紧支撑帕塞瓦尔小波框架的分解与重构

Decomposition and Reconstruction of Tightly Supported Parseval Wavelet Frame

摘要: 本文构造出性质良好的紧支撑帕塞瓦尔小波框架。利用小波框架及其相关尺度函数的数量关系式，在多分辨率分析思想下以小波框架为基础定义一般的空间序列，得到紧支撑帕塞瓦尔小波框架的分解与重构定理，进而得出信号分解与重构的框图，并对算法进行总结。实验结果表明，与Haar小波函数的分解重构算法相比，本文算法具有更好的性能。

Abstract: In this paper, a compact supported Parseval wavelet frame with good properties is constructed. We apply the idea of multi-resolution analysis to define a general spatial sequence based on the wavelet frame by using the quantitative relation of the wavelet frame and the relevant scale function, and get the decomposition and reconstruction theorem of the compact support Parseval wavelet frame, and then make the block diagram of signal decomposition and reconstruction, and summarize the algorithm. The experimental results show that compared with the decomposition and reconstruction algorithm of Haar wavelet function, the proposed algorithm has better performance.