Acoustical Physics, Vol. 51, No. 4, 2005, pp. 367–375. Translated from AkusticheskiÏ Zhurnal, Vol. 51, No. 4, 2005, pp. 437–446. Original Russian Text Copyright © 2005 by Alekseenko, Burov, Rumyantseva. Solution of the Three-Dimensional Inverse Acoustic Scattering Problem on the Basis of the Novikov–Henkin Algorithm N. V. Alekseenko, V. A. Burov, and O. D. Rumyantseva Moscow State University, Vorob’evy gory, Moscow, 119992 Russia e-mail:
[email protected] Received May 5, 2004 Abstract—A theoretical study of the practical abilities of the Novikov–Henkin algorithm, which is one of the most promising algorithms for solving three-dimensional inverse monochromatic scattering problems by func- tional analysis methods, is carried out. Numerical simulations are performed for model scatterers of different strengths in an approximation simplifying the reconstruction process. The resulting estimates obtained with the approximate algorithm prove to be acceptable for middle-strength scatterers. For stronger scatterers, an ade- quate reconstruction is possible on the basis of a rigorous solution. © 2005 Pleiades Publishing, Inc. METHODS FOR SOLVING INVERSE number of computing operations than in the iteration SCATTERING PROBLEMS methods. The functional analytical methods for solving one- The inverse scattering problem consists in the deter- dimensional inverse scattering problems appeared as mination of the characteristics of a scatterer located in ᑬ early as in the 1950s (Gel’fand, Levitan, Marchenko, a spatial domain and described by a function v(r), and others). The first comprehensive studies of the mul- ∈ ᑬ where r , from the measured scattered field. In the tidimensional inverse scattering problem were carried case of an infinite domain ᑬ, the function v(r) is out by Berezanskii in the 1950s and by Faddeev and assumed to be rapidly decreasing at infinity.