Optimal Wiener filtering for self-similar processes

In this paper, we formulate an optimal Wiener filter for the restoration of self-similar processes from time-varying and nonstationary distortions. Fourier techniques and classical Wiener filtering are not applicable for the elimination of such distortions. We derive an optimal Wiener filtering algorithm by modeling time-varying degradation within the scale-invariant system theory and nonstationary, long-term correlated noise within the scale stationarity framework. Additionally, we develop fast and efficient estimation techniques for scale spectra in Mellin domain for the implementation of the proposed Wiener filter. The utility of the proposed techniques are demonstrated on simulation data.