Wave–field reciprocity and optimization in remote sensing

Abstract

A unified approach to local optimization techniques and wave–field reciprocity as applied to constructing solutions to remote sensing, imaging and inversion problems in acoustic, elastic and electromagnetic wave theory is presented. The starting point is a system of linear, first–order partial differential equations in space–time of the class to which the indicated wave phenomena gives rise. For this system, three types of remote sensing problems — the inverse–source, the inverse–scattering, and the inverse–transducted–wave–field problems — are formulated, and the construction of their solutions via local optimization techniques is discussed. Emphasis is placed on iterative algorithms that are based on a guaranteed decrease in the mismatch between modelled and observed data at each update of the medium. Subsequently, the wave–field reciprocity theorems of the time–convolution and the time–correlation types are derived and their occurrence in the optimization procedures is discussed. Also, attention is paid to approximate methods, in particular to the Rayleigh–Gans–Born approximation. Approximations of this sort provide the means to invoke the method of preconditioning in the process of inverting the operator equations. ‘Exotic media’ (for example, chiral media in electromagnetics) are included in the analysis.