Adaptive Image Denoising by a New Thresholding Function

This paper introduces a new thresholding function for image denoising. The function has continuous derivative while the standard hard-thresholding function is not continuous and the derivative of standard soft-thresholding function is not continuous. The new thresholding function are applied to coefficients in contourlet space for adaptive image denoising. Instead of the global hard-thresholding or soft-thresholding algorithm for image denoising, we minimize an estimate of the mean square error based on SURE Risk by using the function. Several numerical experiments show that the proposed new function is very effective and gives better performance both in terms of PSNR and in visual quality. It also gives better MSE performance than other three methods.