Method for reconstructing a three-dimensional image of an object scanned in the context of a tomosynthesis, and apparatus for tomosynthesis

A tomosynthesis method for reconstructing a three-dimensional image of an object, comprising the steps of:

• providing an x-ray source having an x-ray focus;
• providing a radiation detector;
• disposing a three-dimensional object in a three-dimensional object space between said x-ray focus and said radiation detector;
• scanning said object by moving at least said x-ray focus relative to said object to irradiate said object with x-rays from a plurality of different projection angles φ;
• detecting said x-rays attenuated by said object with said radiation detector at each of said projection angles φ as respective projection images in a 2D recording geometry, each of said projection images comprising a set of projection image data of said object in a 2D projection image space;
• in a computer, individually back-projecting the said sets of projection image data into a 3D reconstruction image volume for producing a reconstruction image of said object;
• applying a 3D filtering function Hfilter(ωx,ωy,ωz) to said reconstruction image of said object to obtain a filtered reconstruction image;
• and
• determining said 3D filtering function by the steps of:
• calculating a 3D transmission function Hproj(ωx,ωy,ωz) from the recording geometry for the individual sets of projection image data and back-projecting the individual sets of projection image data into the 3D reconstruction image volume;
• inverting by approximation, the 3D transmission function Hproj(ωx,ωy,ωz) and thereby determining an inversion function Hinv(ωx,ωy,ωz);
• producing a 3D filtering function Hopt(ωx,ωy,ωz) dependent on at least one selected image characteristic of the reconstruction image;
• determining a resulting 3D filtering function Hfilter(ωx,ωy,ωz) by multiplying the 3D filtering function Hopt(ωx,ωy,ωz) and the inversion function Hinv(ωx,ωy,ωz).

A tomosynthesis apparatus for reconstructing a three-dimensional irmiage of an object, comprising:

• an x-ray source having an x-ray focus;
• a radiation detector disposed to detect x-rays attenuated by a three-dimensional object in a three-dimensional object space between said x-ray focus and said radiation detector;
• means for moving at least said x-ray focus relative to said object to scan said object by irradiating said object with x-rays from a plurality of different projection angles φ;
• said radiation detector detecting said x-rays attenuated by said object with at each of said projection angles φ as respective projection images in a 2D recording geometry, each of said projection images comprising a set of projection image data of said object in a 2D projection image space;
• means for applying a 2D filtering function H2Dfilter,φ(ωu,ωv) to said sets of projection image data to obtain filtered sets of projection image data;
• computer means for individually back-projecting said filtered sets of projection image data into a 3D reconstruction image volume for producing a reconstruction image of said object;
• and
• said means for applying said 2D filtering function comprising means for determining said 2D filtering function by calculating a 3D transmission function Hproj(ωx,ωy,ωz) from the recording geometry for the individual sets of projection image data and back-projecting the individual sets of projection image data into the 3D reconstruction image volume, thereby determining an inversion function Hinv(ωx,ωy,ωz), producing a 3D filtering function Hopt(ωx,ωy,ωz) dependent on at least one selected image characteristic of the reconstruction image, determining a resulting 3D filtering function Hfilter(ωx,ωy,ωz) by multiplying the 3D filtering function Hopt(ωx,ωy,ωz) and the inversion function Hinv(ωx,ωy,ωz), and determining said 2D filtering function H2Dfilter,φ(ωu,ωv) frorn the resulting 3D filtering function Hfilter(ωx,ωy,ωz) by coordinate transformation of the 3D object space into the 2D projection image space of the respective individual sets of projection image data at the projection angles φ.

A tomosynthesis apparatus for reconstructing a three-dimensional image of an object, comprising:

• an x-ray source having an x-ray focus;
• a radiation detector disposed to detect x-rays attenuated by a three-dimensional object in a three-dimensional object space between said x-ray focus and said radiation detector;
• means for moving at least said x-ray focus relative to said object to scan said object by irradiating said object with x-rays from a plurality of different projection angles
• said radiation detector detecting said x-rays attenuated by said object with at each of said projection angles φ as respective projection images in a 2D recording geometry, each of said projection images comprising a set of projection image data of said object in a 2D projection image space;
• computer means for individually back-projecting said sets of projection image data into a 3D reconstruction image volume for producing a reconstruction image of said object;
• means for applying a 3D filtering function Hfilter(ωx,ωy,ωz) to said reconstruction image of said object to obtain a filtered reconstruction object;
• and
• said means for applying said 3D filtering function comprising means for determining said 3D filtering function by calculating a 3D transmission function Hproj(ωx,ωy,ωz) from the recording geometry for the individual sets of projection image data and back-projecting the individual sets of projection image data into the 3D reconstruction image volume, inverting by approximation, the 3D transmission function Hproj(ωx,ωy,ωz) and thereby determining an inversion function Hinv(ωx,ωy,ωz), producing a 3D filtering function Hopt(ωx,ωy,ωz) dependent on at least one selected image characteristic of the reconstruction image, and determining a resulting 3D filtering function Hfilter(ωx,ωy,ωz) by multiplying the 3D filtering function Hopt(ωx,ωy,ωz) and the inversion function Hinv(ωx,ωy,ωz) and determining a resulting 3D filtering function Hfilter,φ(ωx,ωy,ωz by multiplying the 3D filtering function Hfilter((ωx,ωy,ωz), and the inversion function Hinv(ωx,ωy,ωz).