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Abstruet-A current topic of great interest is the multiresolu-tion analysis of signals and the development of multiscale signal processing algorithms. In this paper, we describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and/or noisy measurements which may also be at(More)
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)
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 Markovian in scale, and in addition the eigenstructure of these models is given by the wavelet transform. The implication of this is(More)
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)
The membrane potential in murine epididymal sperm was determined with a voltage-sensitive, fluorescent probe. In freshly collected sperm, the potential was inside-negative, viz., -13 mV, and was associated with an intracellular K+ concentration of about 122 mM. Following incubation of sperm in a medium capable of sustaining capacitation and fertilization(More)
Spurred by the emerging theory of multiscale representations of signals and wavelet transforms, researchers in the signal and image processing community have developed multiresolution processing algorithms. These algorithms have promise because they are computa-tionally eecient, especially in 2D, and because they are applicable to a wide variety of(More)
In this paper a method of estimating the conductivity in a bounded 2-D domain at multiple spatial resolutions given boundary excitations and measurements is presented. The problem is formulated as a maximum-likelihood estimation problem and an algorithm that consists of a sequence of estimates at successively finer scales is presented. By exploiting the(More)
The effects of isoacids, urea N, and S on ruminal fermentation of sugarcane bagasse- or corn stover-based diets were studied in sheep. Acetate production was taken as a measure of the fermentation rate. For the sugarcane bagasse diet, neither urea nor S supplementation changed ruminal acetate production. When N and S were combined, acetate production was(More)