Abstract: MATLAB directly uses orthogonal wavelet calculation model to process biorthogonal wavelet, leading to coefficients redundant problem. According to that, this paper proposes 9/7 wavelet prototype as the improved algorithm to hand the nonperiodic signal, compared with the given algorithm in MATLAB, for the signals which have the odd starting-even length and even starting-odd length, after wavelet transformation, two approximate coefficients and one detail coefficient can be saved, for the signals which have the odd starting-odd length and even starting-even length, one approximate coefficient can be saved. When using the improved algorithm to decompose the image with 512×512 points to 4th level, 4256 coefficients can be saved, and reconstruction image’s peak value signal-to-noise ratio is higher than the reconstruction image in MATLAB. So the improved algorithm not only reduces the computation time and data storage capacity, but also improves the quality of the reconstruction image.

Key words: approximate coefficient, detail coefficient, 9/7 wavelet, wavelet toolbox

摘要： 对MATLAB中直接采用正交小波计算模型处理双正交小波，导致小波分解系数冗余的问题进行了研究。针对该问题，提出采用9/7小波原型处理非周期信号的改进算法，与MATLAB所给算法相比，对于奇起点的偶数长信号和偶起点的奇数长信号，分解时可少计算2个近似系数和1个细节系数；对于奇起点的奇数长信号和偶起点的偶数长信号，可少计算1个近似系数。当用改进算法分解512×512点图像至第4级时，便可少计算4 256个系数，且重构图像的峰值信噪比要高于MATLAB中恢复图像。所以，改进算法既降低了计算量和数据存储量，又提高了恢复图像的质量。

关键词: 近似系数, 细节系数, 9/7小波, 小波工具箱