Wave-¯eld reciprocity and optimization in remote sensing

A uni ed approach to local optimization techniques and wave- eld reciprocity as applied to constructing solutions to remote sensing, imaging and inversion prob-lems in acoustic, elastic and electromagnetic wave theory is presented. The starting point is a system of linear, rst-order partial di¬erential 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- eld 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- eld 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