A Bias-Variance Approach for the Nonlocal Means
SIAM Journal on Imaging Sciences
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The wavelet shrinkage denoising approach is able to maintain local regularity of a signal while suppressing noise. However, the conventional wavelet shrinkage based methods are not time-scale adaptive to track the local time-scale variation. In this paper, a new time-scale adaptive denoising method for deterministic signal estimation is presented, based on the wavelet shrinkage. A class of smooth shrinkage functions and the local SURE (Stein's unbiased risk estimate) risk are employed to achieve time-scale adaptive denoising. The system structure and the learning algorithm are developed. The numerical results of our system are presented and compared with the conventional wavelet shrinkage techniques as well as their optimal solutions. Results indicate that the new time-scale adaptive method is superior to the conventional methods. It is also shown that the new method sometimes even achieves better performance than the optimal solution of the conventional wavelet shrinkage techniques.