连续小波变换研究

Study on continuous wavelet transforms

给出了多元可允许小波定义,提出了多元小波变换的一般形式,通常的小波变换只是其中的特例.从数值计算角度出发,在一系列的多元小波变换中,选择一个适当的小波变换,对小波正变换和逆变换进行离散,构造了数值解法,仿真实例表明了此方法的有效性.

In this paper, the definition of multi-admissible wavelet is given, and the general form of multivariate wavelet transform is presented. The common multivariate wavelet transform is a special case. In the view of the numerical analysis, from a series of multivariate wavelet transforms, one proper wavelet transform is selected. By discretizing the transform of wavelet and the inverse transform of wavelet, an algorithm can be constructed. Simulation examples demonstrated this method is effective.