Self-adaptive selection of the regularization parameter for electromagnetic imaging

Regularization techniques are necessarily used for a numerical solution of inverse problems associated with various electromagnetic imaging methods. A proper regularization parameter involved in these techniques is determined by trial and error, which requires a substantial computation time and thus constitutes a major difficulty in obtaining an efficient solution. Based on the Levenberg-Marquardt scheme, this paper presents a simple way for selecting this parameter in the case of the widely used Tikhonov regularization technique. The initial regularization parameter necessary to start the algorithm is determined by considering a stochastic reformulation associated with the inverse problems. The efficiency of the algorithm presented is illustrated by applying it to the Born iterative method for reconstructing a cylindrical dielectric profile.