EAGER: A Multi-User Communication and Information Theoretic Approach to the Sparse Signal Recovery Problem

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This research project examines the theoretical, algorithmic, and computational issues that arise in compressed sensing (CS) and signal processing problems where there is a need to compute solutions to problems in which the solution vector has many zeros. In addition to the exciting compressed sensing area, this research will benefit numerous signal processing applications where the sparsity constraint on the solution vector naturally arises. Brain imaging techniques such as Magnetoencephalography (MEG) and Electroencephalography (EEG) are currently important examples. Sparse communication channels with large delay spread, high resolution spectral analysis, and direction of arrival estimation, are other important examples. An effective solution to this problem will have significant impact, by providing new and valuable tools to the practicing signal processing engineer. In addition, the tools will be of interest to researchers in cognitive science, neuroscience, and machine learning where sparsity issues naturally arise, such as sparse coding of signals in the brain or learning from data which is often assumed to lie on a low dimensional manifold. This project provides a comprehensive and tighter integration of the compressed sensing field and multi-user information theory. This makes it possible to utilize the rich results available in network information theory which have been successfully applied to the implementation of communication systems. The theoretical tools necessary to enable this integration are being developed by the investigators. This research enables significant advances in both theory and practice in the CS field. The information theoretic insights are leveraged to provide insights on performance limits and guidance on practical CS-based system design. The implementation experience gained from communication systems will be translated to practical algorithm development and efficient CS-based system design.