Iterative inverse scattering algorithms: Methods of computing Fr{acute e}chet derivatives
- Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6200 (United States)
Iterative approaches to the nonlinear inverse scattering problem generally attempt to find the scattering distribution that best predicts the data by minimizing a global error norm (e.g., the mean-square error) which quantifies the misfit between a set of measured data and data predicted on the basis of a forward calculation. A crucial quantity in this minimization is the Fr{acute e}chet derivative of the error norm which tells us how to update the current estimate of the scattering distribution to reduce the global error at each iteration. This paper demonstrates how to compute the Fr{acute e}chet derivative using three different, but fundamentally equivalent, methods: the conventional adjoint method, the Lagrange multiplier method, and the integral equation method. The first two begin with the wave equation, while the latter method is based on a Lippmann{endash}Schwinger integral equation. These techniques are not only far more efficient, but also numerically less error prone, than {open_quotes}brute force{close_quotes} methods for computing derivatives based, for example, on finite differences. For simplicity, a variational approach is employed in which the fields and scattering distribution are represented by continuous functions, but the finite-dimensional (discretized) problem is shown to follow directly from the continuous-space results. {copyright} {ital 1999 Acoustical Society of America.}
- OSTI ID:
- 692548
- Journal Information:
- Journal of the Acoustical Society of America, Journal Name: Journal of the Acoustical Society of America Journal Issue: 5 Vol. 106; ISSN 0001-4966; ISSN JASMAN
- Country of Publication:
- United States
- Language:
- English
Similar Records
A general nonlinear inverse transport algorithm using forward and adjoint flux computations
A convergent finite difference scheme for the Navier-Stokes equations of nonisentropic compressible fluid flow