Time-domain profile inversion using contrast sources

This paper describes a time-domain method fur reconstructing the permittivi ty of a two-dimensional object buried in a half-space from knowledge of how the object reflects known incident radiation. Inspired by the contrast sou rce inversion method for monochromatic waves and multi-frequency waves, we have explored the possibilities to formulate the contrast source inversion method directly in the time domain. Therefore, first the formulation of the forward problem is sought in terms of a space-time domain integral equatio n, and then. for a known permittivity, the space-time field solution is obt ained iteratively using a conjugate gradient space-time fast fourier techni que. This conjugate gradient type of iteration is the key to arrive at an i terative algorithm for the inverse problem, where in each iteration, both t he unknown contrast source and the unknown permittivity art: updated from a minimization of a cost functional of two terms, one containing a normalize d norm of the discrepancies between the modelled scattered held and the mea sured scattered field data, and the other containing the normalized norm of the errors in the satisfaction of the space-time domain integral equation in the object domain. Some preliminary numerical results show the effective ness of the reconstruction algorithms.