To perform a perspective cone-beam backprojection of the
Feldkamp-type (FDK) the geometry of the approximately circular scan trajectory has to be available. If the system or the scan geometry is unknown and afflicted with geometric instabilities (misalignment) reconstructing a misaligned scan can cause severe artifacts in the
CT images. We propose an online and image-based iterative correction of a misaligned reconstruction geometry by using entropy minimization. Unlike current methods which use a calibration of the geometry for defined scan protocols and calibration phantoms, the proposed method is performed combining a simplex algorithm
for multi-parameter optimization and a graphics card (GPU)-based
FDK-reconstruction in an iterative scheme.
The simplex algorithm changes the geometric parameters of source and detector with respect to the reduction of entropy. In order to reduce the size of the dimensional space required for minimization the trajectory described by a subset of trajectory points. A virtual trajectory of an approximately circular path is generated after each
iteration of the algorithm. This method was validated using simulations and measurements performed on a Carm CT System equipped with a flat-panel detector (Axiom Artis, Siemens Healthcare, Forchheim, Germany).
Entropy was minimal for the ideal dataset, whereas strong misalignment resulted in a higher entropy value. The use of the
GPU-based reconstruction provided an online geometry correction after a total computation time of only 1-3 s using 100 to 300 iterations of the algorithm, depending on the degree of misalignment and initialization conditions.