Using the adjoint method for solving the nonlinear GPR inverse problem

Abstract

In order to extract accurate quantitative information out of Ground Penetrating Radar (GPR) measurement data, one needs to solve a nonlinear inverse problem. In this paper we reformulate this into a nonlinear least squares problem which is non convex. Solving a non-convex optimization problem requires a good initial estimation of the optimal solution. In this paper we use a three step method to solve the just described non-convex problem. In a first step the qualitative solution of the linearized problem is found to obtain the detection and support of the subsurface scatterers. For this first step Synthetic Aperture Radar (SAR) and MUltiple SIgnal Classification (MUSIC) are proposed and compared. The second step consists out of a qualitative solution of the linearized problem to obtain a first guess for the material parameter values of the detected objects. The method proposed for this is Algebraic Reconstruction Theorem (ART), which is an iterative method, starting from the initial value, given by the first step, and improving on this until an optimum is achieved. The final step then consists out of the solution of the nonlinear inverse problem using a variational method. The paper starts with a discussion of the GPR inverse problem and continues with a short description of the used methods (SAR, MUSIC, ART and adjoint method). Finally an example is given based on simulated data and some conclusions are drawn.