A new thresholding method in wavelet packet analysis for image de-noising

A novel thresholding function is presented based on the wavelet shrinkage put forward by D. L. Donoho and I. M. Johnstone. This new thresholding method is used in wavelet packet analysis for image de-noising. It has many advantages over DJ's soft- and hard-thresholding function. It is simple in expression and as continuous as the soft-thresholding function, and also overcomes the shortcoming that there is an invariable dispersion between the estimated wavelet coefficients and the decomposed wavelet coefficients of the soft-thresholding method. At the same time, the new thresholding function is more elastic than the soft- and hard- thresholding function. All these advantages make it possible to construct an adaptive de-noising algorithm. Simulation results indicate that the de-noising method adopting the new thresholding function suppresses the Pseudo-Gibbs phenomena near the singularities of the image effectively, and the numerical results also show the new method gives better peak signal-to-noise ratio (PSNR) and mean square error (MSE) than DJ's hard- and soft- thresholding methods.