Optimal threshold determination for multiscale product in wavelet denoising

The main difficulty in multiscale product thresholding is to determine a proper threshold. In this paper, a hard thresholding function applied to multiscale product is constructed in the product form of shrinkage coefficient function and wavelet coefficients. This function is infinite-order differentiable with respect to wavelet coefficient, and can adaptively shrink wavelet coefficient in the neighborhood of the threshold. Furthermore, minimizing the Stein unbiased risk estimate (SURE) based on the thresholding function, the optimal threshold value is obtained in the mean square error (MSE) sense. In simulations to denoise multiple classic noisy signals, the traditional multiscale product coefficient thresholding is improved through using our optimal threshold.