A method is based on first projection data, recorded during a relative rotational movement between an x-ray source of a CT device and at least one examination object lying partly outside the field of view of the CT device. Contour data of the surface of the examination object is useable to enhance the reconstruction of the incomplete first projection data. The spatial correlation between the first projection data and the contour data is known. The first projection data is expanded by way of the contour data to modified projection data, so that the modified projection data includes information about the contour of the examination object lying outside the field of view of the CT device. In an embodiment of the inventive reconstruction of image data by way of the modified projection data, fewer or no artifacts occur by comparison with reconstruction of image data from just the first image data.