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ADMM Penalty Parameter Selection with Krylov Subspace Recycling Technique for Sparse Coding

Abstract: 

The alternating direction method of multipliers (ADMM) has been widely used for a very wide variety of imaging inverse problems. One of the disadvantages of this method, however, is the need to select an algorithm parameter, the penalty parameter, that has a significant effect on the rate of convergence of the algorithm. Although a number of heuristic methods have been proposed, as yet there is no general theory providing a good choice of this parameter for all problems. One obvious approach would be to try a number of different parameters at each iteration, proceeding further with the one that delivers the best reduction in functional value, but this would involve a substantial increase in computational cost. We show that, when the forward operator of the inverse problem is represented via a transform operator, requiring iterative methods to solve the main linear system arising in the ADMM solution, it is possible to explore a large range of parameters at marginal additional cost, thus greatly improving the robustness of the method to the choice of penalty parameter.

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Paper Details

Authors:
Youzuo Lin, Brendt Wohlberg, Velimir Vesselinov
Submitted On:
3 October 2017 - 6:45pm
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Brendt Wohlberg
Paper Code:
WQ-L2.4
Document Year:
2017
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[1] Youzuo Lin, Brendt Wohlberg, Velimir Vesselinov, "ADMM Penalty Parameter Selection with Krylov Subspace Recycling Technique for Sparse Coding", IEEE SigPort, 2017. [Online]. Available: http://sigport.org/2254. Accessed: Dec. 16, 2017.
@article{2254-17,
url = {http://sigport.org/2254},
author = {Youzuo Lin; Brendt Wohlberg; Velimir Vesselinov },
publisher = {IEEE SigPort},
title = {ADMM Penalty Parameter Selection with Krylov Subspace Recycling Technique for Sparse Coding},
year = {2017} }
TY - EJOUR
T1 - ADMM Penalty Parameter Selection with Krylov Subspace Recycling Technique for Sparse Coding
AU - Youzuo Lin; Brendt Wohlberg; Velimir Vesselinov
PY - 2017
PB - IEEE SigPort
UR - http://sigport.org/2254
ER -
Youzuo Lin, Brendt Wohlberg, Velimir Vesselinov. (2017). ADMM Penalty Parameter Selection with Krylov Subspace Recycling Technique for Sparse Coding. IEEE SigPort. http://sigport.org/2254
Youzuo Lin, Brendt Wohlberg, Velimir Vesselinov, 2017. ADMM Penalty Parameter Selection with Krylov Subspace Recycling Technique for Sparse Coding. Available at: http://sigport.org/2254.
Youzuo Lin, Brendt Wohlberg, Velimir Vesselinov. (2017). "ADMM Penalty Parameter Selection with Krylov Subspace Recycling Technique for Sparse Coding." Web.
1. Youzuo Lin, Brendt Wohlberg, Velimir Vesselinov. ADMM Penalty Parameter Selection with Krylov Subspace Recycling Technique for Sparse Coding [Internet]. IEEE SigPort; 2017. Available from : http://sigport.org/2254