An algorithm for compactly supported multivariate wavelets
Jizheng Di · Journal of Zhejiang University of Technology · 2012
In the practical application of wavelet analysis,multivariate wavelet is useful for decomposition and reconstruction of graphs and images.However,it is quite difficult to calculate the wavelet coefficients.It may be well-known that wavelet coefficient is defined by integral of the product of the discussed functions and the wavelet basis functions.Since the function is often given by the sample values,the integral mentioned above need to be calculated approximately.If a large number of wavelet coefficients are calculated in this way,it will be a heavy workload.If the idea of Mallat algorithm of univariate wavelet is applied to multivariate wavelet,we can deduce Mallat algorithm of compactly supported multivariate wavelet.Based on an integral limit theorem,an approximate formula is obtained for the calculation of coefficients by sampling values.With the help of these formulas,we can get the wavelet coefficients directly by sampling value of function.