Spatio-temporal filtering using wavelets
type: Item
instance of: scholarly article
title: Spatio-temporal filtering using wavelets
zbMATH Open document ID: 1021.62081
published in: Stochastic Environmental Research and Risk Assessment
publication date: 2003-08-31T00:00:00Z
review text: A class of spatio-temporal processes with first-order autoregressive temporal structure and functional spatio-temporal interactions is introduced. The spatial second-order regularity is allowed to change over time and is characterized in terms of fractional Sobolev spaces. The associated filtering problem is considered, assuming that observations are defined by spatial linear functionals of the process of interest, being affected by additive noise. Conditions under which a stable solution to this problem is obtained are studied. A functional least-squares linear estimation fusion method is derived to calculate this solution A multiscale finite-dimensional approximation to the problem is obtained from the wavelet-based orthogonal expansions of the time cross-section spatial processes, which allows the numerical inversion of the linear operator involved.
Mathematics Subject Classification ID: 62M30
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 1972546
zbMATH Keywords: Eulerian discretization
zbMATH Keywords: fractional generalized random fields
zbMATH Keywords: least-squares linear estimation
zbMATH Keywords: physical models
zbMATH Keywords: regularization
zbMATH Keywords: spatio-temporal processes
zbMATH Keywords: wavelet-based orthogonal expansions
author: María D. Ruiz-Medina
author: J. M. Angulo
MaRDI profile type: Publication
full work available at URL: s00477-002-0099-z
OpenAlex ID: W2118247127
DOI: 10.1007/S00477-002-0099-Z
description: scientific article; zbMATH DE number 1972546