Combining Knowledge And Data Driven Approaches to Inverse Imaging Problems

成像在自然科学、医学和生命科学以及工程和工业应用的许多应用中起着重要作用。一个例子是医生用来检测脑肿瘤如胶质母细胞瘤的大脑MRI图像。在许多成像应用的核心是逆问题，即从由成像机器（例如MRI机器）产生的数据重建图像的数学问题。这种逆成像问题已经以“知识驱动”的方式使用关于设备和成像过程的信息来处理多年。然而，知识驱动的模型不能总是被解决，计算非常昂贵，或提供次优的images.In近年来，新的“数据驱动”的方法，它使用过去的成功重建图像的例子与产生它们的数据，已被证明在图像重建产生一些令人印象深刻的结果。然而，这种数据驱动方法的问题是，目前它们没有“数学保证”，换句话说，人们无法说明结果的可靠程度。它们还有一个特性，即使数据中的微小偏差也可能导致结果的巨大差异。这显然可能对许多应用产生破坏性影响。在本提案中，我们将开发一种新的混合方法，该方法结合了最好的知识驱动和数据驱动的方法来解决逆成像问题，关键是提供必要的数学保证，以便能够在现实世界的应用中使用这些方法。一旦完成了开发这些数学方法的挑战性任务，我们将应用这种学习来产生一个成像管道，将成像过程的各个阶段引入一个步骤，从而进一步优化该过程。我们将把新方法应用到实际应用中。例如，使用项目中开发的数据驱动数学方法，并与放射科密切合作，我们将创建一个端到端的工作流程，其中联合执行多模式图像采集、重建、分割和图像分析，并针对转移性癌症患者的真实的时间治疗反应评估的最终任务进行优化。

Imaging plays an important role in many applications in the natural sciences, medicine and the life sciences, as well as in engineering and industrial applications. An example is an MRI image of a brain used by a physician to detect a brain tumour such as glioblastoma. At the core of many imaging applications is an inverse problem, i.e. the mathematical problem of reconstructing the image from data produced by the imaging machine, for example the MRI machine. Such inverse imaging problems have been approached for many years in a "knowledge-driven" way, using information about the device and the imaging procedure. However, the knowledge-driven models cannot always be solved, are computationally very expensive, or deliver suboptimal images.In recent years, new "data-driven" methods, which use past examples of successfully reconstructed images together with the data that produced them, have been shown to produce some impressive results in image reconstruction. The problem with such data-driven methods, however, is that currently they do not have "mathematical guarantees", in other words one cannot state the degree to which the results are reliable. They also have the property that even small deviations in the data could result in large differences in the results. This clearly could have devastating implications for many applications.In this proposal, we will develop a new hybrid approach that combines the best of knowledge-driven and data-driven methods for inverse imaging problems, crucially providing the mathematical guarantees essential to being able to use the methods in real-world applications. Once the challenging task of developing these mathematical methods is achieved, we will apply this learning to produce an imaging pipeline that draws into a single step the stages of the imaging process, thus optimising the process further. We will apply the new methods to real-world applications. For example, using the data driven mathematical methods developed in the project and working closely with the Radiology Department, we will create an end-to-end workflow where multi-modal image acquisition, reconstruction, segmentation and image analyses are performed jointly and optimised for the end task of real time treatment response assessment in patients with metastatic cancer.