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A hybrid approach is proposed to inspect three-dimensional homogeneous dielectric scatterers by using microwaves. Namely, the considered method consists in two steps: first, the supports of the scatterers are retrieved by the linear sampling method; then the permittivities of the targets are estimated by an ant colony optimization algorithm. The described strategy combines the efficiency of the linear sampling method with the global optimization capabilities of the stochastic procedure. Numerical results assess the capabilities of the approach also in the presence of noise.