Applications Of Wavelet Multi-Resolution Analysis

Scale issues are one of the highlights in Eco-environmental research. Wavelet analysis has advantages of multi-scale analysis in the field because of its "mathematic microscope" properity. This paper focused on the applications of wavelet analysis, including applications in the identification of the characteristic scale(s) with several wavelet parameters, multi-correlation, and classification of data sets. Conclusions of the paper were listed as following:(1) Wavelet variance and wavelet information entropy are better parameters to identify the characteristic scale of the eco-environment, while the wavelet energy entropy is not a ideal parameter. It was proved to be reasonable to take the scale with the maximum of wavelet variance or wavelet information entropy as the characteristic scale for eco-environment.(2) By use of wavelet detail information in relation analysis, it would get the scale effects of correlations between eco-environmental factors. On the characteristic scale, it showed the weak relationship between the factors, which testified the practical reliability of wavelet analysis for the characteristic scale.(3) It was feasible to classify the data sets of eco-environment with wavelet detail information and its position information entropy.The paper provided the methods to use wavelet analysis in the field of eco-environment research and cases, and expanded the application fields of wavelet analysis.