Spatio-Temporal Filtering Using Wavelets
by
Rosaura Fernandez-Pascual
Department of Statistics and Operations Research, University of Jaen, SPAIN
Coauthors: Jose M. Angulo and Maria D. Ruiz-Medina (University of Granada, SPAIN)

The Lagrangian and the Eulerian approaches are suitable for the spatio-temporal modeling of certain random phenomena involving space and time; for example, in the description of exposure and health processes in human exposure analysis (Christakos and Hristopulos, 1998), in the temporal modeling of optical flow in image sequence analysis (Luettgen and Willsky, 1994), etc. In this paper, we consider the problem of spatio-temporal filtering of a random process defined by a first-order Eulerian dynamic model driven by space-time white noise. Under certain conditions, the Eulerian approach provides a good approximation to the Lagrangian method, such as with the optical flow (Luettgen and Willsky, 1994). The discrete approximation of the above equation is given by a first-order autoregressive model. The process is defined in terms of a random spatial initial condition model and the Eulerian dynamic model. We assume that observations in a domain, affected by uncorrelated additive noise, are available at each time we are interested in estimating. The orthogonal expansion in terms of wavelets at each fixed time leads, by truncation, to a finite-dimensional formulation of the estimation problem. Hence, an approximation to the least-squares linear estimate is calculated at each time of interest, and at any location.

Date received: November 16, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafx-14.