Development of new mathematical models and algorithms for analysis of 3D images with applications to monitoring of stents

这个EPSRC iCASE学生奖学金项目位于数值分析和非线性系统的EPSRC战略领域，以医疗保健技术和数学科学为主题。它将通过开发和使用新的和先进的数学模型和算法来研究医疗保健应用中出现的图像分析问题。它的动机是分析和处理具有噪声和条纹伪影的CT图像的挑战，这些伪影使当前模型无法跟踪对象（器官）和金属对象（支架）。该项目将研究许多新的想法，旨在（i）消除或减少噪声和条纹伪影的影响，以便现有模型可以工作;（ii）使用几何和形状信息识别相关器官;（iii）使用图像配准思想跟踪器官变化;（iv）使用图像配准思想跟踪器官变化。（iv）评估深度学习（AI）在存在噪声和拖尾伪影的情况下用于分割任务的可行性。主要重点将放在数学发展和分析准确的，可变的，选择性的模型，可以采取事先信息和跟踪变化。研究了图像的分割、配准和融合等成像问题。我们的模型旨在处理纹理和强度不均匀性，以及不规则图案和金属伪影减少。为了解决由于金属物体导致的CT条纹伪影，我们考虑两种方法：一种是使用人工智能或几何形状来识别器官，另一种是通过重新分析和改进导致这种伪影的断层扫描模型来去除或减少这种伪影。噪声给可靠地分割对象的突出挑战增加了额外的难度，这将通过所谓的域方法来解决。最后，由于我们的监督团队有来自皇家利物浦大学医院的临床医生，我们将设计测试来验证我们的模型在项目期间。这将确保我们的自动分析和综合治疗/疾病进展的成像方法有助于优化治疗计划和监测，一个具体应用是使用一系列成像模式（CT、超声、MR）通过血管内密封治疗腹主动脉瘤。拟开发的方法将有助于更广泛的应用。

This EPSRC iCASE studentship project sits in the EPSRC strategic areas of Numerical Analysis and Non-linear systems, in the themes of Healthcare technologies and Mathematical Sciences. It will study image analysis problems, arising from Healthcare applications, by developing and using new and advanced mathematical models and algorithm. It is motivated by the challenges of analysing and tackling CT images that have noise and streaking artefacts, which render current models fail to track both an object (organ) and the metal object (stent). Many new ideas will be investigated in the project, aiming to (i) remove or reduce the influence of noise and streaking artefacts so that existing models might work; (ii) identify the concerned organs using geometry and shapes information; (iii) track the organ changes by employing image registration ideas; (iv) assess the feasibility of Deep Learning (AI) for the segmentation task in the presence of noise and streaking artefacts.Mathematically, the primary focus will be on mathematical development and analysis of accurate, variational, selective models that can take in prior information and track changes. Several imaging problems are studied and include segmentation, registration and fusion of images. Our models will aim to deal with texture and intensity inhomogeneity, as well as irregular patterns and metal artefact reduction. To tackle streaking artefacts of CTs due to metal objects, we consider two approaches: one to use artificial intelligence or geometry to identify organs and the other to remove or reduce such artefacts by re-analysis and improvement of the tomography models that lead to such artefacts in the first place. The noise adds extra levels of difficulty to the outstanding challenges of segmenting objects reliably which will be tackled by the so-called domain methods. Finally since our supervision team has clinicians from the Royal Liverpool University Hospital, we shall design tests to validate our models during the project. This will ensure that our imaging methods of automatic analyis and colligate treatment / disease progression will be useful to optimising treatment planning as well as monitoring, one specific application being the treatment of abdominal aortic aneurysms by endovascular sealing using a range of imaging modalities (CT, ultrasound, MR). The methodologies to be developed will be useful to a wider class of applications.