Computational methods in medical imaging

我们建议研究医学成像中的计算和数学方法。这项研究是由核医学的应用程序推动的，特别是SPECT(单光子发射计算机断层扫描)，尽管我们的许多结果也应用于其他图像方式，如PET和MRI。我们的主要数学兴趣在于动态SPECT成像。在静态成像中，从患者扫描期间获得的数据重建单个图像；在动态情况下，相同的数据被用于重建3D图像序列(即3D电影)，以显示物质摄取和洗出的动态行为，向医生指示关于器官的功能信息。这是一个不适定的逆问题，挑战是没有足够的数据来确定未知数。因此，必须将附加信息合并到解决方案算法中，以排除物理上没有意义的可能解决方案。我们的方法要么是随机性质的(卡尔曼滤波)，要么是基于大规模约束优化方法。

We propose to investigate computational and mathematical methods in medical imaging. The research is driven by applications from nuclear medicine, in particular SPECT (single photon emission computed tomography), although many of our results have applications to other image modalities such as PET and MRI. Our main mathematical interest lies in dynamic SPECT imaging. In static imaging, one single image is reconstructed from the data obtained during a patient scan; in the dynamic case, the same data are used to reconstruct a sequence of 3-D images (i.e., a 3D movie) to show the dynamic behaviour of uptake and wash-out of substances, indicating to the physician functional information about the organs. This is an ill-posed inverse problem, with the challenge of not having enough data to determine the unknowns. Hence, additional information must be incorporated into the solution algorithms to exclude possible solutions which are not physically meaningful. Our approaches are either of a stochastic nature (Kalman filter) or will be based on large scale constrained optimization methods.