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


Bayram I.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, vol.64, no.6, pp.1597-1608, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64 Issue: 6
  • Publication Date: 2016
  • Doi Number: 10.1109/tsp.2015.2502551
  • Journal Name: IEEE TRANSACTIONS ON SIGNAL PROCESSING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1597-1608
  • Istanbul Technical University Affiliated: No

Abstract

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.