基于先验信息压缩感知SAR成像的信息理论限及实用算法研究

Embedding the target signal and structural prior information into CS-based SAR system is valuable to improve performance and robustness of SAR imaging. For the CS-based SAR imaging, the prior probability and structural information model of SAR object are established and the information-theoretic limits with prior information is deduced, then practical algorithm is designed to embed prior information. Rounding the information-theoretic limits of sparsity recovery with prior information, this research includes three associated parts. Firstly, the establishing of prior information model is groundwork. The prior probability is established by analyzing and adaptive study of object feature. The structural information is represented by tree-sparse model. Secondly, the deducing of information-theoretic limits is important. Based on prior information model, the information-theoretic limits is deduced by typical set theory and channel coding theorem. Lastly, the designing of practical algorithm is crucial. Guiding by information-theoretic limits, the practical sparsity recovery algorithm which embeds the prior information is designed by setting the weights. The research not only is very important for CS-based SAR imaging, but also is very valuable for CS-based radar system designing.

将目标信号先验概率及结构性先验信息嵌入压缩感知SAR成像系统，对改善成像性能和提升算法鲁棒性具有重要意义。本项目以压缩感知SAR成像为背景，通过建立雷达目标先验概率和结构相关信息模型，推导先验信息稀疏恢复的信息理论限，并设计嵌入先验信息的实用稀疏恢复算法。研究围绕基于先验信息稀疏恢复的信息理论限展开，包含相互联系的三个环节。其一，先验信息模型构建是前提。通过SAR目标特性分析和自适应学习方法确定目标先验概率，用树稀疏模型描述目标结构相关信息。其二，信息理论限推导是重点。基于先验信息模型，利用典型集理论和信道编码定理，推导基于先验信息稀疏恢复的信息理论限。其三，实用算法设计是关键。以信息理论限为指导，借助稀疏恢复中的权重系数，设计将先验信息嵌入算法流程的实用稀疏恢复算法。本项目研究不仅支撑压缩SAR成像，对指导基于压缩感知的雷达系统设计也具备重要指导价值。

压缩SAR成像的难点是降低采样数据率，针对此问题，研究围绕两个方面展开。一个是提出了基于One-Bit压缩感知的数据获取系统，用于对谱稀疏信号进行采样和重构。一个是分析了RLA阵列基于G-MUSIC算法DOA估计子的性能，包括估计子的一致性和MSE性能。.其一，One-Bit压缩感知提出的目标是缓解超宽带系统的数据率压力。受One-Bit压缩感知理论启发，提出了一个新的数据获取系统，用于对谱稀疏信号进行采样和重构。系统由一个随机解调器和一个One-Bit量化器组成。前者对信号进行压缩采样，后者对采样进行One-Bit量化。最终用二进迭代硬阈值算法恢复谱稀疏信号。实验证明，提出的方法是高效的，特别是在低信噪比、低比特预算和弱稀疏情况下。.其二，研究在单源情况下随机线性阵列的DOA估计性能。分析了基于G-MUSIC算法的DOA估计子的性能。与经典算法不一样的是，我们研究当阵元数和快拍数一致时的估计子性能。首先，提出了基于G-MUSIC算法的DOA估计子。然后，分析了该估计子的一致性，证明其具有概率意义下的收敛性。最后，推导估计子MSE的闭式表达，其MSE是信噪比、阵元 数与快拍数的比值以及阵元完好概率的函数。实验证明了本理论推导是正确的，对指导SAR雷达天线阵列的设计，分析随机线阵的DOA性能具有十分重要的价值。