Smoothing Approximations for Least Squares Minimization with L1-Norm Regularization

The paper considers the problem of least squares minimization with L1-norm regularization functional. It investigates various smoothing approximations for the L1-norm functional. It considers Quadratic, Sigmoid and Cubic Hermite functionals. A Tikhonov regularization is then applied to each of the resulting smooth least squares minimization problem. Results of numerical simulations for each smoothing approximation are presented. The results indicate that our regularization method is as good as any other non-smoothing method used in developed solvers.