Solving the inverse problem: a model based approach for circular cylindrical structures

The detection of pipes and voids in the ground can be eased significantly by ground penetrating radar systems because even non-metallic objects can be detected and the processing speed is high. In the most applications the ground is scanned with such a system along a straight track and measurement samples are taken at defined spatial increments. An inverse imaging procedure is applied to the data obtained and a ground profile is generated. Our main focus is directed towards the detection of pipes and voids in walls and to resolve their diameters. The objects are assumed to be buried a few centimeters below the surface perpendicular to the chosen scan direction and their dimensions are typically in the region of the far-field imaging resolution limit. Another problem is that large objects appear smaller due to losses in the ground especially if they are buried close to the surface. We propose a two step solution to this task. At first, we solve the inverse problem with a simple and fast migration scheme to find the positions of the buried objects. In the next step we compare the data obtained in the neighborhood of the detected objects with scattered signals we would expect for various cylinders which differ in diameter and surrounding medium. The best correspondence found over all comparisons done gives us an estimate of the diameter and the permittivity of the surrounding material. To generate the scattering data which we store as test functions and recall them later from a database, we developed a two dimensional forward solver. It consists of a hybrid method based on spectral domain methods in conjunction with the analytical solution for the planar waves scattered by dielectric cylindrical objects.