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A new adaptive denoising method is presented based on Stein's (1981) unbiased risk estimate (SURE) and on a new class of thresholding functions. First, we present a new class of thresholding functions that has a continuous derivative while the derivative of standard soft-thresholding function is not continuous. The new thresholding functions make it possible to construct the adaptive algorithm whenever using the wavelet shrinkage method. By using the new thresholding functions, a new adaptive denoising method is presented based on SURE. Several numerical examples are given. The results indicated that for denoising applications, the proposed method is very effective in adaptively finding the optimal solution in a mean square error (MSE) sense. It is also shown that this method gives better MSE performance than those conventional wavelet shrinkage methods.