Based on Neyman-Pearson criterion to maximise the probability of signal detection for a givenfalse alarm

and based on the minimum mean-square error between the reconstructed signal and the original sig-nal

this paper presents an optimum wavelet threshold for the estimation of 1/f-type fractal signals embedded inadditive white Gaussian noise.Also presented in this paper are typical computer simulation results to demonstratethe viability and the effectiveness of the proposed optimum wavelet threshold .