Mean Square Error Estimation in Thresholding

We present a novel approach to estimating the mean square error (MSE) associated with any given threshold level in both hard and soft thresholding. The estimate is provided by using only the data that is being thresholded. This adaptive approach provides probabilistic confidence bounds on the MSE. The MSE bounds can be used to evaluate the denoising method. Our simulation results confirm that not only does the method provide an accurate estimate of the MSE for any given thresholding method, but the proposed method can also search and find an optimum threshold for any noisy data with regard to MSE.