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Multiscale autoregressive models and wavelets

Khalid Daoudi 1 A.B. Frakt A.S. Willsky Austin Frakt Alan Willsky
1 MIT - Massachusetts Institute of Technology
Abstract : The multiscale autoregressive (MAR) framework was introduced to support the development of optimal multiscale statistical signal processing. Its power resides in the fast and flexible algorithms to which it leads. While the MAR framework was originally motivated by wavelets, the link between these two worlds has been previously established only in the simple case of the Haar wavelet. The first contribution of this paper is to provide a unification of the MAR framework and all compactly supported wavelets as well as a new view of the multiscale stochastic realization problem. The second contribution of this paper is to develop wavelet-based approximate internal MAR models for stochastic processes. This will be done by incorporating a powerful synthesis algorithm for the detail coefficients which complements the usual wavelet reconstruction algorithm for the scaling coefficients. Taking advantage of the statistical machinery provided by the MAR framework, we will illustrate the application of our models to sample-path generation and estimation from noisy, irregular, and sparse measurements.
Keywords : Index Terms-Fractional Brownian motion graphical models internal models multiscale estimation multiscale models sto- chastic realization wavelets
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https://hal.inria.fr/inria-00439188
Contributor : Khalid Daoudi <>
Submitted on : Sunday, December 6, 2009 - 6:21:42 PM
Last modification on : Tuesday, November 10, 2020 - 4:41:21 PM

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  • HAL Id : inria-00439188, version 1

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Khalid Daoudi, A.B. Frakt, A.S. Willsky, Austin Frakt, Alan Willsky. Multiscale autoregressive models and wavelets. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 1999, 45 (3), pp.828--845. ⟨inria-00439188⟩

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