Distributed Compressive Sensing: Theoretical Limits and Algorithmic Approaches

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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.