Comparison of two different shape descriptions in the half-space inverse problem

The problem of determining the two different shape description of a perfectly conducting cylinder buried in a half-space by the genetic algorithm is investigated. Assume that a cylinder of unknown shape is buried in one half-space and scatters the field incident from another half-space where the scattered field is measured. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. As a result, the shape of the scatterer which is described by using cubic-spline can be reconstructed. In such a case, Fourier series expansion will fail.