ENHANCEMENT OF FRACTAL SIGNAL USING CONSTRAINED MINIMIZATION IN WAVELET DOMAIN

In recent years, fractal processes have played important roles in vari ous application fields. Since a 1/f process possesses the statistical self-similarity, it is considered as a main part of fractal signal mod eling. On the other hand, noise reduction is often needed in real-worl d signal, processing. Hence, we propose an enhancement algorithm for 1 /f signal disturbed by white noise. The algorithm is based on constrai ned minimization in a wavelet domain: the power of 1/f signal distorti on in the wavelet domain is minimized under a constraint that the powe r of residual noise in the wavelet domain is smaller than a threshold level. We solve this constrained minimization problem using a Lagrangi an equation. We also consider a setting method of the Lagrange multipl ier in the proposed algorithm. In addition, we will confirm that the p roposed algorithm with this Lagrange multiplier setting method obtains better enhancement results than the conventional algorithm through co mputer simulations.