一种紧支集双正交小波基的构造

Construction of a Compactly Supported Biorthogonal Wavelet

基于对偶尺度函数及对偶小波 ,提出了一种构造紧支集双正交小波基的算法 ,并给出严密的证明和推导过程。应用该算法 ,结合函数优化方法 ,构造出一系列包括样条小波、接近正交的双正交小波及其它具有特殊性质的双正交小波。该构造算法丰富了小波理论 ,可以广泛应用于信号分析、图像处理等领域。

In the practical application of wavelet analysis, the most common problem is the choice of wavelet base, and the algorithm of constructing a wavelet base takes on an important significance in theory and practice. Based on dual scaling function and dual wavelet, the algorithm of constructing a compactly supported biorthogonal wavelet is proposed, at the same time, rigorous process of proofness and deduction is shown. Using the algorithm, a series of biorthogonal wavelets such as B-spline wavelet, biorthogonal wavelets which are close to orthonormal wavelets and other wavelets with special characteristic can be constructed. The constructing algorithm enriches the wavelet theory and can be applied extensively in such fields as signal analysis and image processing.