Apparatus for producing a three-dimensional computerized tomography image of an object, comprising:
- a cone beam x-ray source and a corresponding normalized detector plane having an origin and being arranged such that said source and detector plane are operable to scan the object and obtain cone beam projection data, said cone beam projection data being in the form of line integrals through the object organized, for each of a plurality of x-ray source positions, as a two dimensional data set on said detector plane, wherein each of said line integrals are perpendicular to a line defined between one of said source positions and said origin.
- means for determining values representing planar integrals on a set of planes .phi..sub.j in Radon space by, for each of the source positions S.sub.i,
- means for defining in Randon space a corresponding spherical shell on which Radon data can be determined, intersections of the planes .phi..sub.j with the spherical shell corresponding to the source position S.sub.i defining a set of circles D.sub.ij on the spherical shell, and
- for each of the circles D.sub.ij,
- means for defining a rotation axis as a line through the source position S.sub.i, intersecting the circle D.sub.ij, and orthogonal to the plane of the circle D.sub.ij,
- means for defining a set of coaxial integration planes Q.sub.ijk, each of the integration planes Q.sub.ijk containing the rotation axis and intersecting the circle D.sub.ij to define the location of a Radon datum point R.sub.ijk, and the integration planes Q.sub.ijk intersecting the normalized detector plane on respective first lines L.sub.ijk, and
- for each of the first lines L.sub.ijk on the normalized detector plane,
- means for rotating the corresponding integration plane Q.sub.ijk by a small rotation angle .delta..beta. to define a plane Q.sub.ijk ', intersecting the normalized detector plane on a corresponding first line L.sub.ijk ',
- means for integrating along the first lines L.sub.ijk and L.sub.ijk ' to determine respective weighted first line integrals J.sub.ijk and J.sub.ijk ', and
- means for dividing the difference between the weighted first line integrals J.sub.ijk and J.sub.ijk ' by the rotation angle .delta..beta. to yield the radial derivative of the Radon datum at the point R.sub.ijk ;
- and
- means for performing an inverse Radon transform on said values representing planar integrals on the set of planes .phi..sub.j to reconstruct an image of the object.