Approximation Power of Biorthogonal Wavelet with Sampling Property and Computation of Wavelet Sampling Points
具有抽样性质的双正交子波的逼近性能及其子波抽样的计算

The focus in this paper is on the discussion of the approximation performance of the Mallat algorithm under biorthogonal wavelet bases with sampling property. The asymptotic formulae of the approximation errors of the Mallat algorithm and sharper quantitative estimation of the upper bounds are given for relatively small scale and relatively large scale, respectively. The results demonstrate that under such wavelet bases, the rate of decay of the Mallat project, directly replacing wavelet sampling points by uniform sampling points without prefiltering, reaches K order, where K is the order of a synthesis scaling function. The final experiments also show its advantages.