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

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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.