Sub-Nyquist Sampling Recovery Algorithm Based on Kernel Space of the Random-compression Sampling Value Matrix
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摘要:
针对现有调制宽带转换器亚奈奎斯特采样重构算法性能不高问题，该文提出一种基于采样值核空间的支撑重构算法和随机压缩降秩方法，将两者结合得到一种高性能采样重构算法。首先利用随机压缩变换在不改变未知矩阵稀疏特性的前提下将采样方程转化为多个新的多测量向量问题，然后利用采样值矩阵核空间与采样矩阵支撑正交的关系获取联合稀疏支撑集，最后通过伪逆完成重构。从理论和实验两个方面对所提方法进行了分析和验证。数值实验表明，与传统重构算法相比，所提算法提高了重构成功率、降低了高概率重构所需的通道数，而且重构性能总体上随压缩次数增加而提高。
Abstract:To solve the low performance problem of the existing Modulated Wideband Converter (MWC)-based sub-Nyquist sampling recovery algorithm, this paper proposes a support recovery algorithm based on the kernel space of sampling value and a random compression rank-reduction idea. Combining them, a high-performance sampling recovery algorithm is achieved. Firstly random compression transforms are used to convert the sampling equation into several new multiple-measurement-vector problems, without changing the sparsity of the unknown matrix. Then the orthogonal relationship between the kernel space of sampling value and the support vectors of sampling matrix is utilized to obtain joint sparse support set of the unknown. The final recovery is performed by the pseudo inversion. The proposed method is analyzed and verified by theory and experiment. Numerical experiments show that, compared with the traditional recovery algorithm, the proposal can improve the recovery success rate, and reduce the channel number required for high-probability recovery. Furthermore, in general, the recovery performance improves with the rise of compression times.
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