Ray consistency based reconstruction of helical cone beam data

1. A computed tomography (CT) imaging system comprising:

a rotatable gantry having an opening through which at least a portion of an object passes through during a scan;

an energy source configured to project rays toward the object;

a detector assembly configured to detect rays projected by the energy source that pass through the object and generate projection data therefrom; and

a computer programmed to:

receive the projection data from the detector assembly;

for a selected view angle, identify measured rays consistent with each other;

form a two-dimensional sinogram for the selected view angle based on the identified measured rays; and

define an image surface for the selected view angle based on the identified measured rays.

2. The CT imaging system of claim 1 wherein to identify measured rays consistent with each other, the computer is further programmed to:

calculate an inconsistency among rays in the projection data; and

minimize the inconsistency among the rays.

3. The CT imaging system of claim 2 wherein the computer is further programmed to calculate the inconsistency by:

Inconsistency=Σ m=1 to M Σ k=1 to K Σ j=1 to K [w r (ζ k ,S (ζ k ,x m ,y m ))* w r (ζ j ,S (ζ j ,x m ,y m ))*( z ( x m ,y m ,k )− z ( x m ,y m ,j )) 2 +η*w r (ζ j ,S (ζ j ,x m ,y m ))*( w r (ζ k ,S (ζ k ,x m ,y m ))* z ( x m ,y m k )+ w r (ζ k′ ,S (ζ k′ ,x m ,y m ))* z ( x m ,y m ,k′ )− z ( x m ,y m ,j )) 2

where w r is a redundancy weight, S is a function that gives a distance between a point and the origin in an s direction, ζ is a view angle displacement, η relates to a number of rays used to calculate the inconsistency, and k′ is an index of a view that is a conjugate to a view indexed by k.

4. The CT imaging system of claim 2 wherein the computer is further programmed to perform an iterative gradient descent algorithm to minimize the inconsistency.

5. The CT imaging system of claim 2 , wherein the computer is further programmed to store inconsistency data in a memory area, and to form the two-dimensional sinogram for the selected view angle based on the stored consistency data to facilitate an enhanced response time.

6. The CT imaging system of claim 2 , further comprising means for storing the minimized inconsistency among the rays in the projection data such that a subsequent formation of the two-dimensional sinogram for the selected view angle is based on the stored minimized inconsistency.

7. The CT imaging system of claim 1 wherein the computer is further programmed to perform a reconstruction on the two-dimensional sinogram for the selected view angle to obtain image data.

8. The CT imaging system of claim 7 wherein the computer is further programmed to perform one of a two-dimensional filtered backprojection (FBP) and a direct Fourier reconstruction on the two-dimensional sinogram.

9. The CT imaging system of claim 7 wherein the computer is further programmed to axially interpolate the image data from the image surface at the selected view angle to a rectilinear grid.

10. The CT imaging system of claim 1 wherein the computer is further programmed to form the two-dimensional sinogram at the selected view angle by:

p (θ, s,z n )= w r (ζ 1 ,s ) g (β n +ζ 1 ,s ,γ(ζ 1 ,s ))+ w r (ζ 2 −π,−s ) g (β n +ζ 2 ,−s ,γ(ζ 2 ,−s ))

where p is two-dimensional parallel data as a function of θ, s, and z n ; w r is a redundancy weight as a function of ζ 1 and s or ζ 2 and s; g is rebinned beam data as a function of β, s, and γ; γ is a cone angle of a ray; θ is an angle along a helix; s is a signed distance between a rotation axis of the helix and the ray having a cone angle of γ; z n is an n th location in a z-direction; ζ 1 and ζ 2 are functions of θ and β n ; and β n is a parallel view angle.

11. The CT imaging system of claim 1 wherein the computer is further programmed to receive cone beam data in a helix pattern about a longitudinal axis for a plurality of points along the longitudinal axis.

12. The CT imaging system of claim 11 wherein the computer is further programmed to equally space a plurality of view angles along the helix.

13. The CT imaging system of claim 12 wherein the computer is further programmed to specify the plurality of view angles based on a number of two-dimensional sinogram reconstructions that can be performed in a specified time frame.

14. The CT imaging system of claim 11 wherein the image surface is a non-planar surface that approximates the helix pattern.

15. A non-transitory computer readable storage medium having a computer program stored thereon and representing a set of instructions that when executed by a computer causes the computer to:

acquire projection data from a cone beam of x-rays detected by a detector assembly, the cone beam projection data acquired for an imaging volume;

re-bin the cone beam projection data to parallel geometry cone data, wherein x-rays in the parallel geometry cone data are defined as a function of a cone angle, in-plane displacement relative to a rotation axis, and a view angle;

for a selected view angle, identify measured x-rays consistent with each other;

form a two-dimensional sinogram for the selected view angle based on the identified measured x-rays consistent with each other; and

define an image surface for the selected view angle based on the identified measured x-rays.

16. The computer readable storage medium of claim 15 wherein the computer program further causes the computer to reconstruct a two-dimensional image for the sinogram, the two-dimensional image comprised of a plurality of voxels.

17. The computer readable storage medium of claim 16 wherein the computer program further causes the computer to:

determine the location of each of the plurality of voxels within a reconstruction cylinder; and

form an image on a rectilinear grid from the plurality of voxels based on interpolation of the plurality of voxels.

18. The computer readable storage medium of claim 15 wherein the computer program further causes the computer to calculate an inconsistency among the x-rays in the cone beam projection data and to perform an iterative gradient descent algorithm to minimize the inconsistency.

19. The computer readable storage medium of claim 18 , wherein the computer program further causes the computer to store the minimized inconsistency among the x-rays in the cone beam projection data in a memory area to facilitate enhanced response time in a subsequent formation of the two-dimensional sinogram for the selected view angle.

20. The computer readable storage medium of claim 15 wherein the computer program further causes the computer to select a desired number of image surfaces to be determined from the identified measured x-rays.

21. The computer readable storage medium of claim 15 wherein the computer program further causes the computer to define each of the cone angle and the redundancy weight as functions of the view angle and the in-plane displacement from the rotation axis.

22. The computer readable storage medium of claim 15 wherein the computer program further causes the computer to select a free parameter for calculating an inconsistency between the identified measured x-rays, wherein the free parameter represents a weighted average of each of the identified measured x-rays and a conjugate of each of the identified measured x-rays.

23. A method of image reconstruction of cone beam computed tomography (CT) data comprising the steps of:

receiving x-ray projection data in a helix pattern for a plurality of points along a longitudinal axis;

for a selected view angle:

identifying measured x-rays consistent with each other;

generating a two-dimensional sinogram based on the identified measured x-rays; and

defining a two-dimensional image surface based on the identified measured x-rays.

24. The method of claim 23 further comprising:

calculating an inconsistency among x-rays in the projection data; and

minimizing the inconsistency among the x-rays.

25. The method of claim 24 wherein the step of calculating the inconsistency further comprises selecting a variable parameter to estimate a line integral of an x-ray that passes through an intersection point of two x-rays in the projection data.

26. The method of claim 24 , further comprising storing the minimized inconsistency among the x-rays in a memory area to facilitate enhanced response time in a subsequent formation of the two-dimensional sinogram for the selected view angle.

27. The method of claim 23 further comprising the step of reconstructing the two-dimensional sinogram at each of a plurality of view angles.

28. The method of claim 27 further comprising the step of axially interpolating the reconstructed two-dimensional sinograms to a rectilinear grid.

29. The method of claim 23 wherein the step of forming further comprises forming a two-dimensional sinogram having a view angle range of at least 180 degrees of the image surface.