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Augmented Lagrangian without alternating directions: practical algorithms for inverse problems in imaging

Abstract: 

Several problems in signal processing and machine learning can be casted as optimization problems. In many cases, they are of large-scale, nonlinear, have constraints, and nonsmooth in the unknown parameters. There exists plethora of fast algorithms for smooth convex optimization, but these algorithms are not readily applicable to nonsmooth problems, which has led to a considerable amount of research in this direction. In this paper, we propose a general algorithm for nonsmooth bound-constrained convex optimization problems. Our algorithm is instance of the so-called augmented Lagrangian, for which theoretical convergence is well established for convex problems. The proposed algorithm is a blend of superlinearly convergent limited memory quasi-Newton method, and proximal projection operator. The initial promising numerical results for total-variation based image deblurring show that they are as fast as the best existing algorithms in the same class, but with fewer and less sensitive tuning parameters, which makes a huge difference in practice.

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Paper Details

Authors:
Loic Denis, Eric Thiebaut, J-M Becker
Submitted On:
23 February 2016 - 1:38pm
Short Link:
Type:
Poster
Event:
Presenter's Name:
Rahul Mourya

Document Files

draft_ICIP_poster2.pdf

(338 downloads)

Keywords

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[1] Loic Denis, Eric Thiebaut, J-M Becker, "Augmented Lagrangian without alternating directions: practical algorithms for inverse problems in imaging", IEEE SigPort, 2015. [Online]. Available: http://sigport.org/222. Accessed: Aug. 17, 2017.
@article{222-15,
url = {http://sigport.org/222},
author = {Loic Denis; Eric Thiebaut; J-M Becker },
publisher = {IEEE SigPort},
title = {Augmented Lagrangian without alternating directions: practical algorithms for inverse problems in imaging},
year = {2015} }
TY - EJOUR
T1 - Augmented Lagrangian without alternating directions: practical algorithms for inverse problems in imaging
AU - Loic Denis; Eric Thiebaut; J-M Becker
PY - 2015
PB - IEEE SigPort
UR - http://sigport.org/222
ER -
Loic Denis, Eric Thiebaut, J-M Becker. (2015). Augmented Lagrangian without alternating directions: practical algorithms for inverse problems in imaging. IEEE SigPort. http://sigport.org/222
Loic Denis, Eric Thiebaut, J-M Becker, 2015. Augmented Lagrangian without alternating directions: practical algorithms for inverse problems in imaging. Available at: http://sigport.org/222.
Loic Denis, Eric Thiebaut, J-M Becker. (2015). "Augmented Lagrangian without alternating directions: practical algorithms for inverse problems in imaging." Web.
1. Loic Denis, Eric Thiebaut, J-M Becker. Augmented Lagrangian without alternating directions: practical algorithms for inverse problems in imaging [Internet]. IEEE SigPort; 2015. Available from : http://sigport.org/222