Novel inverse methods in land mine imaging

The imaging of buried land mines continues to present significant signal-processing challenges in the development of inverse methods for the detection of plastic mines buried in soil. To address this difficult problem, recent mathematical advances in the development of the Elliptic Systems Method are used to generate images of the buried land mines. The proposed approach adapts earlier methods, successfully applied in laser tomography of breast tumors using the diffusion equation, to the present problem of land mine imaging using the Helmholtz equation. The images generated by the new method represent electromagnetic properties of underground regions, providing effective differentiation of plastic land mines from surrounding soil. Experimental results are presented to demonstrate the new method. 1 INTRODUCTION The imaging of buried land mines presents significant challenges in the development of effective signal-processing methods for solving the inverse problem posed by measured ground-penetrating radar returns from plastic mines. A successful practical solution of this difficult problem requires a significant technological advance, rather than marginal improvements. To this end, a novel signal-processing approach is proposed where the ground-penetrating radar system is designed to take advantage of the latest mathematical advances in inverse problems, rather than working around limitations of current radar technology[1-3]. These novel mathematical advances enable direct characterization of the electromagnetic properties of the soil (relative dielectric constant and conductivity) from the radar signals. In our previous publications, we developed a new approach for the solution of the integro-differential formulation of the inverse problem for the diffusion equation by using a Galerkin-like method. This novel inverse method has been used to solve similar challenging problems in laser tomography [4,5]. More recently, the authors have been investigating adaptation of these earlier successes to imaging underground land mines, which are characterized by a Helmholtz equation [3]. Usually the solution of a linearized inverse problem for the Helmholtz equation is based on the Born or Ryutov approximation as in [7,8]. Other methods which avoid the Born or Ryutov approximation can be divided into two classes: iterative algorithms based on the integral formulation of inverse problem, or optimization approaches [see 9,10,11,12,13]. Both of these types of methods are time consuming because of the huge conditional number of resulting system, even for a very small number of grid points. Thus, the convergence of these methods becomes too slow, except when one assumes a very simple form for the target (i.e., a cylindrical target in [6]) and …