CAREER: Theoretical Framework for Design and Analysis of Snapshot Compressive Imaging Systems

捕获高分辨率3D数据立方体，如视频文件或高光谱图像，是从医学到机器人等许多现代应用的关键要求。然而，由于传感器阵列通常只能获取2D图像，捕获此类数据立方体通常需要沿着第三维扫描，这使得该过程耗时、昂贵且无效。解决这一挑战并实现高效3D成像的一个新兴解决方案是所谓的快照压缩成像（SCI）。在SCI解决方案中，数据采集硬件设计用于捕获编码的2D图像，该图像总结了3D数据立方体中包含的全部信息。然后使用复杂的计算解码算法从单个2D投影重建所需的3D数据立方体。与此类解码问题相关的大多数理论和算法问题仍然广泛开放。在缺乏对问题的坚实理论理解的情况下，现有的解决方案通常是启发式的方法，这些方法在计算上非常密集，效率低下，而且不是最优的。该项目的目标是通过解决相关的基本问题，实现经济、可靠和高效的脊髓损伤成像。这些解决方案可以影响广泛的应用，从医疗诊断到机器人再到农业。为了开发适用于广泛应用的全面实用和强大的SCI解决方案，需要一个新的理论框架，使研究人员能够设计和优化i)受系统硬件约束的3D到2D投影步骤，ii)计算效率高的恢复算法，可以从单个2D测量重现高质量的3D数据立方体。本提案的主要目标是提供这样一个理论平台，使研究人员能够设计，分析和优化SCI系统。为了实现这一目标，研究团队的目标是：1)描述SCI系统参数之间的基本权衡，如投影映射、三维数据立方体结构、可实现的重建质量和分辨率；ii)开发一种自动化的、有理论基础的、高效的结构学习方法，适用于SCI应用中遇到的各种类型的三维数据立方体；iii)设计破坏性的SCI解决方案，将开发的自动结构学习方法纳入有效的近最优SCI恢复算法，该算法执行接近特征基本极限。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Capturing high-resolution 3D data cubes, such as video files or hyperspectral images, is a key requirement in many modern applications, ranging from medicine to robotics. However, since sensor arrays can typically acquire only 2D images, capturing such data cubes often requires scanning along the third dimension, which makes the process time-consuming, costly, and ineffective. One emerging solution to address this challenge and enable efficient 3D imaging is the so-called snapshot compressive imaging (SCI). In SCI solutions, the data-acquisition hardware is designed to capture an encoded 2D image that summarizes the full information contained in the 3D data cube. The desired 3D data cube is later reconstructed from a single 2D projection using complex computational decoding algorithms. Most theoretical and algorithmic questions related to such decoding problems are still widely open. In the absence of a solid theoretical understanding of the problem, existing solutions are generally heuristic methods that are computationally very intensive, inefficient, and sub-optimal. The goal of this project is to enable cost-effective, reliable, and efficient SCI imaging by addressing the related fundamental questions. Such solutions can impact a wide range of applications, from medical diagnosis to robotics to agriculture.To develop fully practical and robust SCI solutions applicable in a wide range of applications, a novel theoretical framework is required that enables researchers to design and optimize i) the 3D to 2D projection step subject to the hardware constraints of the system, and ii) computationally efficient recovery algorithms that can reproduce a high-quality 3D data cube from a single 2D measurement. The main goal of this proposal is to provide such a theoretical platform that enables researchers to design, analyze, and optimize SCI systems. To achieve this goal, the team of researchers aim at i) characterizing the fundamental trade-offs between the parameters of SCI systems, such as projection mapping, 3D data-cube structure, and achievable reconstruction quality and resolution; ii) developing an automated, theoretically-founded, and efficient approach to structure learning that is applicable to various types of 3D data cubes encountered in SCI applications; and iii) designing disruptive SCI solutions that incorporate the developed automated structure-learning method into an efficient near-optimal SCI recovery algorithm that performs close to the characterized fundamental limits.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.