Anisotropic multiresolution analysis in 2D: application to long-range correlations in cloud millimeter-radar fields

摘要

Abstract: Taking a wavelet standpoint, we survey on the one handvarious approaches to multifractal analysis, as a meansof characterizing long-range correlations in data, andon the other hand various ways of statisticallymeasuring anisotropy in 2D fields. In both instances,we present new and related techniques: (1) a simplemultifractal analysis methodology based on DiscreteWavelet Transforms (DWTs), and (2) a specific DWTadapted to strongly anisotropic fields sampled onrectangular grids with large aspect ratios. This DWTuses a tensor product of the standard dyadic Haar basis(dividing ratio 2) and a non-standard triadiccounterpart (dividing ratio 3) which includes thefamous `French to-hat' wavelet. The new DWT is amenableto an anisotropic version of Multi-Resolution Analysis(MRA) in image processing where the natural support ofthe field is 2$+n$/ pixels (vertically) by 3$+n$/pixels (horizontally), n being the number of levels inthe MRA. The complete 2D basis has one scaling functionand five wavelets. The new MRA is used in synthesismode to generate random multifractal fields that mimicquite realistically the structure and distribution ofboundary-layer clouds even though only a few parametersare used to control statistically the waveletcoefficients of the liquid water density field.!20