A Fourier rebinning algorithm for cone beam CT

It is known that x-ray projections collected from a circular orbit of an x-ray source are insufficient for accurate reconstruction of a 3D object. For each local region of the object (except in the plane containing the source trajectory) there is a conical volume in the object's spatial frequency space that is unmeasured due to the circular geometry. The Feldkamp, Davis and Kress (FDK) algorithm based on filtered backprojection (FBP) involves a 3D backprojection step so that these unmeasured spatial frequencies are set to zero, resulting in cone beam artifacts for certain objects. We present a new type of cone beam CT reconstruction algorithm based on the Fourier rebinning (FORE) framework of Defrise et al. The cone beam x-ray projection data are rebinned into a set of in-plane sinograms using the FORE rebinning approximation, followed by 2D FBP to reconstruct each axial slice. The algorithm is able to extrapolate data into the missing region of the object's frequency space in a computationally efficient way, allowing for a reduction of cone beam artifacts for certain objects. Unlike FDK, the algorithm is exact for an impulse object located anywhere along the axis of rotation. Reconstruction errors are dependent on the radial distance, cone angle, and the second-derivative of the projection data in the longitudinal direction. Finally, an extension to the algorithm is presented that permits reconstruction in regions of the object that are not seen by the detector in every view.

[1]  Bruno De Man,et al.  CatSim: a new computer assisted tomography simulation environment , 2007, SPIE Medical Imaging.

[2]  David S. Lalush.  Fourier Rebinning Applied to Multiplanar , 1999 .

[3]  M. Defrise,et al.  A fast rebinning algorithm for 3D positron emission tomography using John's equation , 1999 .

[4]  H. Yang,et al.  FBP-type Cone-Beam Reconstruction Algorithm with Radon Space Interpolation Capabilities for Axially Truncated Data from a Circular Orbit , 2006 .

[5]  L. Feldkamp,et al.  Practical cone-beam algorithm , 1984 .

[6]  R. Ning,et al.  A cone beam filtered backprojection (CB-FBP) reconstruction algorithm for a circle-plus-two-arc orbit. , 2001, Medical physics.

[7]  Xiaochuan Pan,et al.  Image reconstruction with a shift‐variant filtration in circular cone‐beam CT , 2004, Int. J. Imaging Syst. Technol..

[8]  P. Grangeat.  Mathematical framework of cone beam 3D reconstruction via the first derivative of the radon transform , 1991 .

[9]  Paul R. Edholm,et al.  Novel Properties Of The Fourier Decomposition Of The Sinogram , 1986, Other Conferences.

[10]  Li Zhang,et al.  An error-reduction-based algorithm for cone-beam computed tomography. , 2004, Medical physics.

[11]  M. Grass,et al.  3D cone-beam CT reconstruction for circular trajectories. , 2000, Physics in medicine and biology.

[12]  H. Tuy.  AN INVERSION FORMULA FOR CONE-BEAM RECONSTRUCTION* , 1983 .

[13]  G T Gullberg,et al.  A cone-beam tomography algorithm for orthogonal circle-and-line orbit. , 1992, Physics in medicine and biology.

[14]  Ruola Ning,et al.  A cone-beam reconstruction algorithm for circle-plus-arc data-acquisition geometry , 1999, IEEE Transactions on Medical Imaging.

[15]  Ge Wang,et al.  A Grangeat‐type half‐scan algorithm for cone‐beam CT , 2003 .

[16]  Li Zhang,et al.  A half-scan error reduction based algorithm for cone-beam CT , 2004 .

[17]  M. Defrise,et al.  Single-slice rebinning method for helical cone-beam CT. , 1999, Physics in medicine and biology.

[18]  Michel Defrise,et al.  Exact and approximate rebinning algorithms for 3-D PET data , 1997, IEEE Transactions on Medical Imaging.

[19]  M. Daube-Witherspoon,et al.  Treatment of axial data in three-dimensional PET. , 1987, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[20]  Cyril Riddell,et al.  Novel C-arm based cone-beam CT using a source trajectory of two concentric arcs , 2007, SPIE Medical Imaging.

[21]  Ge Wang,et al.  Grangeat-type half-scan algorithm for cone beam CT , 2003, SPIE Medical Imaging.