An auto-focus algorithm for imaging of objects under a lossy earth from multi-frequency and multi-monostatic data

The problem of auto-focusing imaging of 2D dielectric objects imbedded in a lossy earth is considered. Under Born approximation, the half-space spectrum Green’s function is employed to formulate the half-space imaging algorithm from multi-frequency and multi-monostatic data. Hence the fast Fourier transform can be used to achieve real-time imaging in a very short computing time. Since the proposed algorithm has avoided the time-consuming regularization of a large-scale ill-posed matrix, the computing time can be greatly cut down. Inspired by the principle of time reversed imaging and the minimum entropy criterion, an auto-focusing imaging algorithm is presented to remove the image degradation caused by estimated error of the unknown dielectric parameters of the earth. Numerical results have shown that the proposed algorithm can provide good quality focused images for both low-contrast and high-contrast targets in a short computing time despite the inaccurate estimation of the earth electric parameters. The proposed algorithm can be extended to three-dimensional case naturally.