加窗截取改善信号非稀疏表达的稀疏性

Window-Added Sampling for Improving Sparsity of Non-Sparse Representation of Signals

为了把压缩传感技术应用到变换域非稀疏信号中,提出了一种能够改善信号非稀疏表达稀疏性的新方法。该方法采用可移动窗口函数把信号在变换域中的非稀疏表达截取成多个窗截表达,只要控制每个窗口函数宽度远小于信号的长度,则每个窗截表达具有较好的稀疏性。通过稀疏的窗截表达实现对非稀疏表达的压缩传感。结合高斯和矩形窗口函数给出了详细的理论分析,无噪和加噪信号的实验结果证明了该方法的有效性。

In order to apply compressed sensing technique to a non-sparse signal in transform domains, a novel method is presented to improve the sparsity of the non-sparse representation of a signal. The method employs a movable window function to decompose the non-sparse representation of a signal in transform domains into multiple window-cutting representation, as long as the width of each window function is far less than the length of the signal, and then each window-cutting representation has good sparsity. The compressed sensing of non- sparse representation is realized by the sparse window-cutting representations. The detailed theoretical analysis using Gausian and rectangle window functions is presented and the experimental results of both noise-free image and noise-added image demonstrate that the method is valid.