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


Numerical methods for non-smooth L^1 optimization: applications to free surface flows and image denoising

Alexandre Caboussat 1, Roland Glowinski 1, Victoria Pons 1

1 Department of Mathematics, University of Houston, 4800 Calhoun Rd, Houston, TX 77204-3008, USA.

Received by the editors October 30, 2008 and, in revised form, January 5, 2009.
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.

AMS subject classifications: 65K10, 65N30, 68U10, 65D10, 93E14
Key words: L^1 optimization, over-relaxation algorithm, augmented Lagrangian methods, smoothing, image denoising.
Email: caboussat@math.uh.edu, roland@math.uh.edu, vpons@math.uh.edu
 

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