Accelerating the iterative inverse scattering algorithms by using the fast recursive aggregate T‐matrix algorithm

A review and a convergence analysis of the Born and distorted Born iterative methods are given. The fast recursive aggregate T-matrix algorithm is reviewed and then applied to the solution of the direct scattering part in the iterative inverse scattering algorithms. Together with the conjugate gradient method in the inversion part of the iterative inverse scattering algorithms, the overall computational complexity for the iterative inverse scattering algorithms is reduced from O(N3) to O(N2), representing a significant reduction of their computational complexity. The resulting distorted Born iterative algorithm is demonstrated to have a high-resolution ability of reconstructing one- or two-pixel pulse objects.

[1]  Y. M. Wang,et al.  Limited‐Angle inverse scattering problems and their applications for geophysical explorations , 1990, Int. J. Imaging Syst. Technol..

[2]  Weng Cho Chew,et al.  An efficient algorithm for solution of a scattering problem , 1990 .

[3]  S. Johnson,et al.  Inverse Scattering Solutions by a Sinc Basis, Multiple Source, Moment Method -- Part II: Numerical Evaluations , 1983, Ultrasonic imaging.

[4]  T. J. Cavicchi,et al.  Application of the sinc basis moment method to the reconstruction of infinite circular cylinders , 1986, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[5]  E. Merzbacher.  Quantum mechanics , 1961 .

[6]  A. Devaney,et al.  Nonuniqueness in inverse source and scattering problems , 1982 .

[7]  A. J. Devaney,et al.  Radiating and nonradiating classical current distributions and the fields they generate , 1973 .

[8]  J. Richmond.  Scattering by a dielectric cylinder of arbitrary cross section shape , 1965 .

[9]  R. Taylor,et al.  The Numerical Treatment of Integral Equations , 1978 .

[10]  Weng Cho Chew,et al.  An iterative solution of the two‐dimensional electromagnetic inverse scattering problem , 1989, Int. J. Imaging Syst. Technol..

[11]  W. Chew.  Waves and Fields in Inhomogeneous Media , 1990 .

[12]  William D. O'Brien,et al.  Numerical Study of Higher-Order Diffraction Tomography via the Sinc Basis Moment Method , 1989 .

[13]  Jack K. Cohen,et al.  Nonuniqueness in the inverse source problem in acoustics and electromagnetics , 1975 .

[14]  S. S. Stuchly,et al.  A Solution of Electromagnetic Imaging Using Pseudoinverse Transformation , 1984, IEEE Transactions on Medical Imaging.

[15]  S. Johnson,et al.  Inverse Scattering Solutions by a Sinc Basis, Multiple Source, Moment Method -- Part I: Theory , 1983, Ultrasonic imaging.

[16]  Weng Cho Chew,et al.  Application of the fast recursive algorithm to a large inhomogeneous scatterer for TM polarization , 1991 .

[17]  W. Chew,et al.  Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method. , 1990, IEEE transactions on medical imaging.

[18]  Weng Cho Chew,et al.  A fast algorithm for solution of a scattering problem using a recursive aggregate τ matrix method , 1990 .

[19]  A. Tarantola.  Inverse problem theory : methods for data fitting and model parameter estimation , 1987 .