Restoration of Noisy 1/f Family Fractal Signal Based on Haar Wavelets and Wiener Filter

<正> In order to restore noisy fractal Brownian motion(FBM),discrete fractional gaussiannoise(DFGN) combined with noise increments is decomposed by Haar wavelets based on Mallatalgorithm.Considering the correlation of detail coefficients,a bank of Wiener filters are used to estimatethe detail coefficients to reconstruct DFGN considering the estimated approximation coefficients in thecoarsest scale in the minimum mean square sense.Then,the reconstructed DFGN is used to restore FBM.In the digital simulation,in light of the restoration mean square error,we show that the suppose that thecorrelation of detail coefficients and the approximation coefficients in the coarsest scale for any Hurstcould be avoided is unrealistic.Moreover,we calculate the estimation root mean square error of the hurstparameter of the restored FBM to show the validity of our algorithm.