Abstract: A novel thresholding function is presented based on the wavelet shrinkage put forward by D.L.Donoho and I.M.Johnstone. This new thresholding function 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 has a high order derivative which makes convenient some kinds of mathematical disposals. It also overcomes the shortcoming that there is an invariable dispersion between the estimated wavelet coefficients and the decomposed wavelet coefficients of the soft-thresholding function. All these advantages make it possible to construct an adaptive denoising algorithm. Simulation results indicate that the de-noising method adopting the new thresholding functionsuppresses the Pseudo-Gibbs phenomena near the singularities of the signal effectively, adn the numerical results also show the new method gives better MSE performance and SNR gains than DJ's hard- and soft-thresholding methods.

Key words: wavelet transform, wavelet shrinkage, thresholding function, MSE, SNR