Fluoresenssidatan mallinnus ja inversio optisessa projektiotomografiassa

Optical projection tomography (OPT) is a biomedical imaging technique that uses visible and near-infrared light to investigate the spatial distribution and shapes of objects contained in a sample. It bears close resemblance to the better known X-ray computed tomography used in medical applications as well. The OPT imaging methods come in roughly two varieties: the transmission and fluorescent modes. This thesis focuses on developing a forward model for measurement data generation in the latter case. Additionally the inversion of the model using an iterative approach is discussed. The presented model is based on the generalisation of the Radon transform. While the attenuation of electromagnetic radiation is satisfactorily described by the simple Radon transform, the fluorescent case relies on a type of attenuated Radon transform. The object of interest in fluorescent OPT is the emission function describing the locations and strengths of fluorescent sources within the sample, whereas the attenuation function central to transmission mode is more of a parameter to the model. For these reasons the inversion of these models differ from each other. The transmission mode OPT can be inverted using the filtered backprojection method, perhaps the most popular technique in applications. The different forward model, however, implies that this is not sufficient in the fluorescent case. Following earlier work in the context of X-ray fluorescent computed tomography, an iterative inversion procedure is varied by the application of attenuation recovery and relaxation and the methods are compared in numerical experiments. Using both techniques results in significant improvements in the reconstruction mean squared error compared to the backprojection and other variations of the iterative method