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Medical CT aims at faster rotation speeds and a higher number of simultaneously acquired slices. These efforts are pushed further by cardiac CT (4D reconstruction) which is currently the most prominent special-purpose application in CT. Currently, 16-slice scanners and rotation times of below 0.5 s are state of the art. Scanners with far more slices have already been announced. Among those developments are prototypes with up to 256 slices. The basic requirements for image reconstruction are the support of circular, sequence and spiral scans. Arbitrary pitch selection is of high importance. Further, the complete area of the detector is to be exposed and each measured ray should contribute to the image to achieve optimized dose usage. Only approximate reconstruction approaches have the potential to handle all these requirements. Currently, the only known phase-correlated true cone-beam approach is an extension to the advanced single-slice rebinning (ASSR) algorithm. However, this generalized approach ASSR CI is limited to 32 slices. We have therefore developed a new approximate Feldkamp-type algorithm, the extended parallel backprojection (EPBP). Its main features are a phase-weighted backprojection and a voxel-by-voxel 180° normalization. The first feature ensures 3D and 4D capabilities with one and the same algorithm, the second ensures 100% detector usage (each ray counts!). The algorithm is evaluated using simulated circular, sequential and spiral data of a thorax phantom and of a cardiac motion phantom and measured patient data for scanners with up to 256 slices. The standard reconstructions (EPBP Std) are of excellent quality even for as many as 256 slices regardless of the scan trajectory. The cardiac reconstructions (EPBP CI) are of high quality as well and show no significant deterioration of objects even far off the center of rotation. Since EPBP CI uses the cardio interpolation (CI) phase weighting the temporal resolution is equivalent to that of the well known single-slice and multi-slice cardiac approaches 180°CI, 180°MCI, and ASSR CI, respectively, and lies in the order of 50 ms to 100 ms for rotation times between 0.375 s and 0.5 s.