Abstract: A method for determining attenuation coefficients for an object using a movable x-ray source and a detector for recording projections is provided. The method includes defining a trajectory for the movable x-ray source, defining filtering lines for the filtering of projection data, and defining positions on the filtering lines, at which the projection derivative is to be formed using a mathematical algorithm for a back-projection. The method also includes defining sampling positions on the trajectory, traversing, by the x-ray source, the trajectory and recording a projection for each sampling position. Projection derivatives with respect to the trajectory path are calculated numerically for each of the positions directly on the filtering lines, and using a mathematical algorithm, attenuation coefficients are determined for the object from the calculated projection derivatives, for the reconstruction.

Abstract: A method and an X-ray image acquisition system for the acquisition of X-ray images of a region of interest of an examination object from a multiplicity of angles of view for an 3-D image reconstruction are provided. The X-ray image acquisition system comprises an X-ray focus and an X-ray detector, which can be separately positioned and oriented relative to each other. The X-ray focus is moved along a combination of straight line segments and/or arc segments for the acquisition of X-ray images. The X-ray detector is oriented relative to the X-ray focus and moved in such a way that the region of interest is projected completely onto the X-ray detector upon each image acquisition.

Abstract: A method and a device for determining attenuation coefficients for an object using a movable X-ray source and a detector, which is provided for recording projections, is provided. The method includes specifying a trajectory for the movable X-ray source, specifying positions on the trajectory for determining a derivative of projections recorded by the detector, specifying a plurality of scanning positions for each of the specified positions, following the trajectory with the X-ray source and recording a projection for each scanning position, numerically calculating a projection derivative in relation to the trajectory path for each of the positions using the projections recorded for the associated plurality of scanning positions, and determining attenuation coefficients for the object from the calculated projection derivatives using a theoretically exact or approximate rule for the reconstruction.

Abstract: In a method for reconstructing a CT image from data acquired from an examination subject, a reconstruction algorithm is employed that is based on an ideal short-scan circle-and-line trajectory. To adapt the reconstruction algorithm to a “real world” scan trajectory, data are acquired with a C-arm CT apparatus wherein the focus is moved through an actual short-scan circle-and-line trajectory. For each position of the focus in the actual trajectory, a projection matrix is electronically generated and the reconstruction algorithm with the ideal trajectory is adapted to the actual trajectory using the projection matrices.

Abstract: In a method for reconstructing a CT image from data acquired from an examination subject, a reconstruction algorithm is employed that is based on an ideal short-scan circle-and-line trajectory. To adapt the reconstruction algorithm to a “real world” scan trajectory, data are acquired with a C-arm CT apparatus wherein the focus is moved through an actual short-scan circle-and-line trajectory. For each position of the focus in the actual trajectory, a projection matrix is electronically generated and the reconstruction algorithm with the ideal trajectory is adapted to the actual trajectory using the projection matrices.