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An overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing. As described, a natural framework for developing such a theory is the study of stochastic processes indexed by nodes on… (More)

- Kenneth C Chou, Alan S Willsky, Ramine Nikoukhah, K C Chou
- 1991

In 111 we introduced a class of multiscale dynamic models described in terms of scale-recursive state space equations on a dyadic tree. An algorithm analogous to the Rauch-hg4triebel algorithm-onsisting of a he-to-coarse Kalman filter-like sweep followed by a coarse-to-he smoothing step-was developed In this paper we present a detailed system-theoretic… (More)

- K C Chou, A S Willskyl, A Benveniste, M Basseville

A current topic of great interest is the multi-resolution analysis of signals and the development of multi-scale or multigrid algorithms. In this paper we describe part of a research effort aimed at developing a corresponding theory for stochastic processes described at multiple scales and for their efficient estimation or reconstruction given partial… (More)

- M Basseville, A Benveniste, K C Chou, A S Willsky

Motivated by the recently-developed theory of multiscale signal models and wavelet transforms, we introduce stochastic dynamic models evolving on homogeneous trees. In particular we introduce and investigate both AR and state models on trees. Our analysis yields generalizations of Levinson and Schur recursions and of Kalman filters, Riccati equations, and… (More)

- K C Chou, S A Golden, A S Willsky, Kenneth C Chou, Alan S Willsky

In this paper we describe and analyze a class of multiscale stochastic processes which are modeled using dynamic representations evolving in scale based on the wavelet transform. The statistical structure of these models is Marko-vian in scale, and in addition the eigenstructure of these models is given by the wavelet transform. The implication of this is… (More)

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