Abstract
Solving the inverse scattering problem for the Helmholtz wave equation without employing the Born or Rytov approximations is a challenging problem, but some slow iterative methods have been proposed [1, 2], One such method suggested and demonstrated by us is based on solving systems of nonlinear algebraic equations that are derived by applying the method of moments to a sine basis function expansion of the fields and scattering potential [2, 3]. In the past, we have solved these equations for a 2-D object of n by n pixels in a time proportional to n5 [1–3], We now describe further progress in the development of new methods based on FFT convolution and the concept of backprojection [4, 5], which solves these equations in time proportional to n3 • log(n).
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References
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© 1984 Plenum Press, New York
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Johnson, S.A., Zhou, Y., Tracy, M.K., Berggren, M.J., Stenger, F. (1984). Fast Iterative Algorithms for Inverse Scattering Solutions of the Helmholtz and Riccati Wave Equations. In: Kaveh, M., Mueller, R.K., Greenleaf, J.F. (eds) Acoustical Imaging. Acoustical Imaging, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2779-0_7
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DOI: https://doi.org/10.1007/978-1-4613-2779-0_7
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