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Multiresolution Spatial Analysis
MOREHART, Mitchell J. (firstname.lastname@example.org), U.S. Department of Agriculture, Economic Research Service, 1800 M Street N.W., Room 4121N, Washington, D.C. 20036-5831; MURTAGH, Fionn (email@example.com), The Queen's University, Department of Computer Science, BT7 1NN, Belfast, Ireland; STARCK, Jean-Luc (firstname.lastname@example.org), CEA/DSM/DAPNIA, 91191, Gif-Sur-Yvette Cedex, France
Key Words: wavelets, spatial analysis, multiresolution, nonparametric regression, geographic information systems
Geographic information systems (GIS) are increasingly used as tools for topographical applications and research. A comprehensive GIS is characterized by its capabilities in the areas of data processing, analysis, and post processing. This paper explores the use of the wavelet transform as a spatial analysis tool for modeling complex multivariate geographic relationships. The use of wavelets in spatial statistics is a relatively recent phenomenon that is rapidly developing. The appeal of wavelet methods stems from their ability to process noisy data with local structures and represents discontinuities such as jumps or peaks in a function. Several examples from agricultural data are used to illustrate the exploratory data analysis inherent in the wavelet transform. The resulting maps provide a convenient means of visually conveying tremendous amounts of information. The redundant `a trous discrete wavelet transform is shown to aid enormously in feature detection and exploration in the succession of resolution views of the data. Analysis is carried out through use of the MR/1 multiresolution image and data analysis package.