Method and apparatus for exact cone beam computed tomography

A computed tomography method which comprises the steps of:

• generating, using a radiation source, a conical radiation beam which traverses an examination zone or an object present therein;
• generating a relative motion of the radiation source about the examination zone, which relative motion comprises a rotation about an axis of rotation and a displacement parallel to the axis of rotation and is shaped as a helix;
• acquiring measuring values which are dependent on the intensity of the radiation beam that traverses the examination zone and is incident on a detector unit during the relative motions;
• and
• reconstructing a CT image of the examination zone from the measuring values, in which reconstruction of an exact 3D back projection comprising the following steps is carried out:
• determining the partial derivative of measuring values of parallel rays with different radiation source positions in conformity with the angular position of the radiation source;
• performing a weighted-integration of the partial derivative of the measuring values along K lines;
• multiplying the integrated partial derivative of the measuring values by a first weighting factor which corresponds to the cosine of the cone angle of the ray associated with the measuring values and by a second weighting factor which corresponds to the reciprocal value of the cosine of a fan angle of the beam associated with the measuring values;
• and
• reconstructing the absorption of each object point by back projection of the weighted, integrated partial derivative of the measuring values,
• wherein the weighted-integration of the measuring values along the K lines comprises the following steps:
• determining a K plane for each radiation source position and each location to be reconstructed in the examination zone,
• determining the K lines, wherein the K lines are lines of intersection between the K planes and a detector surface of the detector unit,
• multiplying the partial derivative of the measuring values on each K line by a weighting factor which corresponds to the reciprocal value of the sine of a K angle, and
• integrating the partial derivative of the measuring values along the K lines.

A computer tomograph, comprising:

• a radiation source and a diaphragm arrangement which is situated between the examination zone and the radiation source in order to generate a radiation beam which traverses an examination zone or an object present therein,
• a detector unit which is coupled to the radiation source,
• a drive arrangement which serves to displace an object present in the examination zone and the radiation source relative to one another about an axis of rotation and/or parallel to the axis of rotation,
• a reconstruction unit configured to reconstruct the spatial distribution of the absorption within the examination zone from measuring values acquired by the detector unit,
• a control unit configured to control the radiation source, the detector unit, the drive arrangement and the reconstruction unit in conformity with the steps of,
• determining the partial derivative of measuring values of parallel rays with different radiation source positions in conformity with the angular position of the radiation source,
• performing a weighted-integration of the derived measuring values along K lines,
• multiplying the integrated, derived measuring values by a first weighting factor which corresponds to the cosine of the cone angle of the ray associated with the measuring values and by a second weighting factor which corresponds to the reciprocal value of the cosine of a fan angle of the beam associated with the measuring values, and
• reconstructing the absorption of each object point by back projection of the weighted, integrated partial derivative of the measuring values.

A method, comprising:

• producing measuring values indicative of radiation that traverses an examination zone and is detected by a radiation sensitive detector;
• reconstructing the measuring values as a function of corresponding projection angles and weighting factors dependent on the location of the measuring value on the detector to generate an image indicative of the examination zone;
• determining a partial derivative of the measuring values;
• performing a weighted-integration of the partial derivative;
• and
• reconstructing the integrated partial derivative to generate the image.

A system, comprising:

• a detector that detects radiation from a conical radiation beam traversing an examination zone and that generates measuring values indicative of the detected radiation;
• and
• a reconstructor that integrates the measuring values over projection angles corresponding to angles enclosed by a PI line of an object point projected in a plane perpendicular to an axis of rotation;
• wherein the measuring values are multiplied by a weighting factor dependent on the location of the measuring value on the detector, wherein the reconstructor determines the partial derivative of the measuring values, performs a weighted integration partial derivative, and integrates the weighted integration of the partial derivative of the measuring values.