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Multiscale Autoregressive Models and Wavelets
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 complete 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 MAR models for stochastic processes. This will be done by incorporating a powerful synthesis algorithm for the detail coefficients which compliments the usual wavelet synthesis 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.
Cited literature [40 references]
https://hal.inria.fr/inria-00108069
Contributor : Publications Loria Connect in order to contact the contributor
Submitted on : Friday, November 13, 2020 - 1:15:18 PM
Last modification on : Sunday, November 15, 2020 - 3:24:15 AM
Long-term archiving on: : Sunday, February 14, 2021 - 6:54:00 PM
Contributor : Publications Loria Connect in order to contact the contributor
Submitted on : Friday, November 13, 2020 - 1:15:18 PM
Last modification on : Sunday, November 15, 2020 - 3:24:15 AM
Long-term archiving on: : Sunday, February 14, 2021 - 6:54:00 PM
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