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The problem of imaging of 2-D dielectric objects embedded in a lossy earth is considered with unknown permittivity and conductivity of the lossy background. Under Born approximation, the spectral form of the Green's function in half-space is employed to formulate the half-space imaging algorithm with multi-frequency and multi-monostatic data. Hence the fast Fourier transform can be used to achieve real-time imaging in a very short computation time. Inspired by the principle of time reversed imaging, a refocusing time factor has been introduced into the refocusing formulation. The optimal focusing time can be determined according to minimum entropy criterion. At the optimal focusing time a satisfactory image can be obtained regardless of the unknown characteristics of the earth. Numerical results have shown that the proposed algorithm can provide a high quality focused image in a short time despite the inaccurate estimation of earth electric parameters.

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