基于高度冗余Gabor框架的欠Nyquist采样系统子空间探测

Subspace Detection of Sub-Nyquist Sampling System Based on Highly Redundant Gabor Frames

基于指数再生窗Gabor框架的欠Nyquist采样系统对窄脉冲信号完成采样与重构一般情况下效果较好,但是当框架高度冗余时,使用传统面向系数域的方法对信号进行子空间探测会面临失败或较大误差。该文采用面向信号域的思想,构建了分块的对偶Gabor字典,并对信号分块稀疏表示;根据信号的分块表示推导了采样系统的测量矩阵,提出了测量矩阵受字典相干性约束的分块e-相干性;将信号合成模型引入多观测向量问题,提出基于分块e-闭包的同步正交匹配追踪算法(,B FSOMPe),用于信号子空间探测。此外还证明了算法的收敛约束条件。仿真结果表明,所提子空间探测方法相比传统方法提高了信号重构成功率,降低了采样通道数,并增强了系统鲁棒性。

The sampling system based on Gabor frames with exponential reproducing windows holds nice performance for short pulses in general cases, but when the frames are highly redundant, the traditional coefficient oriented methods for subspace detection may fail or have large error. Firstly, the signal oriented idea is introduced and the blocked dual Gabor dictionaries are constructed, finishing the block sparse representation. By introducing the blocked dictionaries, the measurement matrix is constructed and the block e-coherence restricted by the coherence of the dictionaries is proposed. Consequently, the synthesis model for signal representation is introduced to subspace detection based on Multiple Measurement Vector problem and the Simultaneous Orthogonal Matching Pursuit is proposed based on blocked e-closure（,B FSOMPe）, using for subspace detection. Additionally, the convergence of the algorithm is proved. At last, simulation experiments prove that the new method improves the recovery rate, decreases the channel numbers and enforces the robustness of the sampling system compared with the traditional methods.