Globally convergent numerical methods for coefficient inverse problems for imaging inhomogeneities

How can we differentiate between an underground stone and a land mine? We discuss a class of methods for solving such problems. This class of methods concerns globally convergent numerical methods for Coefficient Inverse Problems, unlike conventional locally convergent algorithms. Numerical results are presented modeling imaging of the spatially distributed dielectric permittivity function in an environment where antipersonnel land mines are embedded along with stones. While these results are concerned with the first generation of globally convergent algorithms, images obtained by the most recent second generation are also presented for a generic case of imaging of the dielectric permittivity function. The mathematical apparatus is sketched only very briefly with references to corresponding publications