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Numerical Methods for Non-Smooth L1 Optimization: Applications to Free Surface Flows and Image Denoising

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

Year:    2009

International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 3 : pp. 355–374

Abstract

Non-smooth optimization problems based on L1 norms are investigated for smoothing of signals with noise or functions with sharp gradients. The use of L1 norms allows to reduce the blurring introduced by methods based on L2 norms. Numerical methods based on over-relaxation and augmented Lagrangian algorithms are proposed. Applications to free surface flows and image denoising are presented.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2009-IJNAM-772

International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 3 : pp. 355–374

Published online:    2009-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    L1 optimization over-relaxation algorithm augmented Lagrangian methods smoothing image denoising.