Image de-noising by integer wavelet transforms and generalized cross validation

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 has linear complexity and is fully automatic, i.e., it does not require an estimate for the noise energy. This paper uses the method for wavelet transforms that map integer gray-scale pixel values to integer wavelet coefficients. An image with artificial noise is used to illustrate the optimality properties of the estimator. Not all theoretical requirements for a successful application of the method are strictly fulfilled in the integer transform case. However, this has little influence on practical results.