Computational methods in medical imaging

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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.