Distributed Compressive Sensing: Theoretical Limits and Algorithmic Approaches

从信息论和统计物理的角度研究了分布式压缩感知的理论极限，包括无噪声分布式压缩感知和有噪声分布式压缩感知。利用这些理论知识，设计了具有可行计算复杂度的大型分布式压缩感知网络联合恢复的近似消息传递算法。这些算法使我们能够从统计力学的角度验证复制品方法得到的非严谨结果，并为采样和低复杂度信号恢复提出理论上的最优方法。所提出的研究将改进分布式压缩感知重建算法的性能，例如更高的压缩比和/或更高的重建保真度。

The theoretical limits of distributed compressive sensing are studied by tools from both information theory and statistical physics.The investigations cover both noise-free and noisy distributed compressive sensing. The theoretical insights are utilized to design approximate message passing algorithms for joint recovery of large distributed compressive sensing networks with feasible computational complexity. These algorithms enable us to verify the non-rigorous results obtained by the replica method from statistical mechanics, and also, to propose theoretically optimal approaches for sampling and low-complexity signal recovery. The proposed research will lead to improved performance of reconstruction algorithms for distributed compressive sensing, e.g. higher compression rates and/or higher fidelity of reconstruction.