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.

我的研究在成像中深度学习和反问题的交集中有效。解决逆问题是通过（通常）已知的向前模型计算间接测量的未知物理量的任务。一个典型的例子是，当成像技术用于医学，工程，天文学和地球物理时。有趣的逆问题几乎总是不适合，并且在决策制定基于恢复的图像的应用中解决这一点至关重要。特别是，有时恢复的数据不足以准确解决重建问题，并且必须将有关对象的某种形式的先验知识纳入解决方案过程中。为这些情况开发新的和改进现有的方法是我项目的目的。提出的方法使用深度学习方法来学习生成模型。生成模型隐含地模拟了来自观测值的数据的高维分布。然后，在解决逆问题时，可以将学习的分布用作先验，以确保解决方案可行。博学的先验者可以提供比先前的手工制作的更具体信息，同时保持远期问题的变化灵活。例如，我们可以学习一个生成模型，该模型可以产生所有可行的脑心脏和肺CT图像。然后，从CT扫描仪接收低辐射剂量数据，我们搜索可行图像集以找到最适合数据的图像。尽管提供了少量数据，但最终的图像仍将是高质量的。新型工程和/或物理科学研究的范围很广。找到最适合数据的生成模型产生的图像所需的优化既是非线性和非凸问题，并且需要应用或开发最先进的技术。需要数值分析工具来绑定错误和收敛。还需要开发与计算机科学家紧密合作的数学方法，以检查并确保生成模型可以生成地面真相图像。这将增加一个快速增长的研究领域，包括各种自动编码器和生成对抗网络。