Regularization Parameter Selection via L-Curve and Θ-Curve Approaches towards TomoSAR Imaging

Abstract

Nonlinear inverse problems like Synthetic Aperture Radar Tomography are often ill-posed, since their solutions are very sensitive to small perturbations in the input data and are, therefore, difficult to compute numerically. Ill-posed problems are commonly tackled with regularization approaches; however, there is a crucial problem in regularization, related to the selection of regularization parameters. In the search for optimal values of such regularization parameters, this article addresses an extension of the L-curve method, called Θ-curve. Furthermore, aimed at reducing converge time, the k-criterion is added, based on the first and second derivatives of the L-curve.