Multiscale autoregressive models and wavelets

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 t...

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Bibliographic Details
Published in:IEEE transactions on information theory 1999-04, Vol.45 (3), p.828-845
Main Authors: Daoudi, K., Frakt, A.B., Willsky, A.S.
Format: Article
Language:English
Subjects:
1f noise
Algorithms
Approximation
Complement
Computer Science
Data transmission
Least squares approximation
Machinery
Mathematical models
Noise generators
Optimization
Other
Reconstruction algorithms
Signal processing
Signal processing algorithms
Signal resolution
Stochastic models
Stochastic processes
Synthesis
Wavelet
Wavelet transforms
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.761321