Wavelet Estimation of Fractional Brownian Motion Embedded in a Noisy Environment

This correspondence proposes a wavelet-based fractional Brownian motion (fBm) signal estimation scheme. Despite the fact that wavelet transform approximately whitens the fBm processes, it is observed that statistical dependencies still exist across adjacent wavelet scales and between neighboring wavelet coefficients. These dependencies can be exploited to improve the estimation of fBm signals embedded into noise. The idea is to reorganize the wavelet coefficients into a scale–time mixture model and then carry out the minimum mean-square-error estimation (MMSE) using the model. Experiments show that the proposed scheme obtains better estimates than Wornell and Oppenheim's algorithm, in which the wavelet dependencies are not utilized.