Inverse Scattering Problems

  1. B. Katsenelenbaum, G. Matviyiv, N. Voitovich. How to find the shape of the body, then its several scattering patterns are known. Proc. of 1995 URSI Int. Symp. on Electromagn. Theory, St.Petersburg, 1995, p.133-135.

    Abstract. The patterns of the field scattered on a body are orthogonal to some function of angles at any illumination, when the frequency is an eigen frequency of inner volume of this body. The function depends only on the body shape and its position. This fact is used for findfinding the shape of the body when several scattering patterns are given but the illuminated fields are unknown. The scalar two-dimensional problems are discussed in the paper. The results of two numerical experiments are given. To find not too complicated body it is sufficient to know about 5-7 patterns.

     

  2. B. Z. Katsenelenbaum, N. N. Voitovich, G. M. Matviyiv. Determination of moving body shape by several patterns of field scattered by it. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-95), Lviv, 1995, p. 56-57 (In Russian).

    Abstract. The paper develops to the case of the moving body the results of the previous work where a method was proposed for calculating the fixed body shape at its resonant frequencies via preparation of a set of scattering patterns on it. The method consists in minimization of a positive functional depending of an auxiliar angular function and the body position. If the minimum is sufficiently small (zero in ideal), then the frequencdy is close to (coincides with) a resonant one and the body shape is close to (coincides with) a zero line of a real field constructed by the above auxiliar function.

  3. B. Z. Katsenelenbaum, G. M. Matviyiv, N. N. Voitovich. Finding the shape of the moving body according to several scattering patterns. 11th Int. Microwave Conf. MIKON-96, Warsaw, 1996, v.2, p. 391-395.

    Abstract. The method proposed above for finding shape of a fixed body is developed and applied to the case when the body is moved. Method's idea and numerical results are presented.

     

  4. A. Golubyatnikov, B. Katsenelenbaum, G. Matviyiv, N. Voitovich. Finding the body shape according to several scattering patterns. Int. Conf. on Operator Theory and its Applications to Science and Industrial Problems (Abstracts), Winnipeg, 1998, p. 47.

  5. M. M. Voitovich, O. V. Kusyi. Body shape restoration by given scattering parrerns. Matematychni Metody i Fizyko-Mekhanichni Polya, v. 46, No.2, 2003, p. 162-170 (in Ukrainian).

    Abstract. A method of body shape reconstruction based on properties of scattering patterns measured at resonant frequency of inner domain is developed. Several approaches to the functional minimization problem are described, numerical experiments on model examples are conducted and their results are analized.

     
  6. M. M. Voitovich, O. V. Kusyi.. Body shape reconstruction by the scattering patterns. Mathematical problems of mechanics of nonhomogeneous structures (Proc.), Lviv, 2003, p. 509-511.

  7. B. Z. Katsenelenbaum, O. V. Kusyi, N. N. Voitovich. Shape reconstruction of uniformly moving body by its scattering patterns. MIKON-2004, Warsaw 2004, v. 2, 529-531.

    Abstract. A method of body shape reconstruction based on properties of scattering patterns measured at resonant frequency of inner domain is developed for the case of uniformly moving body. Numerical results for a two-dimensional model problem concerning the kite-shaped body are presented.

     
  8. O. V. Kusyi, P. Stevrin, N. N. Voitovich, O. F. Zamorska. Reconstruction of irregular waveguide geometry using a moving source. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2004): Proc. of IXth Int. Seminar/Workshop, Lviv-Tbilisi, 2004, p. 121-124.

    Abstract. A method for reconstructing the shape of irregular waveguide is proposed. The method uses amplitudes of the normal modes excited by the point source moving along the irregular part of the waveguide and measured at its output. Mean-square residual of the measured and calculated mode amplitudes integrated over the source path is minimized. Direct problem is solved by the cross-section method. Numerical results concerning a 2D model problem are presented.

     
  9. O. V. Kusyi, N. N. Voitovich. Body shape reconstruction from scattering patterns at resonant frequencies. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2005): Proc. of Xth Int. Seminar/Workshop, Lviv 2005, 145-148.

    Abstract. The paper develops a method of body shape reconstruction based on the property that a set of scattering patterns, measured at a resonant frequency of inner domain, is noncomplete. The method consists in numerical determination of the orthogonal complement function which generates some auxiliary real field, one of zero lines of which is the sought body contour. The variational technique is used. The method is transferred onto the case of uniformly moving body. Numerical results for two-dimensional model problems concerning the pencil- and kite-shaped bodies are presented. They show, in particular, that for reconstruction of complicated shapes the measurements should be made at higher resonant frequencies.

     
  10. O. V. Kusyi, N. N. Voitovich, O. F. Zamorska. Recognition of irregular waveguide geometry using opposite directions technique.. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2006): Proc. of IXth Int. Seminar/Workshop, Tbilisi, Georgia, Lviv-Tbilisi, 2006, p. 17-20.

    Abstract.

     
  11. B. Z. Katsenelenbaum, N. N. Voitovich. Calculation of complex impedance coating for the back scattering minimization. Proc. of XIIth International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory. Lviv, Ukraine, Lviv, 2007, p. 16-19.

    Abstract. A method for decreasing the back scattering from bodies having complex impedance boundaries is developed. A system of nonlinear integral equations is given for determining the impedance distribution which provides minimal back scattering. Numerical results for a model problem of scattering on the infinite circular cylinder are given. Frequency dependencies of scattering at obtained impedance distributions are shown.

     
  12. O. V. Kusyi, N. N. Voitovich. Properties of orthogonal complement fucntions in body shape recostruction problems. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2007): Proc. of XIIth Int. Seminar/Workshop, Lviv, 2007, p. 122-125.

    Abstract. Method for body reconstruction at its resonant frequencies is further investigated. Applicability of the method is numerically confirmed for some cases when the classical Herglotz functions with kernels being orthogonal complement functions to a set of patterns scattered on the body at a resonant frequency of its interior domain, do not exist.

       
  13. M. Voitovich, O. Kusyi. Construction of approximate Herglotz function in inverse scattering problems. Proc. of 2nd Int. Conf. "Modern Problems of Mechanics and Mathematics" , Lviv , 2008, v. 3, p. 16-18 (in Ukrainian).

    Abstract. A method for solving body shape reconstruction problem is presented. It consists in construction of approximate Herglotz functions at resonant frequencies of inner volume of the body. The body boundary is approached by the zero lines of this function.

     
  14. O. V. Kusyi, N. N. Voitovich. Computational aspects of constructing the approximating Herglotz functions in inverse scattering problems. Proc. of XIIIth International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory. Tbilisi, Georgia. Lviv-Tbilisi, 2008, p. 123-133.

    Abstract. Method proposed earlier for body reconstruction at its resonant frequencies is further developed. An attempt is made to establish the connection between the method applicability and existence of the Herglotz functions approximating the eigenoscillation field inside the body. Two propositions are given concerning convergence of the method for two cases when a Herglotz function coinciding with this field exists or not. Numerical results shoving the fast decreasing of the appropriate functional with increasing the number of measured patterns, are presented. Two ways of computer modeling of the input data are numerically compared.

     
  15. Katsenelenbaum B. Z., Voitovich N. N. Reducing the backscattering via complex impedance coating. IEEE Trans. on Antennas and Propagation. 2009, vol. 57, no. 7, p. 2123-2129.  

    Abstract. A method for decreasing the back scattering from bodies having complex impedance boundaries is developed. A system of nonlinear integral equations is given for determining the impedance distribution which provides minimal back scattering. Numerical results for a model problem of scattering on the infinite circular cylinder are given. Frequency dependencies of scattering at obtained impedance distributions are shown.