Generative Models Applied to Inverse Problems

应用于反问题的生成模型

• 批准号: 2128682
• 金额: --
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2128682
• 关键词: Generative; Models; Applied; Inverse; Problems

My research works at the intersection of deep learning and inverse problems in imaging. Solving an inverse problem is the task of computing an unknown physical quantity given indirect measurements via a (usually) known forward model. A typical example is when imaging technologies are used in medicine, engineering, astronomy and geophysics. Interesting Inverse Problems are nearly always ill-posed and addressing this is critical in applications where decision making is based on the recovered image. In particular, sometimes the data recovered is not sufficient to solve the reconstruction problem accurately and some form of prior knowledge about the object must be incorporated in the solution process. Developing new and improving existing approaches to these cases is the aim of my project. The proposed approaches uses deep learning methods to learn a generative model. Generative models implicitly model high-dimensional distributions of data from observations. The learnt distribution can then be used as a prior when solving the inverse problem, ensuring solutions are feasible. Learnt priors could provide more specific information than that of a hand-crafted prior while remaining flexible to changes in the forward problem. For example, we could learn a generative model that can produce all feasible brain heart and lung CT images. Then receiving low radiation dose data from the CT scanner, we search through the set of feasible images to find the image that best fits the data. The resulting image will be high quality despite the small amount of provided data. There is wide scope for novel engineering and/or physical sciences research. The resulting optimisation required for finding the image produced by the generative model that best fits the data is both a non-linear and non-convex problem and will require application or development of state of the art techniques. Numerical analysis tools are needed to bound errors and convergence. Mathematical approaches working closely with computer scientists also need to be developed for checking and ensuring that the ground truth images can be produced by the generative model. This will add to a fast growing research area including variational autoencoders and generative adversarial networks.

我的研究工作是深度学习和成像逆问题的交叉点。解决反演问题是通过（通常）已知的正演模型计算给定间接测量的未知物理量的任务。一个典型的例子是成像技术应用于医学、工程、天文学和地球物理学。有趣的反问题几乎总是不适定的，在基于恢复图像进行决策的应用中解决这一问题至关重要。特别是，有时恢复的数据不足以准确地解决重建问题，并且必须在解决过程中结合某种形式的有关对象的先验知识。我的项目的目标是针对这些案例开发新的和改进现有的方法。所提出的方法使用深度学习方法来学习生成模型。生成模型隐式地对观测数据的高维分布进行建模。然后，在解决反问题时，可以将学习到的分布用作先验，确保解决方案可行。学习先验可以提供比手工制作的先验更具体的信息，同时对前向问题的变化保持灵活性。例如，我们可以学习一个生成模型，可以生成所有可行的脑、心和肺 CT 图像。然后从 CT 扫描仪接收低辐射剂量数据，我们搜索可行的图像集，找到最适合数据的图像。尽管提供的数据量很少，但生成的图像将是高质量的。新颖的工程和/或物理科学研究有广泛的范围。找到最适合数据的生成模型生成的图像所需的最终优化既是非线性又是非凸问题，并且需要应用或开发最先进的技术。需要数值分析工具来限制误差和收敛。还需要开发与计算机科学家密切合作的数学方法来检查和确保生成模型可以生成地面实况图像。这将增加一个快速发展的研究领域，包括变分自动编码器和生成对抗网络。