Multifrequency Bayesian compressive sensing methods for microwave imaging.

The Bayesian retrieval of sparse scatterers under multifrequency transverse magnetic illuminations is addressed. Two innovative imaging strategies are formulated to process the spectral content of microwave scattering data according to either a frequency-hopping multistep scheme or a multifrequency one-shot scheme. To solve the associated inverse problems, customized implementations of single-task and multitask Bayesian compressive sensing are introduced. A set of representative numerical results is discussed to assess the effectiveness and the robustness against the noise of the proposed techniques also in comparison with some state-of-the-art deterministic strategies.

Inverse scattering approach based on the field equivalence principle: inversion without a priori information on incident fields.

An inverse scattering approach based on the field equivalence principle is developed for reconstructing the parameters of the medium of a scattering object. A problem equivalent to the original scattering problem but internal to the measurement surface is set up. The equivalent surface currents determined by the measured total-field data rigorously yield the incident fields in the region under test, so the approach does not require explicit knowledge of the incident fields. Taking into account the fact that the equivalent surface currents produce a null field external to the surface, a functional of the medium's parameters is introduced, and a genetic algorithm is applied to minimization of the functional. Numerical simulations for imaging defects in a known dielectric cylinder from only total-field data measured on an observation surface are performed to illustrate the efficacy of the proposed inversion method.