滤波长度为4的双正交多尺度分析的构造

该文研究了滤波长度为4的双正交多尺度分析的一般构造，依据Lawton条件，通过解决一个线性代数问题，求出了其实滤波系数所在的范围，给出了一些构造的例子，并通过计算和分析这些小波用于图像压缩的熵和信噪比数据，研究了它们用于图像压缩的性能。

Construction of Biorthonormal Multiresolution Analysis with Length 4

By Lawton's condition, it is known that whether two banks of filter coefficients can generate a pair of biorthonormal MRAs depends upon whether the eigenvalues of the so called transition operators defined by these filter coefficients are less than 1. Since such transition operators can be expressed equivalently by matrices, by computing The eigenvalues of the matrices, this paper discusses the conditions the filter coefficients satisfy such that they can generate a pair of biorthonormal MRAs. Therefore, the domains of the filter real coefficients which can generate biorthonormal MRAs and orthonormal MRAs are obtained. Finally, some examples of wavelet are given, and their validity applied to image compression is analyzed by calculating their entropy and peak signal-to-noise ratio. The results show that some wavelets are better than the famous Daubechies wavelet with filter length 4.