Nonsmooth Nonconvex Optimization for Low-Frequency Geosounding Inversion

Abstract

A study of the application of nonconvex regularization operators to the electromagnetic sounding inverse problem is presented. A comparison is presented among three nonconvex regularization algorithms: one smooth usually considered, two nonsmooth, and a convex one, the total variation (TV) operator. One of the nonsmooth nonconvex regularization methods is a novel implementation based on the Legendre–Fenchel transform and the Bregman iterative algorithm. The nonconvex regularization operator is approximated by the convex dual, and the minimization is then implemented considering the equivalence between the Bregman iteration and the augmented Lagrangian methods. The algorithm is simple and provides for better models when applied to synthetic data, than those obtained with TV, and other nonconvex smooth regularizers. Results of the application to field data are also presented, observing that NS2 recovers a model in better agreement with the truth, compared to those obtained with additional magnetometric resistivity data by other researchers.