Browsing by Author "Kainulainen, Henna"

In this thesis we consider dynamic X-ray computed tomography (CT) for a two dimensional case. In X-ray CT we take X-ray projection images from many different directions and compute a reconstruction from those measurements. Sometimes the change over time in the imaged object needs to be taken into account, for example in cardiac imaging or in angiography. This is why we're looking at the dynamic (something changing in time, while taking the measurements) case. At the beginning of the thesis in chapter 2 we present some necessary theory on the subject. We first go through some general theory about inverse problems and the concentrate on X-ray CT. We talk about ill-posedness of inverse problems, regularization and the measurement proses in CT. Different measurement settings and the discretization of the continuous case are introduced. In chapter 3 we introduce a solution method for the problem: total variation regularization with Barzilai-Borwein minimization method. The Barzilai-Borwein minimization method is an iterative method and well suited for large scale problems. We also explain two different methods, the multi-resolution parameter choice method and the S-curve method, for choosing the regularization parameter needed in the minimization process. The 4th chapter shows the materials used in the thesis. We have both simulated and real measured data. The simulated data was created using a rendering software and for the real data we took X-ray projection images of a Lego robot. The results of the tests done on the data are shown in chapter 5. We did tests on both the simulated and the measured data with two di erent measurement settings. First assuming we have 9 xed source-detector pairs and then that we only one source-detector pair. For the case where we have only one pair, we tested the implemented regularization method we begin by considering the change in the imaged object to be periodic. Then we assume can only use some number of consecutive moments, based on the rate the object is chancing, to collect the data. Here we only get one X-ray projection image at each moment and we combine measurements from multiple di erent moments. In the last chapter, chapter 6, we discuss the results. We noticed that the regularization method is quite slow, at least partly because of the functions used in the implementation. The results obtained were quite good, especially for the simulated data. The simulated data had less details than the measured data, so it makes sense that we got better results with less data. Already with only four angles, we cold some details with the simulated data, and for the measured data with 8 angles and with 16 angles details were also visible in the case of measured data.