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Volume 6, Issue 3
Numerical Methods for Non-Smooth $L^1$ Optimization: Applications to Free Surface Flows and Image Denoising

A. Caboussat, R. Glowinski & V. Pons

Int. J. Numer. Anal. Mod., 6 (2009), pp. 355-374.

Published online: 2009-06

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  • 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.

  • Keywords

$L^1$ optimization, over-relaxation algorithm, augmented Lagrangian methods, smoothing, image denoising.

  • AMS Subject Headings

65K10, 65N30, 68U10, 65D10, 93E14

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-355, author = {A. Caboussat, R. Glowinski and V. Pons}, title = {Numerical Methods for Non-Smooth $L^1$ Optimization: Applications to Free Surface Flows and Image Denoising}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {3}, pages = {355--374}, 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/772.html} }
TY - JOUR T1 - Numerical Methods for Non-Smooth $L^1$ Optimization: Applications to Free Surface Flows and Image Denoising AU - A. Caboussat, R. Glowinski & V. Pons 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 -

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.

A. Caboussat, R. Glowinski and V. Pons. (2009). Numerical Methods for Non-Smooth $L^1$ Optimization: Applications to Free Surface Flows and Image Denoising. International Journal of Numerical Analysis and Modeling. 6 (3). 355-374. doi:
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