TY - JOUR
T1 - The projected GSURE for automatic parameter tuning in iterative shrinkage methods
AU - Giryes, R.
AU - Elad, M.
AU - Eldar, Y. C.
N1 - Funding Information:
This research was partly supported by the European Community’s FP7-FET program, SMALL project, under grant agreement no. 225913, by the ISF grant number 599/08 and by the Israel Science Foundation under Grant no. 1081/07 and by the European Commission in the framework of the FP7 Network of Excellence in Wireless COMmunications NEWCOM++ (contract no. 216715).
PY - 2011/5
Y1 - 2011/5
N2 - 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.
AB - 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.
KW - Inverse problems
KW - Iterated shrinkage
KW - Separable surrogate function
KW - Stein unbiased risk estimator
UR - http://www.scopus.com/inward/record.url?scp=79953103015&partnerID=8YFLogxK
U2 - 10.1016/j.acha.2010.11.005
DO - 10.1016/j.acha.2010.11.005
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AN - SCOPUS:79953103015
SN - 1063-5203
VL - 30
SP - 407
EP - 422
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
IS - 3
ER -