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

这项研究解决了当(A)无法测量关键相位信息，以及(B)可用测量非常少时，测量系统设计和感兴趣的大规模结构化信号的恢复的基础科学。这项研究在技术文献中也被称为压缩相位恢复，它在光学、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都有应用。无法测量相位信息使得信号恢复问题特别具有挑战性。大多数以前的方法要么在计算上令人望而却步，因此很难扩展，要么基于没有性能保证的未经证实的启发式方法。相反，这项研究从根本上解决了压缩相位恢复系统在理论、设计、实验评估和应用方面的规模挑战和可证明的性能保证。这项研究为下一代压缩相位恢复系统奠定了理论和算法基础。这些是从编码理论、图论、统计信号处理以及它们集成到涉及光学成像和量子信息系统的应用中的工具的新的跨学科组合中衍生出来的。这项研究围绕着一种建立在稀疏图码族上的新范式，它代表了与现有方法的根本背离，这些方法要么基于计算密集型的凸松弛方法，要么基于没有性能保证的贪婪启发式方法。这项研究有可能彻底改变下一代压缩相位恢复系统的设计和应用，类似于低密度奇偶校验码(LDPC)如何在以下方面改变现代通信系统：(I)测量成本(接近基本极限)；(Ii)计算和存储成本(实现实时或近实时处理)；以及(Iii)可证明的性能保证(关于问题规模和对噪声的鲁棒性)。

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).