Inverse Scattering via Heisenberg's Uncertainty Principle.
YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE
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We present a stable method to recursively linearize the acoustic inverse scattering problem. It turns out that the ill posedness of the problem can be beneficially used to solve it. It means that, due to ill-posedness, not all equations in the nonlinear system are strongly nonlinear, and that when solved recursively in a proper order, they can be reduced to a collection of linear problems. Our method requires solution of a series of forward scattering problems with ascending wave numbers or frequencies. At each frequency, a linear least-squares problem is solved to obtain an approximate forward model which produces the prescribed scattering data. The robustness of the procedure is demonstrated by several numerical examples in the inversion of the Helmholtz equation in two dimensions.