基于压缩感知的信号重构研究

按照Nyquist采样定理,信号的采样率必须为信号最高频率的2倍以上,这会产生大量的冗余数据。压缩感知是一种新兴的采样理论,对于可以稀疏表示的信号,它能够以远低于Nyquist采样速率对信号进行采样,并通过优化算法实现重构。介绍了压缩感知的基本理论,并分别选取时域稀疏、频域稀疏和图像信号进行了仿真分析,实验结果显示,压缩感知理论能较好的重构原始信号。

Research on Signal Reconstruction Based on Compressive Sensing

According to Nyquist sampling theorem, the signal sampling rate must be more than twice of the maximum signal frequency ,which will generate lots of redundant data.Compressive sensing is a novel sampling theory.For a signal in sparse representation, its sampling rate is far below the Nyquist sampling rate, and the signal can be reconstructed by optimization algorithm. This paper introduces the basic theory of compressive sensing and selects time domain sparsity, frequency domain sparsity and image signal for simulation analysis.The experimental results show that the compressive sensing theory can reconstruct the original signal effectively.