Multichannel SURE-LET Wavelet Denoising

We extend the denoising approach initially developed for grayscale images, to multichannel (e.g., color) images. A non-redundant---orthonormal---wavelet transform is first applied to the noisy data, followed by the (subband-dependent) thresholding of individual wavelet coefficients which are finally brought back to the image domain by inverse wavelet transform. This wavelet thresholding function is pointwise and depends on the coefficients of same location in the other channels, as well as on their parents in the coarser wavelet subband. Two key ingredients make this approach novel, feasible, and even computationally efficient:

• The quality criterion to optimize is a statistical estimate of the Mean-Squared Error (MSE) of the full denoising process, which depends only on noisy data (Stein's Unbiased Risk Estimate---SURE);
• The thresholding function is parametrized as a linear combination of known elementary multivariate thresholding functions (Linear Expansion of Thresholds---LET).

Thanks to the SURE, no a priori image model is needed to optimize the denoising process, which then merely amounts to solving a linear system of equations in each wavelet subband.

Extensive comparisons with the state-of-the-art multiresolution image denoising algorithms indicate that despite being non-redundant, our algorithm matches the quality of the best redundant approaches, and even outperforms them when the number of channels increases.