Numerical Methods for Non-Smooth $L^1$ Optimization: Applications to Free Surface Flows and Image Denoising

Abstract

Non-smooth optimization problems based on $L^1$ norms are investigated for smoothing of signals with noise or functions with sharp gradients. The use of $L^1$ norms allows to reduce the blurring introduced by methods based on $L^2$ norms. Numerical methods based on over-relaxation and augmented Lagrangian algorithms are proposed. Applications to free surface flows and image denoising are presented.