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Proceedings Paper

Anisotropic multiresolution analysis in 2D: application to long-range correlations in cloud millimeter-radar fields
Author(s): Anthony B. Davis; Alexander Marshak; Eugene E. Clothiaux
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Paper Abstract

Taking a wavelet standpoint, we survey on the one hand various approaches to multifractal analysis, as a means of characterizing long-range correlations in data, and on the other hand various ways of statistically measuring anisotropy in 2D fields. In both instances, we present new and related techniques: (1) a simple multifractal analysis methodology based on Discrete Wavelet Transforms (DWTs), and (2) a specific DWT adapted to strongly anisotropic fields sampled on rectangular grids with large aspect ratios. This DWT uses a tensor product of the standard dyadic Haar basis (dividing ratio 2) and a non-standard triadic counterpart (dividing ratio 3) which includes the famous `French to-hat' wavelet. The new DWT is amenable to an anisotropic version of Multi-Resolution Analysis (MRA) in image processing where the natural support of the field is 2n pixels (vertically) by 3n pixels (horizontally), n being the number of levels in the MRA. The complete 2D basis has one scaling function and five wavelets. The new MRA is used in synthesis mode to generate random multifractal fields that mimic quite realistically the structure and distribution of boundary-layer clouds even though only a few parameters are used to control statistically the wavelet coefficients of the liquid water density field.

Paper Details

Date Published: 22 March 1999
PDF: 14 pages
Proc. SPIE 3723, Wavelet Applications VI, (22 March 1999);
Show Author Affiliations
Anthony B. Davis, Los Alamos National Lab. (United States)
Alexander Marshak, NASA Goddard Space Flight Ctr. (United States)
Eugene E. Clothiaux, The Pennsylvania State Univ. (United States)

Published in SPIE Proceedings Vol. 3723:
Wavelet Applications VI
Harold H. Szu, Editor(s)

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