Statistical Analysis of Multiwavelet Image Transform
多小波图象变换的统计分析

Multiwavelet is a new kind of wavelets and application of multiwavelet to signal processing is also a new practice these years. Perhaps this is why we hardly find the statistical data such as mean, variance and the proportion of zero valued quantized coefficients of multiwavelet transforms in literatures. In this paper, we collect five multiwavelets from literatures and Internet and make a statistical analysis of their performance in multiwavelet transform. From our analysis we can conclude that (1) After CL multiwavelet transform, the energy of an image will converge not only to the lowest resolution subimage, but further to the first component of the subimage. Therefore, CL multiwavelet is most qualified for image coding. (2) After CARDBAL multiwavelet transform, the energy of the lowest resolution subimage of an image will spread in average among its four components. Therefore, CARDBAL multiwavelet image coding has to appeal to correlative coding between the components of subimage to improve its compression ratio. (3) After GHM multiwavelet transform, the distribution of the lowest resolution subimage's energy is not concentrated on one of its components, not averaged among its components. Therefore, GHM multiwavelet is not particularly suitable to image coding, even though it is the first multiwavelet to be discovered and now widely used in applications.