Optimization of derivative kernels for exact cone-beam ROI reconstruction in spiral computed tomography

A recent comparison study showed that exact, FBP-based solutions of the long object problem are numerically stable and that their image quality is mostly affected by filter design. In this paper the impact of the kernel design on image quality is demonstrated systematically in the case of the local ROI algorithm. First of all the implementation is improved by use of the Linogram technique to eliminate interpolations in the filter step and to speed up computation. In the case of the local ROI method favorable kernels for 1-D partial derivatives have to be designed. Finite differences are fast to compute but cause ringing artifacts. More sophisticated kernels can be designed in a straightforward manner in Fourier space identifying the window function most appropriate to a given application. No ringing artifacts are observed for the windowed kernels under investigation. In addition, windowed kernels are superior to the finite differences regarding the spatial resolution versus noise properties. For partial derivatives in directions with data truncation the projection data have to be extrapolated before convolution. Alternatively, very short derivative kernels can be used, generally at a decreased image quality. Kernels of different design and length can be combined.