Optimal Interpolation of Fractional Brownian Motion Given Its Noisy Samples

Abstract

We consider the problem of estimating a fractional Brownian motion known only from its noisy samples at the integers. We show that the optimal estimator can be expressed using a digital Wiener-like filter followed by a simple timevariant correction accounting for nonstationarity.Moreover, we prove that this estimate lives in a symmetric fractional spline space and give a practical implementation for optimal upsampling of noisy fBm samples by integer factors.

Reconstruction of fractional Brownian motion signals from its sparse samples based on Compressive Sampling

“…The reconstruction problem will be more complicated if the fBm signal is contaminated by noise. The estimation of an fBm signal from its noisy measurement has been described in [2], [3], and [4]. In [5], an fBm equalization method and its application to improve DEM (Digital Elevation Model) reconstruction for a given InSAR (Interferometric Synthetic Aperture Radar) phase image were proposed.…”