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

De-noising algorithms based on wavelet thresholding replace smalt wavelet c oefficients by zero and keep or shrink the coefficients with absolute value above the threshold. The optimal threshold minimizes the error of the resu lt as compared to the unknown, exact data. To estimate this optimal thresho ld, we use Generalized Cross Validation. This procedure has linear complexi ty and is fully automatic, i.e., it does not require an estimate for the no ise energy. This gaper uses the method for wavelet transforms that map inte ger gray-scale pixel values to integer wavelet coefficients. An image with artificial noise is used to illustrate the optimality properties of the est imator. Not all theoretical requirements for a successful application of th e method are strictly fulfilled in the integer transform case. However, thi s has little influence on practical results. (C) 1999 American Association of Physicists in Medicine. [S0094-2405(99)00404-6].