Abstract
Abstract Image quality in tomographic applications depends strongly on the precise knowledge of the geometrical parameters of x-ray source and detector. However, in some situations these geometrical data are not immediately available. One way to overcome this problem is to use calibration phantoms which consist of several opaque markers in a known geometry. A main question is what properties are needed in order to reliably determine the searched for geometry data. In this paper we give sufficient conditions for the calibration phantom such that the reconstruction problem has a unique solution. We also use our theoretical approach to derive a numerical method which can determine the needed geometry data. Our analyses show that this numerical method is stable and that the solutions are as good as those of standard nonlinear procedures like Gauss–Newton-type methods. Furthermore, our new algorithm is much faster than standard methods and it also does not depend on initial values.
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