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

该研究项目探讨了压缩感知（CS）和信号处理问题中出现的理论，算法和计算问题，其中需要计算解决方案向量有许多零的问题。除了令人兴奋的压缩感知领域，这项研究将有利于许多信号处理应用的稀疏约束的解决方案向量自然出现。脑成像技术，如脑磁图（MEG）和脑电图（EEG）是目前重要的例子。具有大延迟扩展的稀疏通信信道、高分辨率频谱分析和到达方向估计是其他重要示例。一个有效的解决方案，这个问题将有重大的影响，通过提供新的和有价值的工具，实践信号处理工程师。此外，这些工具将引起认知科学、神经科学和机器学习领域研究人员的兴趣，这些领域自然会出现稀疏性问题，例如大脑中信号的稀疏编码或从通常假设位于低维流形上的数据中学习。该项目提供了压缩感知领域和多用户信息理论的全面和更紧密的结合。这使得有可能利用丰富的成果，可在网络信息理论已成功地应用到通信系统的实施。研究人员正在开发使这种整合成为可能所必需的理论工具。这项研究使CS领域的理论和实践都取得了重大进展。利用信息理论的见解，以提供洞察力的性能限制和指导实际CS为基础的系统设计。从通信系统中获得的实施经验将转化为实际的算法开发和有效的基于CS的系统设计。

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.