  Interventional C-arm systems allow flexible 2-D imaging of a 3-D scene while
being capable of cone beam computed tomography. Due to the flexible structure
of the C-arm, the rotation speed is limited, increasing the acquisition time
compared to conventional computed tomography. Therefore, patient motion
frequently occurs during data acquisition inducing inconsistencies in the
projection raw data. A framework using Grangeat's theorem and epipolar
consistency was successfully applied for compensating rigid motion. This
algorithm was efficiently parallelized, however, before each iteration, the
pseudoinverse of each projection matrix must be calculated. We present a
geometric modification of the presented algorithm which can be used without a
pseudo-inverse. As such, the complete algorithm can be implemented for
low-level hardware without the need of a linear algebra package that supports
the calculation of matrix inverse. Both algorithms are applied for head motion
compensation and the runtime of both is compared.
