EAGER: Ultra-FFAST Alias Codes for Sparse Spectrum Estimation: Next Generation Compressed Sensing

该提案针对超大规模稀疏信号恢复和频谱估计问题的理论基础和算法设计，并应用于快速MRI采集，认知无线电的低功率频谱感知和深空探测的低功率频谱。 虽然压缩感知最近已经成为理解稀疏信号处理的基本限制的强大框架，但基于凸优化的当前算法难以有效地扩展。 因此，该提议的动机是解决稀疏信号恢复问题的理论和设计中的规模挑战，目标是实现实时处理能力。 该建议为超大规模稀疏信号恢复和谱估计问题提供了数学基础和实用的次线性时间算法。 理论和算法是通过来自编码理论，图论，数论和统计信号处理的跨学科智能工具的混合而得出的。 这导致了被称为稀疏图别名码的新计算原语的提议，其类似于已经彻底改变了现代通信系统的低密度奇偶校验（LDPC）码。 所提出的框架被设想为在以下方面对下一代稀疏信号处理系统提供类似的影响：（i）采集开销;（ii）计算和能量效率;以及（iii）性能保证和稳定性。

This proposal targets the theoretical foundations and algorithmic design of ultra-large-scale sparse signal recovery and spectral estimation problems, with applications to fast MRI acquisition, low-power spectrum-sensing for cognitive radio, and low-power spectroscopy for deep-space exploration. While compressed sensing has recently emerged as a powerful framework for understanding the fundamental limits of sparse signal processing, current algorithms based on convex optimization, are difficult to scale efficiently. This proposal is motivated therefore to address the challenge of scale in the theory and design of sparse signal recovery problems, with the goal of enabling real-time processing capability. This proposal develops the mathematical foundations as well as practical sub-linear-time algorithms for ultra-large-scale sparse signal recovery and spectral estimation problems. The theory and algorithms are derived through an interdisciplinary mix of intellectual tools from coding theory, graph theory, number theory, and statistical signal processing. This leads to the proposal of new computational primitives dubbed as sparse-graph alias codes that are analogous to Low-Density-Parity-Check (LDPC) codes that have revolutionized modern communication systems. The proposed framework is envisioned to provide a similar impact on next-generation sparse signal processing systems with respect to (i) acquisition overhead; (ii) computational and energy efficiency; and (iii) performance guarantees and stability.