On the Convergence of the Iterative Shrinkage/Thresholding Algorithm With a Weakly Convex Penalty

We consider the iterative shrinkage/thresholding algorithm (ISTA) applied to a cost function composed of a data fidelity term and a penalty term. The penalty is nonconvex but the concavity of the penalty is accounted for by the data fidelity term so that the overall cost function is convex. We provi...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 64; no. 6; pp. 1597 - 1608
Main Author: Bayram, Ilker
Format: Journal Article
Language:English
Published: New York IEEE 15.03.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Acceleration
Convergence
Convex functions
Cost function
Forward backward splitting
Iterative algorithms
iterative shrinkage/thresholding
majorization minimization
Minimization
Signal processing algorithms
weakly convex
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:We consider the iterative shrinkage/thresholding algorithm (ISTA) applied to a cost function composed of a data fidelity term and a penalty term. The penalty is nonconvex but the concavity of the penalty is accounted for by the data fidelity term so that the overall cost function is convex. We provide a generalization of the convergence result for ISTA viewed as a forward-backward splitting algorithm. We also demonstrate experimentally that for the current setup, using large stepsizes in ISTA can accelerate convergence more than existing schemes proposed for the convex case, like TwIST or FISTA.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2015.2502551