Collaborative Research: CIF: Medium: Taming Deep Unsupervised Representation Learning in Imaging: Theory and Algorithms

深度神经网络正在推动工程和科学应用领域的重大突破。它们的成功通常取决于能否获得大量高质量的数据集。然而，对于许多反问题或分类问题，如计算机断层扫描（CT）、磁共振成像（MRI）和冷冻电子显微镜（cryo-EM），获得配对训练数据可能非常困难或昂贵。训练数据也可能是有限的或严重损坏的。虽然最近的进展通过深度图像先验或自监督学习等方法解决了这些挑战，但其中的训练过程往往是临时的，并且这些方法背后的潜在机制远未得到很好的理解，这是由于缺乏精确的数学建模和对学习表征的理解。为了应对这些挑战，该项目旨在开发强大的无监督深度学习方法，通过结合物理模型和约束，有效地捕获内在数据结构和不变性，在有限和损坏数据的环境中提供严格的保证。将在各种成像应用中展示所开发方法的效用，并将广泛传播所产生的结果和软件。此外，该项目将开发一个新的教育计划，包括每年一次的全球参与的虚拟研讨会，并在密歇根州东南部有针对性的K-12外展，以提高机器学习和计算项目的参与度，特别是来自代表性不足的学生。该项目旨在开发鲁棒的、无监督的深度表示学习方法，并为医疗、工业和科学成像中的反问题或分类问题提供严格的保证。重点将放在从有限和/或损坏的未配对数据中学习深度模型上。通过利用传统浅层学习方法（例如字典/转换学习）的思想，将设计和学习深度表示来捕获数据的内在结构和低维度。通过理解在深度表示学习的不同阶段捕获的图像特征，将结合物理模型、先验和约束，使深度网络能够从损坏的数据中有效地学习。深度表示也将被设计成对典型的对称歧义（如平移和旋转）不变性。基于这种原则性的建模，将开发出高效、鲁棒的优化方法，为学习数据的内在结构提供理论保证，并将开发的方法应用于各种成像问题。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。

Deep neural networks are driving significant breakthroughs across engineering and scientific applications. Their success is often predicated on the availability of large and high-quality data sets. However, for many inverse problems or classification problems such as in computed tomography (CT), magnetic resonance imaging (MRI), and cryo-electron microscopy (cryo-EM), obtaining paired training data can be extremely difficult or expensive. The training data may also be limited or highly corrupted. While recent progress addresses these challenges via methods such as deep image prior or self-supervised learning, the training procedures therein are often ad hoc and the underlying mechanisms behind the approaches are far from well-understood, which are due to the lack of precise mathematical modeling and the lack of understanding of learned representations. To deal with these challenges, this project aims to develop robust unsupervised deep learning methods with rigorous guarantees in settings with limited and corrupted data by incorporating physical models and constraints that capture the intrinsic data structures and invariances effectively. The utility of the developed methods will be demonstrated on a variety of imaging applications, and the resulting findings and software will be widely disseminated. Furthermore, this project will develop a new educational program involving yearly virtual workshops with global participation and targeted K-12 outreach in southeast Michigan to enable improved participation in machine learning and computing programs, especially from underrepresented students.This project aims to develop robust, unsupervised deep representation learning methods with rigorous guarantees for application in inverse problems or classification problems in medical, industrial, and scientific imaging. The focus will be on learning deep models from limited and/or corrupted unpaired data. Deep representations will be designed and learned to capture the intrinsic structures and low-dimensionality of the data by leveraging ideas from traditional shallow learning methods (e.g., dictionary/transform learning). By understanding image characteristics captured during different stages of deep representation learning, physical models, priors, and constraints will be incorporated that enable deep networks to be learned efficiently from corrupted data. The deep representations will also be designed to be invariant to typical symmetry ambiguities such as translations and rotations. Based upon such principled modeling, efficient and robust optimization methods will be developed with theoretical guarantees for learning the intrinsic structures of the data, and the developed methods will be applied to a variety of imaging problems.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.