A new inverse scattering method is presented to estimate both the boundaries of the rough interface separating air and ground and the object buried beneath this rough interface. This method is based on a state-of-the-art forward solver. Simultaneous reconstruction of surface and object boundaries is posed as a linear least squares optimization problem for a parametric representation of the shape of the object as well as the boundary of the interface with a cost function defined by the misfit of modeled to measured data.
We make use of a newly-developed forward model, the Semi-Analytic Mode-Matching method (SAMM) within the context of the inversion procedure where a moderately low-order superposition of cylindrical modes (in 2-D configuration) satisfying the Helmholtz wave equation are used to represent the scattered fields for the object under the rough surface.
The proposed inverse method is a combined analytical-numerical algorithm to decrease the cost function by optimizing the boundary control parameters in an iterative procedure. The shape of the object as well as the interface is defined in low-dimensional parametric forms. The object boundary is modeled by a B-spline curve which is parameterized by a collection of “control points”. Accuracy and reliability of this method is verified by numerical experiments.