ujm-01122878
https://ujm.hal.science/ujm-01122878
https://ujm.hal.science/ujm-01122878/document
https://ujm.hal.science/ujm-01122878/file/388-Bt3f-151.pdf
[UNIV-ST-ETIENNE] Université Jean Monnet - Saint-Etienne
[ENS-LYON] École Normale Supérieure de Lyon
[INSU] INSU - Institut National des Sciences de l'Univers
[IOGS] Institut d'Optique Graduate School
[CNRS] CNRS - Centre national de la recherche scientifique
[UNIV-LYON1] Université Claude Bernard - Lyon I
[LAHC] LAboratoire Hubert Curien
[PARISTECH] ParisTech
[CRAL] Centre de Recherche Astrophysique de Lyon
[UDL] UDL
[UNIV-LYON] Université de Lyon
AUGMENTED LAGRANGIAN WITHOUT ALTERNATING DIRECTIONS: PRACTICAL ALGORITHMS FOR INVERSE PROBLEMS IN IMAGING
Mourya, Rahul
Denis, Loic
Thiébaut, Éric
Becker, Jean-Marie
[SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing
[PHYS.PHYS.PHYS-OPTICS] Physics [physics]/Physics [physics]/Optics [physics.optics]
COMM
total variation
deblurring
proximal operator
ADMM
hierarchical optimization
non-smooth optimization
Index Terms— Constrained convex optimization
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 may be 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.
2015-09
2015-03-04
en
IEEE International Conference on Image Processing (ICIP)
Quebec, Canada