Sampling and Discretization Problems in X-ray-CT

Today, in medical X-ray-CT, the image reconstruction is almost without exception carried out with the aid of digital computers. Discretizational questions have therefore a central significance in CT. On the one hand the discretization of the measured values should be fine enough to ensure sufficient resolution with adequate freedom from artifacts due to the discretization and on the other, the increase in the patient’s dose associated with greater fineness of the discretization as well as the increased technical sophistication must not exceed certain limits. Thus, the discretization problem becomes a problem of optimizing image quality and expenditure. The most effective aid in dealing with discretization problems is the sampling theorem (see also [l, 2, 3]). Using the sampling theorem, the propagation of discretization errors from the measuring process up to the final image are systematically pursued, if indeed, only in the still relatively simple parallel scanner principle (Fig. l). Additional complications, characteristic of fan-beam machines will be examined in Section 6.