On Interpolation of Sparsely Sampled Sinograms

摘要

Certain situations, for instance in flat-panel cone beam CT, permit that only a relatively low number of projections are acquired. The reconstruction quality of the volume to be imaged is then compromised by streaking artifacts. To avoid these degradations, additional projections are interpolated between the genuinely acquired ones. Since straightforward linear, non-adaptive interpolation generally results in loss of sharpness, techniques were developed which adapt to, e.g., local orientation within the sinogram. So far, such directional interpolation algorithms consider only single local orientations. Especially in x-ray imaging, however, different non-opaque orientated structures may be superimposed. We therefore show how such multiply-oriented structures can be detected, estimated, and included in the interpolation process. Furthermore, genuine sinograms meet certain conditions regarding their moments as well as regarding their spectra. Moments of 2D sinograms depend on the projection angle in the form of sinosoids, while the Fourier spectrum of the sinogram takes the form of a 'bow tie'. The consistency of the interpolated data with these conditions may therefore be viewed as additional measures of the interpolation quality. For linear interpolation, we analyze how well the interpolated data comply with these constraints. We also show how the moment constraint can be integrated into the interpolation process.