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中文摘要：
小波的分解重构算法是小波通向实际应用的关键步骤，基于方括号积关系的多尺度分析的建立以及一类新小波的构造．得到了半双正交小波，并通过对尺度空间和小波空间之间关系的分析，得到其对应基之间关系的半双正交小波的分解重构算法。研究表明该算法可归结为对Toeplitz线性方程组的求解，且当尺度函数φ和~↑φ双正交时．算法退化为现有的双正交小波的分解重构算法。
英文摘要：
Wavelet decomposition and reconstruction algorithms are a critical step for wavelets towards the practical application. The semi-biorthogonal wavelets are introduced according to the established bracket products multiresolution analysis and the construction of a new class of wavelets. Based on the analysis of scaling space and wavelet space ,together with the relationship between the corresponding bases of the spaces ,the decomposition and reconstruction algorithms of semi-biorthogonal wavelets are proposed. The further discussion showed that the algorithms could be converted to solve pairs of Toeplitz linear equations. Furthermore,as the scaling functions φ and ~↑φ are biorthogonal, the algorithms could be degenerated to the existing decomposition and reconstruction algorithms of biorthogonal wavelets.
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