Automatic parameter setting for iterative shrinkage methods

Raja Giryes*, Michael Elad, Yonina C. Eldar

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Linear inverse problems are very common in signal and image processing. Algorithms that solve such problems typically involve several unknown parameters that need to be tuned. Here we consider an iterated shrinkage method that is based on the separable surrogate functions (SSF) idea, which exploits the sparsity of the unknown vector in an appropriate representation. The key parameter controlling the algorithm's success is the prior weight, denoted λ. Previous work has addressed the automatic tuning of λ based on a generalized Stein Unbiased Risk Estimator (SURE) of the mean-squared error (MSE). The approach taken was to obtain a constant value of λ that leads to optimized results over a given set of iterations. In this work we also rely on the generalized SURE, and propose an alternative, and highly effective method for tuning λ. Our algorithm chooses λ per iteration, based on the local estimated risk, considering the current iteration and a possible short look-ahead. We demonstrate this method and its superiority over the global approach both in terms of the resulting MSE and the convergence rate. We also show that the proposed scheme serves as a very reliable automatic halting mechanism for the iterative process.

Original languageEnglish
Title of host publication2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008
Pages820-824
Number of pages5
DOIs
StatePublished - 2008
Externally publishedYes
Event2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008 - Eilat, Israel
Duration: 3 Dec 20085 Dec 2008

Publication series

NameIEEE Convention of Electrical and Electronics Engineers in Israel, Proceedings

Conference

Conference2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008
Country/TerritoryIsrael
CityEilat
Period3/12/085/12/08

Keywords

  • Inverse problem
  • Iterated shrinkage
  • Separable surrogate function
  • Stein Unbiased Risk Estimator

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