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

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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.