An optimization algorithm for reconstructing permittivity distributions of stratified media in time domain measurements

Reconstruction of permittivity distributions of stratified media or buried objects is a very important problem in relation to practical applications such as ground penetrating radar, geophysical sensing, nondestructive testing, and so on. Considering an underground survey, the authors propose a novel algorithm for reconstructing permittivity distributions of stratified media from measurements of back-scattering responses of a pulsed wave. The reconstruction algorithm is based on an iterative procedure of matching the measured response with the response calculated on a certain distribution of the permittivity. The authors employ the same finite-difference time-domain code to obtain both measured and calculated data. In their algorithm, the authors expand the distribution function of the permittivity in terms of rectangular pulse functions, and hence the inverse problem is reduced to the optimization problem for the expansion coefficients. As a numerical example, the authors apply this algorithm to the reconstruction of a lossless dielectric slab and consider the validity of the algorithm