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SURE-LET Interscale-Intercolor Wavelet Thresholding for Color Image Denoising

F. Luisier, T. Blu

Proceedings of the SPIE Optics and Photonics 2007 Conference on Mathematical Methods: Wavelet XII, San Diego CA, USA, August 26-29, 2007, vol. 6701, pp. 67011H-1/67011H-10.



We propose a new orthonormal wavelet thresholding algorithm for denoising color images that are assumed to be corrupted by additive Gaussian white noise of known intercolor covariance matrix. The proposed wavelet denoiser consists of a linear expansion of thresholding (LET) functions, integrating both the interscale and intercolor dependencies. The linear parameters of the combination are then solved for by minimizing Stein's unbiased risk estimate (SURE), which is nothing but a robust unbiased estimate of the mean squared error (MSE) between the (unknown) noise-free data and the denoised one. Thanks to the quadratic form of this MSE estimate, the parameters optimization simply amounts to solve a linear system of equations.

The experimentations we made over a wide range of noise levels and for a representative set of standard color images have shown that our algorithm yields even slightly better peak signal-to-noise ratios than most state-of-the-art wavelet thresholding procedures, even when the latters are executed in an undecimated wavelet representation.


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