Which Wavelet Bases Are the Best for Image Denoising?

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.