Design criteria for geometrical calibration phantoms in fan and cone beam CT systems
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Peter Jonas
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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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- TGV-based multiplicative noise removal approach: Models and algorithms
- Design criteria for geometrical calibration phantoms in fan and cone beam CT systems
- Under-relaxed quasi-Newton acceleration for an inverse fixed-point problem coming from Positron Emission Tomography
- An adaptive iteration reconstruction method for limited-angle CT image reconstruction
- Accuracy estimates of regularization methods and conditional well-posedness of nonlinear optimization problems
- A non-smooth and non-convex regularization method for limited-angle CT image reconstruction
- Optimization analysis of the inverse coefficient problem for the nonlinear convection-diffusion-reaction equation
- A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation
- A numerical algorithm for constructing an individual mathematical model of HIV dynamics at cellular level
Artikel in diesem Heft
- Frontmatter
- TGV-based multiplicative noise removal approach: Models and algorithms
- Design criteria for geometrical calibration phantoms in fan and cone beam CT systems
- Under-relaxed quasi-Newton acceleration for an inverse fixed-point problem coming from Positron Emission Tomography
- An adaptive iteration reconstruction method for limited-angle CT image reconstruction
- Accuracy estimates of regularization methods and conditional well-posedness of nonlinear optimization problems
- A non-smooth and non-convex regularization method for limited-angle CT image reconstruction
- Optimization analysis of the inverse coefficient problem for the nonlinear convection-diffusion-reaction equation
- A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation
- A numerical algorithm for constructing an individual mathematical model of HIV dynamics at cellular level
