Time-domain profile inversion using contrast sources

This paper describes a time-domain method for reconstructing the permittivity of a two-dimensional object buried in a half-space from knowledge of how the object reflects known incident radiation. Inspired by the contrast source 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 equation, and then, for a known permittivity, the space-time field solution is obtained iteratively, using a conjugate gradient space-time fast fourier technique. This conjugate gradient type of iteration is the key to arrive at an iterative algorithm for the inverse problem, where in each iteration, both the unknown contrast source and the unknown permittivity are updated from a minimization of a cost functional of two terms, one containing a normalized norm of the discrepancies between the modelled scattered field and the measured 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 effectiveness of the reconstruction algorithms