TY - JOUR
T1 - Numerical Methods for Non-Smooth $L^1$ Optimization: Applications to Free Surface Flows and Image Denoising
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 355
EP - 374
PY - 2009
DA - 2009/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/772.html
KW - $L^1$ optimization, over-relaxation algorithm, augmented Lagrangian methods, smoothing, image denoising.
AB - <p style="text-align: justify;">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.</p>