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Optimal Interpolation of Fractional Brownian Motion Given Its Noisy Samples

T. Blu, M. Unser

Proceedings of the Thirty-First IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'06), Toulouse, French Republic, May 14-19, 2006, pp. III-860-III-863.



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 time-variant 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.


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