Abstract
Two variants of a functional-analytical algorithm intended for solving inverse tomography problems are discussed and numerically carried out. The acoustic fields that are transmitted and received by transducers, which are equivalent to point ones, serve as experimental data. These data are used to calculate the classical or generalized scattering amplitude, and the scatterer characteristics are then reconstructed. The algorithm requires neither model linearization, no iterations for refining the estimates of scatterers, thus making it attractive for solving acoustic-tomography problems in different applications. The results of the numerical reconstruction of inhomogeneities in the sound velocity and absorption in a medium are presented.
Similar content being viewed by others
References
V. V. Goncharov, V. Yu. Zaitsev, V. M. Kurtepov, A. G. Nechaev, and A. I. Khil’ko, Acoustical Tomography of Ocean (IPF RAN, N. Novgorod, 1997) [in Russian].
K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory (Springer-Verlag, Berlin, 1977).
L. D. Faddeev, in Modern Problems of Mathematics, J. Soviet Math. 5, 334 (1976).
R. G. Novikov and G. M. Henkin, Russian Mathem. Survey 42(3), 109 (1987).
V. A. Burov and O. D. Rumyantseva, Sov. Phys.-Acoust. 38, 226 (1992).
V. A. Burov, S. N. Vecherin, S. A. Morozov, and O. D. Rumyantseva, Acoust. Phys. 56, 541 (2010).
P. G. Grinevich and S. V. Manakov, Funct. Anal. Appl. 20, 94 (1986).
R. G. Novikov, Funct. Anal. Appl. 20, 246 (1986).
R. G. Novikov, J. Funct. Anal. 103, 409 (1992).
R. G. Novikov, Phys. Lett. A 238, 73 (1998).
R. G. Novikov, Proc. V. A. Steklov Inst. Math. Solitons, Geometry, Topology-On Crossroads 225, 285 (1999).
V. A. Burov, N. V. Alekseenko, and O. D. Rumyantseva, Acoust. Phys. 55, 843 (2009).
R. G. Novikov, Int. Math. Res. Pap., No. 6, 287 (2005).
R. G. Novikov, J. Geom. Anal. 18, 612 (2008).
N. V. Alekseenko, V. A. Burov, and O. D. Rumyantseva, Acoust. Phys. 54, 407 (2008).
R. G. Novikov, Func. Anal. Appl. 22, 263 (1988).
R. G. Novikov and M. Santacesaria, Int. Mathem. Res. Not. (2012). doi: 10.1093/imrn/rns025
V. A. Burov, A. S. Shurup, O. D. Rumyantseva, and D. I. Zotov, Bull. Russ. Acad. Sci. Phys. 76, 1365 (2012).
V. A. Burov, I. P. Prudnikova, and N. S. Sirotkina, Sov. Phys. Acoust. 38, 555 (1992).
A. I. Nachman, Annals of Math. 128, 531 (1988).
V. A. Burov, O. D. Rumyantseva, and A. V. Saskovets, Moscow Univ. Phys. Bull. 49, 47 (1994).
V. A. Burov and O. D. Rumyantseva, Acoust. Phys. 39,419 (1993).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.A. Burov, A.S. Shurup, D.I. Zotov, O.D. Rumyantseva, 2013, published in Akusticheskii Zhurnal, 2013, Vol. 59, No. 3, pp. 391–407.
Rights and permissions
About this article
Cite this article
Burov, V.A., Shurup, A.S., Zotov, D.I. et al. Simulation of a functional solution to the acoustic tomography problem for data from quasi-point transducers. Acoust. Phys. 59, 345–360 (2013). https://doi.org/10.1134/S1063771013030044
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063771013030044