小波基的構(gòu)造方法和算法設(shè)計(jì)
THE CONSTRUCTION METHODS AND ALGORITHM DESIGN OF WAVELET BASES
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摘要: 本文首先對(duì)小波分析的基本原理作了簡(jiǎn)要介紹;然后從分解信號(hào)完全恢復(fù)的角度,對(duì)幾種典型的小波基進(jìn)行了概括;并且著重指出:對(duì)于兩帶分解的小波基設(shè)計(jì)等價(jià)于在正則性條件下,設(shè)計(jì)一個(gè)兩帶完全恢復(fù)或近似完全恢復(fù)恢復(fù)的濾波器組;最后給出了相應(yīng)于Daubechies基的小波生成算法和實(shí)驗(yàn)結(jié)果。
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關(guān)鍵詞:
- 小波分析; 小波基設(shè)計(jì); 算法構(gòu)成
Abstract: Based on the brief introduction of the principle of wavelet analysis, this paper gives a summary of several typical wavelet bases from the point of veiw of perfect reconstruction of signal and emphasizes that designing wavelet bases which are used to decompose the signal into two-band form is equivalent to designing a two-band filters with perfect or nearly perfect property. The generating algorithm corresponding to Daubechies bases and some simulated results are also shown in this paper. -
Daubechies I. Comm[J].Pure Appl. Math.1988, 41:909-996[2]Antonini M.[J].Sarlaud M, Mathieu P, Daubechies I. Image Coding Using Vector Quantiztion is the Wavelet Transform Domain. Proe. of ICASSP90, New Mexico, USA.2297,1990:-[3]Mallat S, Zhong S F. IEEE Trans. on PAMI, 1992, PAMI-14(7):710-732.[4]Papoulis A. Signal Analysis, New York: McGraw-Hill, 1977, 30-55. -
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