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
Approximation Power of Biorthogonal Wavelet with Sampling Property and Computation of Wavelet Sampling Points
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摘要: 本文主要讨论在具有抽样性质的双正交子波基下Mallat算法的逼近性能及其子波系数的计算。当尺度较小以及尺度较大时,我们依次得到了Mallat算法逼近误差的渐近公式和比较精确的定量估计。结果表明:在这样的子波基下,直接用均匀抽样点代替子波抽样点而无需进行预先滤波,其逼近速度可以达到K阶,这里K是综合尺度函数的阶。模拟实验也显示出它的优点。Abstract: 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.
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