Adaptive denoising based on wavelet thresholding method

The paper presents a novel adaptive denoising method based on a wavelet thresholding method. First, it presents a new thresholding function that has a continuous derivative while the derivative of a standard thresholding function is not continuous. The new thresholding function makes it possible to construct an adaptive algorithm based on the wavelet thresholding method. Second, by using the new thresholding function, the paper presents an adaptive method based on SURE (Stein's unbiased risk estimate) risk. Finally, several numerical analysis examples are given; the results show that the proposed method is very effective in finding the optimal solution in the mean square error (MSE) sense. It also indicates that this method gives better MSE performance than other wavelet thresholding methods.