Inverse Estimation in Space and Time
by
Maria D. Ruiz-Medina
Department of Statistics and Operations Research, University of Granda, SPAIN
Coauthors: Jose M. Angulo (University of Granada, SPAIN)

The problem of least-squares linear estimation of a spatio-temporal random process is studied from the observation of noisy linear functionals of such a process. This problem arises in many applied areas such as medicine, hydrology, geophysics, astronomy, etc. Two main difficulties in its resolution are the ill-posed nature of the problem, and the large amount of information that must be usually processed. In this paper, we consider a regularization method, based on considering appropriate fractional Sobolev norms, and an orthogonal discretization method of the spatial information, based on orthogonal expansions of random fields in terms of wavelets. The information processing problem is tackled by fusion of the spatial observations according to the temporal dynamics of the spatio-temporal model considered. The methodology developed allows a functional spatial estimate of the random process of interest at each time to be calculated. The class of spatio-temporal random processes considered is defined in terms of autoregressive temporal models with spatial covariance functions lying in a fractional Sobolev space. Applications of the spatio-temporal inverse estimation method presented in image-sequence analysis are given.

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-15.