 32, 433 (1986).

    MathSciNet  ADS  Google Scholar 

  4. A. A. Luchin, Zarubezhn. Radioelektr., No. 8, 30 (1999).

    Google Scholar 

  5. N. N. Bojarski, IEEE Trans. Adv. Packing 30, 980 (1982).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  6. I. N. Troitskii, Statistical Theory of Tomography (Radio Svyaz’, Moscow, 1989) [in Russian].

    Google Scholar 

  7. V. A. Burov, S. N. Sergeev, and A. S. Shurup, Acoust. Phys. 57, 344 (2011).

    Article  ADS  Google Scholar 

  8. V. A. Burov, A. S. Shurup, D. I. Zotov, and O. D. Rumyantseva, Acoust. Phys. 59, 345 (2013).

    Article  ADS  Google Scholar 

  9. V. V. Goncharov, V. N. Ivanov, O. Yu. Kochetov, B. F. Kur’yanov, and A. N. Serebryanyi, Acoust. Phys. 58, 562 (2012).

    Article  ADS  Google Scholar 

  10. V. V. Goncharov, Yu. A. Chepurin, and O. A. Godin, Acoust. Phys. 59, 170 (2013).

    Article  ADS  Google Scholar 

  11. A. S. Il’inskii, V. V. Kravtsov, and A. G. Sveshnikov, Mathematical Models of Electrodynamics (Vysshaya Shkola, Moscow, 1991) [in Russian].

    Google Scholar 

  12. I. Ya. Bakel’man, A. L. Verner, and B. E. Kantor, Introduction in Differential Geometry “as a whole” (Nauka, Moscow, 1973) [in Russian].

    Google Scholar 

  13. A. D. Aleksandrov and N. Yu. Netsvetaev, Geometry. A Tutorial (Nauka, Moscow, 1990) [in Russian].

    Google Scholar 

  14. E. L. Shenderov, Sound Radiation and Dispersion (Sudostroenie, Leningrad, 1989) [in Russian].

    Google Scholar 

  15. Radioelectronic Systems. Foundations of Construction and Theory. An Handbook, Ed. by Ya. D. Shirman (Radiotekhnika, Moscow, 2007), [in Russian].

    Google Scholar 

  16. M. V. Fedoryuk, Asymptotic. Integrals and Rows (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  17. A. A. Kharkevich, Spectra and Analysis (Fizmatgiz, Moscow, 1962) [in Russian].

    Google Scholar 

  18. L. E. Franks, Signal Theory (Prentice Hall, 1968; Sov. Radio, Moscow, 1974).

    Google Scholar 

  19. Ya. I. Khurgin and V. P. Yakovlev, Finite Functions in Physics and Technics (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

  20. F. G. Friedlander, Sound Pulses (Cambridge University Press, Cambridge, 1958; IIL, Moscow, 1962).

    MATH  Google Scholar 

  21. A. V. Pogorelov, Minkovskii’s Multidimensional Model (Nauka, Moscow, 1975) [in Russian].

    Google Scholar 

  22. A. Majda, Commun. Pure Appl. Math. 30, 165 (1977).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  23. A. V. Pogorelov, Monzy-Amper Multidimensional Equation (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  24. G. M. Makhonin, I. I. Markovich, G. L. Chernikhovskaya, and V. Yu. Doroshenko, in Proc. Sci. Conf. “Sess. Sci. Counsel Russ. Acad. Sci. on Acoustics and 14th Sess. Russ. Acoust. Soc.,” vol. 2 (GEOS, Moscow, 2011), p. 225.

    Google Scholar 

  25. Yu. O. Pokrovskii and G. L. Chernikhovskaya, in Proc. 7th Int. Conf. “Applied Technologies of Hydroacoustics and Hydrophysics, Application to Scient.-Techn. Coll. Papers “Hydroacoustics,” (FGUP TsNII, “Morfizpribor”, St. Petersburg), 2004.

    Google Scholar 

  26. G. M. Makhonin and G. L. Chernikhovskaya, in Proc. 18th Sess. Russ. Acoust. Soc. (GEOS, Moscow, 2006), p. 18.

    Google Scholar 

  27. V. N. Matvienko and Yu. F. Tarasyuk, Operating Range of Hydroacoustical Devices (Sudostroenie, Leningrad, 1981) [in Russian].

    Google Scholar 

  28. V. I. Smirnov, Course of College Mathematics (Nauka, Moscow, 1974), Part 1.

    Google Scholar 

  29. A. D. Polyanin and A. V. Manzhirov, Integral Equations. An Handbook (Fizmatlit, Moscow, 2003) [in Russian].

    Google Scholar 

  30. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems (Nauka, Moscow, 1986), [in Russian].

    Google Scholar 

  31. G. M. Makhonin, V. P. Fedosov, and G. L. Chernikhovskaya, Radiotekhnika, No. 2, 90 (2006).

    Google Scholar 

  32. N. V. Nair, B. Shanker, and L. Kempel, J. Acoust. Soc. Am. 132, 1261 (2012).

    Article  ADS  Google Scholar 

  33. A. V. Pogorelov, External Geometry of Convex Surfaces (Fizmatgiz, Moscow, 1969) [in Russian].

    Google Scholar 

  34. A. F. Toth, Lagerungen in der Ebene auf der Kugel und in Raum (Springer-Verlag, Berlin, 1953; Fizmatgiz, Moscow, 1958).

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Southern Federal University, ul. Bol’shaya Sadovaya 105/42, Rostov-on-Don, 344006, Russia

    G. M. Makhonin

  2. Scientific Design Bureau for Digital Signal Processing, ul. Shevchenko 2, Taganrog, 347922, Russia

    G. M. Makhonin

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  1. G. M. Makhonin
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Correspondence to G. M. Makhonin.

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Original Russian Text © G.M. Makhonin, 2014, published in Akusticheskii Zhurnal, 2014, Vol. 60, No. 5, pp. 546–554.

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Makhonin, G.M. Reconstruction of the shape of echo-sounded objects. Acoust. Phys. 60, 588–596 (2014). https://doi.org/10.1134/S106377101405008X

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  • DOI: https://doi.org/10.1134/S106377101405008X

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