Wavelet Transform and Noise Modeling of Spatial Data

See the following article, which has been submitted for publication:

"Spatial Representation of Economic and Financial Measures used in Agriculture via Wavelet Analysis", M. Morehart (US Department of Agriculture), F. Murtagh and J.-L. Starck (request copy from F. Murtagh, fmurtagh@acm.org).

Abstract: A foundation is set forth for use of the wavelet transform as a spatial analysis tool for modelling the geographic representation of economic and financial measures used in agriculture. This provides a framework from which to estimate a smooth nonparametric function which describes complex, multivariate relationships embedded in spatial data, with the resulting maps conveying large amounts of information in a familiar format. We illustrate this approach for tasks which include the graphical presentation of information, density estimation and wavelet-based nonparametric regression. A redundant wavelet transform is used, and we detail the properties which make it particularly appropriate for these objectives.

Perspective plot (from south) of wavelet transform of 1995 Debt Capacity Utilization Ratio. Data from USDA. Carried out in MR/1.

Result of wavelet regression, based on a heteroscedastic noise model, of 1995 wheat dependence data. Data from USDA. The noise modeling and filtering was carried out in MR/1 and IDL, followed by geo-referencing in ArcView.

Commands used included:

mr_visu -v 3 for the perspective plot.

mr_filter -m 8 -K -p -k for wavelet regression with heteroscadistic noise (-m 8), suppression of isolated detected pixels (-k), ignoring of the last smooth scale (-K), and detection of positive structure only (-p).