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A New Threshold Function for Signal Denoising Based on Wavelet Transform

A novel thresholding function is presented based on the wavelet thresholding denoising method put forward by D. L. Donoho and I. M. Johnstone. This new thresholding function has many advantages over soft- and hard-threshold function. It is simple in expression and as continuous as the soft-thresholding function. 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 method. At the same time, the new thresholding function is more elastic than the soft- and hard-thresholding, function. MATLAB Simulation results indicate that the denoising method adopting the new thresholding function suppresses the Pseudo-Gibbs phenomena near the singularities of the signal effectively, and the numerical results also show the new method gives better SNR gains than DJps hard- and soft-thresholding methods.