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
We use a comprehensive set of non-redundant orthogonal wavelet transforms and apply a denoising method called <i>SUREshrink</i> 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.