Tomographic imaging via non-linear estimation: a bilinear approach

A non-linear estimation approach to reconstructing the space-varying permittivity profile of unknown objects is considered. It is shown that the equations governing the scattering are described by a bilinear model, and can be approximated into finite dimensional spaces on the basis of the finite degrees of freedom of data, and that one can not expect to reconstruct an arbitrary function from a finite number of independent equations. As a consequence, a discrete model, well suited to numerical inversion, can be developed. The bilinear nature of the equations, and the suitable choice of the unknowns allow for the functional adopted in the estimation to be minimized in an accurate manner. Numerical experiments validate the effectiveness of the proposed approach