Wavelet tresholding using generalized cross validation
Maarten Jansen, Adhemar Bultheel · Lirias (KU Leuven) · 1997
De-noising algorithms based on wavelet thresholding replace small wavelet coefficients by zero and keep or shrink the coefficients 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 biorthogonal transforms and correlated noise is possible by applying leveldependent thresholds. We also present experiments with integer wavelet transforms, and illustrate the method with some results in image denoising.