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Which Wavelet Bases Are the Best for Image Denoising?

F. Luisier, T. Blu, B. Forster, M. Unser

Proceedings of the SPIE Optics and Photonics 2005 Conference on Mathematical Methods: Wavelet XI, San Diego CA, USA, July 31-August 3, 2005, vol. 5914, pp. 59140E-1/59140E-12.


We use a comprehensive set of non-redundant orthogonal wavelet transforms and apply a denoising method called SUREshrink in each individual wavelet subband to denoise images corrupted by additive Gaussian white noise. We show that, for various images and a wide range of input noise levels, the orthogonal fractional (α, τ)-B-splines give the best peak signal-to-noise ratio (PSNR), as compared to standard wavelet bases (Daubechies wavelets, symlets and coiflets). Moreover, the selection of the best set (α, τ) can be performed on the MSE estimate (SURE) itself, not on the actual MSE (Oracle).

Finally, the use of complex-valued fractional B-splines leads to even more significant improvements; they also outperform the complex Daubechies wavelets.

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AUTHOR="Luisier, F. and Blu, T. and Forster, B. and Unser, M.",
TITLE="Which Wavelet Bases Are the Best for Image Denoising?",
BOOKTITLE="Proceedings of the {SPIE} Conference on Mathematical Imaging:
	{W}avelet {XI}",
YEAR="2005",
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volume="5914",
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pages="59140E-1--59140E-12",
address="San Diego CA, USA",
month="July 31-August 3,",
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© 2005 SPIE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from SPIE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
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