CIF:Small:Next-Generation Compressive Phase-Retrieval Using Sparse-Graph Codes: Theory, Design and Applications

CIF：Small：使用稀疏图代码的下一代压缩相位检索：理论、设计和应用

• 批准号: 1527767
• 负责人: Kannan Ramchandran
• 金额: $ 50万
• 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: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1527767&HistoricalAwards=false
• 关键词: CIF; Small; Next; Generation; Compressive

This research addresses the fundamental science of measurement system design and recovery of large-scale structured signals of interest when (a) critical phase information cannot be measured, and (b) very few measurements are available. Also known in the technical literature as compressed phase-retrieval, this research has applications to a plethora of important scientific fields like optics, quantum physics, bio-medical imaging, astronomy, and material science. The inability to measure phase information renders the signal recovery problem particularly challenging. Most prior approaches are either computationally prohibitive and therefore hard to scale, or based on unproven heuristics that come with no performance guarantees. In contrast, this research fundamentally addresses the challenge of scale together with provable performance guarantees in the theory, design, experimental evaluation, and applications of compressed phase-retrieval systems. This research addresses the theoretical and algorithmic foundations for next-generation compressed phase-retrieval systems. These are derived from a novel interdisciplinary mix of tools from coding theory, graph theory, statistical signal processing, as well as their integration into applications involving optical imaging and quantum information systems. The research revolves around a novel paradigm built on a family of sparse-graph codes that represent a radical departure from existing approaches based on either computationally intensive convex relaxation methods or greedy heuristics without performance guarantees. This research has the potential to revolutionize the design and applications of next-generation compressed phase retrieval systems, similar to how Low-Density-Parity-Check (LDPC) codes have revolutionized modern communication systems, with respect to (i) measurement cost (approaching the fundamental limits); (ii) computational and memory cost (enabling real-time or near-real-time processing); and (iii) provable performance guarantees (with respect to the problem scale and robustness to noise).

这项研究涉及测量系统设计的基础科学以及在（a）无法测量关键相位信息和（b）可用的测量很少时恢复感兴趣的大规模结构化信号。 这项研究在技术文献中也称为压缩相位检索，可应用于光学、量子物理、生物医学成像、天文学和材料科学等众多重要科学领域。 无法测量相位信息使得​​信号恢复问题特别具有挑战性。 大多数现有方法要么计算量大，因此难以扩展，要么基于未经证实的启发式方法，没有性能保证。相比之下，这项研究从根本上解决了规模挑战，并在压缩相位检索系统的理论、设计、实验评估和应用中提供了可证明的性能保证。 这项研究解决了下一代压缩相位检索系统的理论和算法基础。 这些源自编码理论、图论、统计信号处理的新型跨学科工具组合，以及它们与涉及光学成像和量子信息系统的应用的集成。 该研究围绕一种建立在一系列稀疏图代码之上的新颖范式展开，该范式与基于计算密集型凸松弛方法或没有性能保证的贪婪启发式方法的现有方法截然不同。 这项研究有可能彻底改变下一代压缩相位检索系统的设计和应用，类似于低密度奇偶校验（LDPC）码如何彻底改变现代通信系统，在（i）测量成本（接近基本限制）； (ii) 计算和内存成本（实现实时或近实时处理）； (iii) 可证明的性能保证（关于问题规模和对噪声的鲁棒性）。