Abstract
This paper describes a time-domain method for reconstructing thepermittivity of a two-dimensional object buried in a half-spacefrom knowledge of how the object reflects known incidentradiation. Inspired by the contrast source inversion method formonochromatic waves and multi-frequency waves, we have exploredthe possibilities to formulate the contrast source inversionmethod directly in the time domain. Therefore, first theformulation of the forward problem is sought in terms of aspace-time domain integral equation, and then, for a knownpermittivity, the space-time field solution is obtainediteratively, using a conjugate gradient space-time fast fouriertechnique. This conjugate gradient type of iteration is the keyto arrive at an iterative algorithm for the inverse problem,where in each iteration, both the unknown contrast source andthe unknown permittivity are updated from a minimization of acost functional of two terms, one containing a normalized normof the discrepancies between the modelled scattered field and themeasured scattered field data, and the other containing thenormalized norm of the errors in the satisfaction of thespace-time domain integral equation in the object domain. Somepreliminary numerical results show the effectiveness of thereconstruction algorithms.
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