中文摘要：

针对窄脉冲信号的采样与重构,基于指数再生窗Gabor框架的欠Nyquist采样方法已经得到验证,但是当框架高度冗余时,使用传统方法对信号进行子空间探测会导致重构较大误差甚至失败。本文设计了分块的对偶Gabor字典,构建了基于该字典采样系统的重构模型;将分块思想引入冗余字典条件下信号空间投影,提出了基于Gabor分块字典的信号空间投影的SCoSaMP（simultaneous compressive sensing matching pursuit）算法,分析了算法的收敛条件;推导了噪声条件下基于近似oracle估计的误差边界,并对算法进行降噪分析。仿真结果表明,提出的子空间探测方法相比传统方法,提高了信号恢复精度,降低了采样通道数,并增强了系统的鲁棒性。

英文摘要：

For short pulses, it has been verified that the sub-Nyquist sampling system based on Gabor frames with exponential reproducing windows holds nice performance, but when the frames are highly redundant, the traditional methods for subspace detection may fail for have large errors. Firstly, we design the dual Gabor dictionaries, dividing it to blocks. Then the reconstruction model is built under the blocked dictionaries. Consequently, we introduce the signal space projection into the reconstruction model and propose simultaneous compressive sensing matching pursuit （SCoSaMP） based on block Gabor dictionaries signal space projection, with the converge restricted conditions analyzed. Additionally, the error bound based on oracle estimation is deduced when the sampling system is contaminated by noise, and the denoising method is analyzed. Finally, simulation experiments prove that the new method improves the recovery accuracy, decreases the channel number and enforces the robustness of the sampling system compared with the traditional methods.