最小L1范数实现周期非均匀采样与重构研究

根据周期非均匀采样需要多个采样通道的特点,利用联合子空间理论将采样与重构转换为矩阵向量运算。结合最小L1范数算法,提出了一种针对稀疏信号的周期非均匀采样与重构方法,分析了最小L1范数算法在周期非均匀采样系统中的完整重构条件。最后,以多带正弦信号为例,分别从可完整重构概率和系统整体验证两个方面证明了该方法能够实现稀疏信号的采样与重构。

Periodic Non-Uniform Sampling and Reconstruction Based on Minimum L1 Normal

A method to realize the sampling and reconstruction of the sparse signals is proposed in this paper based on minimum L1 normal. According to the feature of periodic non-uniform sampling that it needs multiple channels,the sampling and reconstruction of signals are transformed into matrix and vector operations by using theory of union of subspaces. Necessary condition of reconstruction is analyzed. Finally, taking multi-band sinusoidal signals as an example, we prove that the method can achieve the sampling and reconstruction of sparse signals.