Wavelet-based methods for the nonlinear inverse scattering problem using the extended Born approximation
Article first published online: 7 DEC 2012
Copyright 1996 by the American Geophysical Union.
Volume 31, Issue 1, pages 51–65, January-February 1996
How to Cite
1996), Wavelet-based methods for the nonlinear inverse scattering problem using the extended Born approximation, Radio Sci., 31(1), 51–65, doi:10.1029/95RS03130., and (
- Issue published online: 7 DEC 2012
- Article first published online: 7 DEC 2012
- Manuscript Accepted: 11 SEP 1995
- Manuscript Received: 30 MAR 1995
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 (MAP) framework, we introduce the relative Cramér-Rao bound (RCRB) as a tool for analyzing the level of detail in a reconstruction supported by a data set as a function of the physics, the source-receiver geometry, and the nature of our prior information. The MAP estimate is determined using a novel implementation of the Levenberg-Marquardt algorithm in which the RCRB is used to achieve a substantial reduction in the effective dimensionality of the inversion problem with minimal degradation in performance. Additional reduction in complexity is achieved by taking advantage of the sparse structure of the matrices defining the EBA in scale space. An inverse electrical conductivity problem arising in geophysical prospecting applications provides the vehicle for demonstrating the analysis and algorithmic techniques developed in this paper.