Restoration of Noisy 1/f Family Fractal Signal Based on Haar Wavelets and Wiener Filter
Cao Kunyong, YU Sheng-lin · 中国电子科技：英文版 · 2003
In order to restore noisy fractal Brownian motion(FBM), discrete fractional gaussian noise(DFGN) combined with noise increments is decomposed by Haar wavelets based on Mallat algorithm. Considering the correlation of detail coefficients, a bank of Wiener filters are used to estimate the detail coefficients to reconstruct DFGN considering the estimated approximation coefficients in the coarsest 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 the correlation of detail coefficients and the approximation coefficients in the coarsest scale for any Hurst could be avoided is unrealistic. Moreover, we calculate the estimation root mean square error of the hurst parameter of the restored FBM to show the validity of our algorithm.