An X-ray CT apparatus adapted to compensate for projection data of a scanned object at a selected point located outside a detection range of an asymmetric CT detector in order to restore asymmetrically truncated imaging data, comprising: an X-ray source configured to project X-rays at the scanned object; an asymmetric CT detector configured to detect said X-rays and to generate helical cone-beam CT projection data of the scanned object wherein the asymmetric CT detector is asymmetrically displaced for a center line of the cone-beam; and a compensating unit including: means configured to determine for the selected point at least one complementary projection angle and coordinates of at least one complementary point based on a source projection angle and the coordinates of the selected point relative to the asymmetric CT detector; and means for calculating at least one weight corresponding to the at least one complementary point, said at least one weight being used to compensate for the unavailability of the projection data of the scanned object at the selected point in reconstructing an image of the scanned object, and wherein said compensating unit is configured to determine for the projection data at said selected point based on the generated projection data and based on coordinates of the selected point relative to the asymmetric CT detector. an X-ray source configured to project X-rays at the scanned object; an asymmetric CT detector configured to detect said X-rays and to generate helical cone-beam CT projection data of the scanned object wherein the asymmetric CT detector is asymmetrically displaced for a center line of the cone-beam; and a compensating unit including: means configured to determine for the selected point at least one complementary projection angle and coordinates of at least one complementary point based on a source projection angle and the coordinates of the selected point relative to the asymmetric CT detector; and means for calculating at least one weight corresponding to the at least one complementary point, said at least one weight being used to compensate for the unavailability of the projection data of the scanned object at the selected point in reconstructing an image of the scanned object, and wherein said compensating unit is configured to determine for the projection data at said selected point based on the generated projection data and based on coordinates of the selected point relative to the asymmetric CT detector. means configured to determine for the selected point at least one complementary projection angle and coordinates of at least one complementary point based on a source projection angle and the coordinates of the selected point relative to the asymmetric CT detector; and means for calculating at least one weight corresponding to the at least one complementary point, said at least one weight being used to compensate for the unavailability of the projection data of the scanned object at the selected point in reconstructing an image of the scanned object, and wherein said compensating unit is configured to determine for the projection data at said selected point based on the generated projection data and based on coordinates of the selected point relative to the asymmetric CT detector.