CAREER: Reconciling Model-Based and Learning-Based Imaging: Theory, Algorithms, and Applications

计算成像是一个快速发展的领域，它试图通过将成像视为一个计算问题来增强成像仪器的能力。目前有两种不同的方法来设计计算成像方法：基于模型的和基于学习的。基于模型的方法利用分析信号属性，通常带有理论保证和洞察力。基于学习的方法通过对大数据集的训练，利用数据驱动的表示法来获得最佳的经验性能。这个项目通过制定一个统一的框架来调和这两种观点，该框架提供了对经典成像理论的基于学习的扩展。这些结果将在广泛的科学、工程和生物医学应用中产生广泛的用途和变革效应，例如3D活细胞成像、复杂材料的结构分析、阿尔茨海默病的早期诊断以及改善患者在磁共振成像中的舒适度。该项目还将为扩大研究参与、改善工程教育和参与学术界创造独特的机会。目前的计算成像理论不足以分析最近的学习算法。目前的算法也不适用于处理包含数十亿变量的3D(空间)、4D(空间-时间)或5D(空间-时间-频谱)数据集。该项目开发的框架通过集成物理模型和学习模型来快速处理海量数据集，从而弥补了这一差距。当与底层模型的数学条件相结合时，该框架还提供了新的理论见解和严格的性能保证。该框架将在动态和定量磁共振成像、X射线显微镜和低温电子显微镜等新兴应用中实现高分辨率计算成像。虽然这个项目明确寻求对计算成像的影响，但它有可能通过对音频和语音、通信理论和图形结构信号的概括来转换更广泛的信号和信息处理。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Computational imaging is a rapidly growing area that seeks to enhance the capabilities of imaging instruments by viewing imaging as a computational problem. There are currently two distinct approaches for designing computational imaging methods: model-based and learning-based. Model-based methods leverage analytical signal properties and often come with theoretical guarantees and insights. Learning-based methods leverage data-driven representations for best empirical performance through training on large datasets. This project reconciles both viewpoints by formulating a unifying framework that provides a learning-based extension to the classical imaging theory. The results will have broad use and transformative effects across a wide range of scientific, engineering, and biomedical applications, such as 3D live-cell imaging, structural analysis of complex materials, early diagnosis of Alzheimer disease, and improved patient comfort in magnetic resonance imaging. The project will also create unique opportunities for broadening research participation, improving engineering education, and engaging the academic community.The current theory of computational imaging is inadequate for analyzing recent learning algorithms. Current algorithms are also impractical for processing 3D (space), 4D (space-time), or 5D (space-time-spectrum) datasets containing billions of variables. The framework developed in this project addresses this gap by integrating physical and learned models for fast processing of massive datasets. The framework also offers new theoretical insights and rigorous performance guarantees when combined with mathematical conditions on the underlying models. The framework will enable high-resolution computational imaging in emerging applications, such as dynamic and quantitative magnetic resonance imaging, x-ray microscopy, and cryogenic electron microscopy. While this project explicitly seeks impact on computational imaging, it has the potential to transform broader signal and information processing via generalizations to audio and speech, communication theory, and graph structured signals.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.