A method is for the reconstruction of an image data set from projection images of an examination object recorded at different projection directions with a computed tomography apparatus. In an embodiment, the method includes establishing an item of contour information describing a contour of at least one of the examination object and the additional object; enhancing projection data of the projection images via forward projection in regions in which at least one of the examination object and the additional object was not acquired; and reconstructing the image data set based upon the projection data enhanced. The examination object and the additional object are acquired from sensor data of at least one camera. Finally, an item of sensor information at least partially describing at least one of the is of the examination object and of the additional object being established and used for establishing the contour information.