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SURE-LET Wavelet Denoising

Florian Luisier and Thierry Blu


We introduce a new approach to orthonormal wavelet image denoising. Instead of postulating a statistical model for the wavelet coefficients, we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights. We then minimize an estimate of the mean square error between the clean image and the denoised one.

The key point is that we have at our disposal a very accurate, statistically unbiased, MSE estimate---Stein's Unbiased Risk Estimate (SURE)---that depends on the noisy image alone, not on the clean one. Like the MSE, this estimate is quadratic in the unknown weights and its minimization amounts to solving a linear system of equations. The existence of this a priori estimate makes it unnecessary to devise a specific statistical model for the wavelet coefficients. Instead, and contrary to the custom in the literature, these coefficients are not considered random anymore.

We describe an interscale orthonormal wavelet thresholding algorithm based on this new approach and show its near optimal performance---both regarding quality and CPU requirement---by comparing with the results of three state-of-the-art nonredundant denoising algorithms on a large set of test images. An interesting fallout of this study is the development of a new, group-delay based, parent-child prediction in a wavelet dyadic tree.

Multichannel extension

A multichannel version of the SURE-LET denoising has been developped for color images. An applet for color images is also available.


[1] F. Luisier, T. Blu, M. Unser, "A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding," IEEE Transactions on Image Processing, vol. 16, no. 3, pp. 593-606, March 2007.

Matlab Software

The Matlab code available here is the algorithm described in [1]. This package implements the interscale orthonormal wavelet thresholding algorithm based on the SURE-LET principle. Download the stuffit archive, the tar archive, or the the zip archive. To understand how to use these files, please read the file README.txt or the online help in the routines.

If you have any comments, please feel free to contact: Florian Luisier

Java Applet Demonstration


Conditions of use

You are free to use this software for research purposes, but you should not redistribute it without our consent. In addition, we expect you to include an adequate citation and acknowledgment whenever you present or publish results that are based on it.

© 2022 EPFL • • 11.08.2022