Analysis of signal de-noising method based on an improved wavelet thresholding

Based on the multi-analysis wavelet threshold de-nosing method which put forward by D.L. Dohono and I.M. Johnstone, a new thresholding function is proposed. This new thresholding function is 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 threshold method. In new thresholding function, by adjusting k parameter, a near-optimum function between hard and soft functions is resulted. Moreover, by turning parameter m, the near-optimum thresholding function is adjusted to the optimum one through applying small changes. In other words, optimizing parameter k works similar to a global search and optimizing parameter m works like local search in finding the best thresholding function. The simulation results show that the new thresholding function can offer the best de-noising signal only by changing the variable parameters. The enhancement of the SNR and the reduction of the RMSE indicates that the performance of this method is better then the hard and soft threshold methods.