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

计算成像是一个快速增长的领域，它试图通过将成像视为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：基于模型和基于学习。基于模型的方法利用分析信号特性，通常具有理论保证和见解。基于学习的方法通过在大型数据集上进行训练，利用数据驱动的表示来获得最佳经验性能。该项目通过制定一个统一的框架，提供了一个基于学习的扩展到经典的成像理论，调和这两种观点。研究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性影响，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磁共振成像中的患者舒适度。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。目前的算法对于处理包含数十亿个变量的3D（空间）、4D（空间-时间）或5D（空间-时间-频谱）数据集也是不切实际的。该项目开发的框架通过集成物理和学习模型来快速处理大规模数据集，从而解决了这一差距。该框架还提供了新的理论见解和严格的性能保证时，结合基础模型的数学条件。该框架将在新兴应用中实现高分辨率计算成像，如动态和定量磁共振成像，X射线显微镜和低温电子显微镜。虽然该项目明确寻求对计算成像的影响，但它有潜力通过对音频和语音，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，并被认为值得通过使用基金会的智力价值和更广泛的影响评审标准进行评估来支持。

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.