具有抽樣性質(zhì)的雙正交子波的逼近性能及其子波抽樣的計(jì)算
Approximation Power of Biorthogonal Wavelet with Sampling Property and Computation of Wavelet Sampling Points
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摘要: 本文主要討論在具有抽樣性質(zhì)的雙正交子波基下Mallat算法的逼近性能及其子波系數(shù)的計(jì)算。當(dāng)尺度較小以及尺度較大時(shí),我們依次得到了Mallat算法逼近誤差的漸近公式和比較精確的定量估計(jì)。結(jié)果表明:在這樣的子波基下,直接用均勻抽樣點(diǎn)代替子波抽樣點(diǎn)而無(wú)需進(jìn)行預(yù)先濾波,其逼近速度可以達(dá)到K階,這里K是綜合尺度函數(shù)的階。模擬實(shí)驗(yàn)也顯示出它的優(yōu)點(diǎn)。
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關(guān)鍵詞:
- 抽樣性質(zhì); 雙正交子波; Mallat算法
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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