Wavelet thresholding using generalized cross validation

De-noising algorithms based on wavelet thresholding replace small wavelet coeecients by zero and keep or shrink the coeecients with absolute value above the threshold. The optimal threshold minimizes the error of the result as compared to the unknown, exact data. To estimate this optimal threshold, we use Generalized Cross Validation. This procedure is fast and does not require an estimation for the noise energy. Moreover, the method is shown to be asymptotically optimal. In its original form,this method assumes uncorrelated noise and orthogonal wavelet transforms. It turns out that extension to biorthog-onal transforms and correlated noise is possible by applying level-dependent thresholds. We also present experiments with integer wavelet transforms, and illustrate the method with some results in image de-noising.