Optimal SURE Parameters for Sigmoidal Wavelet Shrinkage

A.M. Atto, D. Pastor, G. Mercier

EUSIPCO 2009

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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Outline

Sigmoid-based shrinkage in the wavelet domain (SigShrink)• Shrinkage in the wavelet domain (principle, limitations)• Smooth sigmoid-based shrinkage (SSBS) functions• Experimental results

SURE-based optimization of the SigShrink parameters• The SURE approach (Stein)• Proposition• Experimental results

Conclusion

[Atto, P., Mercier]: « Smooth Adaptation by Sigmoid Shrinkage »: Extended version to appear in EURASIP Journal on Image and Video Processing

[P., Atto]: « Wavelet shrinkage: from sparsity and robust testing to smooth adaptation », Pastor & Atto, to appear in "Fractals and Related Fields", Eds: J. Barral & S. Seuret, Birkhaüser, 2009

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Shrinkage in the wavelet domain (WaveShrink)

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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Shrinkage in the wavelet domain [Donoho & Johnstone, 94]

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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Shrinkage in the wavelet domain [Donoho & Johnstone]

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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Some standard shrinkage functions

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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Smooth sigmoid-based shrinkage (SigShrink)

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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Smooth sigmoid-based shrinkage (SSBS)

functions

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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A.M. Atto, D. Pastor, G. Mercier

Denoised images by SigShrink

Noise std = 35PSNR = 17.2494

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A.M. Atto, D. Pastor, G. Mercier

Sure-based optimization of the SigShrink parameters

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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A.M. Atto, D. Pastor, G. Mercier

Stein’s SURE approach

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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A.M. Atto, D. Pastor, G. Mercier

Proposition

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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A.M. Atto, D. Pastor, G. Mercier

Comparison to SURELET [Luisier, Blu, Unser, 2007]

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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A.M. Atto, D. Pastor, G. Mercier

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Conclusion

SigShrink (Wavelet Shrinkage based on Smooth Sigmoid Based functions)

SURE-Based optimization of the SigShrink parameters Experimental results Pespectives• Improve the SigShrink denoising performance by introducing inter-scale

and/or intra-scale predictors• Comparison to BLS-GSM• Sparsity and level-dependent detection thresholds

- [Atto, P., Mercier]: « Smooth Adaptation by Sigmoid Shrinkage »: Extended version to appear in EURASIP Journal on Image and Video Processing

- [P., Atto]: « Wavelet shrinkage: from sparsity and robust testing to smooth adaptation », Pastor & Atto, to appear in "Fractals and Related Fields", Eds: J. Barral & S. Seuret, Birkhaüser, 2009

Optimal SURE Parameters for SigShrink - EUSIPCO 2009

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A.M. Atto, D. Pastor, G. Mercier

Experimental results

Noise std = 35,

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A.M. Atto, D. Pastor, G. Mercier