Nearly 1/f processes are known as important stochastic models for scale invariant data analysis in a number of fields. In this paper, two parameter estimation methods of nearly 1/f processes based on wavelets are proposed. The conventional method based on wavelet transform with EM algorithm does not give the reliable parameter estimation value when the data length is short. Moreover, the precise parameter value is not estimated when the spectrum gap exists in 1/f processes. First, in order to improve the accuracy of the estimation when the data length is short, a parameter estimation method based on wavelet transform with complementary sampling is proposed. Next, in order to reduce the effect of spectrum gap, a parameter estimation method based on wavelet packet with EM algorithm is proposed. Simulation results are given to verify the effectiveness of the proposed methods.

In recent years, fractal processes have played important roles in various application fields. Since a 1/f process possesses the statistical self-similarity, it is considered sa a main part of fractal signal modeling. On the other hand, noise reduction is often needed in real-world signal processing. Hence, we propose an enhancement algorithm for 1/f signal disturbed by white noise. The algorithm is based on constrained minimization in a wavelet domain: the power of 1/f signal distortion in the wavelet domain is minimized under a constraint that the power of residual noise in the wavelet domain is smaller than a threshold level. We solve this constrained minimization problem using a Lagrangian equation. We also consider a setting method of the Lagrange multiplier in the proposed algorithm. In addition, we will confirm that the proposed algorithm with this Lagrange multiplier setting method obtains better enhancement results than the conventional algorithm through computer simulations.