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

EAGER：用于稀疏频谱估计的 Ultra-FFAST 别名代码：下一代压缩感知

• 批准号: 1439725
• 负责人: Kannan Ramchandran
• 金额: $ 20万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-01 至 2016-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1439725&HistoricalAwards=false
• 关键词: EAGER; Ultra; FFAST; Alias; Codes

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.

本课题针对超大尺度稀疏信号恢复和频谱估计问题的理论基础和算法设计，在MRI快速采集、认知无线电低功率频谱感知、深空探测低功率光谱等方面的应用。虽然压缩感知最近成为理解稀疏信号处理基本限制的强大框架，但目前基于凸优化的算法难以有效扩展。因此，本提案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。该方案为超大规模稀疏信号恢复和频谱估计问题提供了数学基础和实用的亚线性时间算法。理论和算法是通过跨学科的混合智力工具从编码理论，图论，数论，和统计信号处理推导出来的。这导致了被称为稀疏图别名码的新计算原语的提出，它类似于彻底改变了现代通信系统的低密度奇偶校验（LDPC）码。所提出的框架预计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；计算和能源效率；（三）性能保证和稳定性。