SIMULTANEOUS RECONSTRUCTION OF APPROXIMATE PROFILES OF AN INHOMOGENEOUS LOSSY MEDIUM THROUGH A COLLOCATION METHOD

In this paper a one-dimensional inverse-scattering problem is consider ed. Two approximate inversion formulae are derived. Using these formul ae, approximate permittivity and conductivity profiles of an inhomogen eous lossy medium are simultaneously generated from the partial knowle dge of the reflection coefficient in the frequency domain. These formu lae are deduced through the application of linear transformations to t wo nonlinear differential equations for the reflection coefficient in the frequency domain. Discrete versions of the inversion formulae are also developed. The transformed equations for the reflection coefficie nt in the frequency domain are applicable irrespective of whether the derivative of the unknown permittivity profile exists. An example to d emonstrate these approximate inversion formulae is given.