A Recursive Born Approach to Nonlinear Inverse Scattering

A Bayesian approach for nonlinear inverse scattering tomographic imaging

Inverse scattering as nonlinear tomography

Abstract. The reconstruction problem for the acoustic tomography with non-homogeneous background is discussed. We develop a method of beamlike solutions of a Helmholtz equation which is not sensitive to caustics. For small perturbations of the speed the inverse scattering problem is reduced to inversion of a ray integral transform. An explicit formula is given for beam-like solutions in a homog...

Linear and Nonlinear Inverse Scattering

In this paper we discuss one dimensional scattering and inverse scattering for the Helmholtz equation on the half line from the point of view of the layer stripping. By full or nonlinear scattering, we mean the transformation between the index of refraction (actually half of its logarithmic derivative) and the reflection coefficient. We refer to this mapping as nonlinear scattering, because the...

Wavelet-based methods for the nonlinear inverse scattering problem using the extended Born approximation

In this paper, we present an approach to the nonlinear inverse scattering problem using the extended Born approximation (EBA) on the basis of methods from the fields of multiscale and statistical signal processing. By posing the problem directly in the wavelet transform domain, regularization is provided through the use of a multiscale prior statistical model. Using the maximum a posteriori (MA...

Geometrical Approach to Inverse Scattering forthe Dirac

The high-energy-limit of the scattering operator for multidimensional relativistic dynamics, including a Dirac particle in an electromagnetic eld, is investigated by using time-dependent, geometrical methods. This yields a reconstruction formula, by which the eld can be obtained uniquely from scattering data.