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

这个EPSRC iCASE学生项目位于EPSRC数值分析和非线性系统的战略领域，主题是医疗技术和数学科学。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程序中出现的图像分析问题。它的动机是分析和处理含有噪声和条纹伪影的CT图像的挑战，这使得当前的模型无法同时跟踪对象(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，以使现有模型适用；(Ii)利用几何和形状信息识别相关器官；(Iii)利用图像配准思想跟踪器官变化；(Iv)评估深度学习(AI)在存在噪声和条纹伪影的情况下用于分割任务的可行性。数学上，主要关注于数学发展和分析准确的、变分的、选择性的模型，这些模型可以吸收先验信息并跟踪变化。研究了图像的分割、配准和融合等成像问题。我们的模型将致力于处理纹理和强度不均匀，以及不规则图案和金属伪影减少。为了处理由金属物体引起的CT条纹伪影，我们考虑了两种方法：一种是使用人工智能或几何来识别器官，另一种是通过重新分析和改进最初导致此类伪影的断层扫描模型来移除或减少此类伪影。噪声给可靠地分割目标这一突出挑战增加了额外的难度，这将由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，我们将在项目期间设计测试来验证我们的模型。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将有助于优化治疗计划和监测，其中一个具体应用是使用一系列成像方式(CT、超声波、MR)通过腔内封闭治疗腹主动脉瘤。将要开发的方法将对更广泛的应用程序有用。

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.