The projected GSURE for automatic parameter tuning in iterative shrinkage methods

R. Giryes*, M. Elad, Y. C. Eldar

*Corresponding author for this work

Research output: Contribution to journalLetterpeer-review

97 Scopus citations


Linear inverse problems are very common in signal and image processing. Many algorithms that aim at solving such problems include unknown parameters that need tuning. In this work we focus on optimally selecting such parameters in iterative shrinkage methods for image deblurring and image zooming. Our work uses the projected Generalized Stein Unbiased Risk Estimator (GSURE) for determining the threshold value λ and the iterations number K in these algorithms. The proposed parameter selection is shown to handle any degradation operator, including ill-posed and even rectangular ones. This is achieved by using GSURE on the projected expected error. We further propose an efficient greedy parameter setting scheme, that tunes the parameter while iterating without impairing the resulting deblurring performance. Finally, we provide extensive comparisons to conventional methods for parameter selection, showing the superiority of the use of the projected GSURE.

Original languageEnglish
Pages (from-to)407-422
Number of pages16
JournalApplied and Computational Harmonic Analysis
Issue number3
StatePublished - May 2011
Externally publishedYes


FundersFunder number
European Community’s FP7-FET
FP7 Network of Excellence in Wireless COMmunications NEWCOM++
Seventh Framework Programme216715, 225913
European Commission
Israel Science Foundation1081/07, 599/08


    • Inverse problems
    • Iterated shrinkage
    • Separable surrogate function
    • Stein unbiased risk estimator


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