Reconstruction method using direct and iterative techniques

1. A computer-implemented method for deriving a full-volume volumetric image of an object being imaged, the method comprising:

calculating a first volumetric image of the object using a direct reconstruction method from a plurality of radiation measurements of the object taken from a plurality of directions, wherein calculating the first volumetric image comprises calculating a value for each voxel in the first volumetric image; and

performing at least one iteration of a nonregulating iterative reconstruction method to compute a second volumetric image of the object, wherein the iterative reconstruction method is initialized with the first volumetric image of the object, wherein the second volumetric image comprises a corresponding voxel for each voxel in the first volumetric image, and wherein performing the at least one iteration comprises calculating a value for each voxel in the second volumetric image,

wherein the iterative reconstruction method comprises ordered subset maximum likelihood, algebraic reconstruction technique, simultaneous algebraic reconstruction technique, simultaneous iterative reconstruction technique, least-squares QR method, expectation maximization, ordered subset convex method, or ordered subset expectation maximization, and

wherein the plurality of radiation measurements does not satisfy a volumetric reconstruction requirement.

2. The computer-implemented method of claim 1 , wherein performing at least one iteration comprises performing an iteration of the iterative reconstruction method one, two, three, four, five, six, seven, eight, nine or ten times.

3. The computer-implemented method of claim 1 , wherein the direct reconstruction method comprises filtered back projection, direct Fourier reconstruction, analytic cone beam method, or approximate cone beam method.

4. The computer-implemented method of claim 1 , wherein calculating the first volumetric image of the object using a direct reconstruction method further comprises using a plurality of different direct reconstruction methods to produce a plurality of volumetric images and selecting the first volumetric image from the plurality of volumetric images based on an error criterion.

5. The computer-implemented method of claim 1 , wherein performing at least one iteration comprises:

calculating, for each iteration, an error value in the projection image domain; and

performing another iteration of the iterative reconstruction method if the error value is above a threshold amount.

6. The computer-implemented method of claim 1 , wherein the volumetric reconstruction requirement is a requirement selected from the group consisting of a Tuy condition, a pi-line condition, a Nyquist condition, and a non-truncation condition.

7. The computer-implemented method of claim 1 , wherein a volume of each voxel in the second volumetric image is less than or equal to five cubic millimeters.

8. A system for deriving a full-volume volumetric image of an object comprising: at least one processor configured to:

calculate a first volumetric image of the object using a direct reconstruction method from a plurality of radiation measurements of the object taken from different directions, wherein the at least one processor is configured to calculate the first volumetric image by calculating a value for each voxel in the first volumetric image; and;

perform at least one iteration of a nonregulating iterative reconstruction method to compute a second volumetric image of the object, wherein the iterative reconstruction method is initialized with the first volumetric image of the object, wherein the second volumetric image comprises a corresponding voxel for each voxel in the first volumetric image, and wherein the at least one processor is configured to perform the at least one iteration by calculating a value for each voxel in the second volumetric image,

wherein the iterative reconstruction method comprises ordered subset maximum likelihood, algebraic reconstruction technique, simultaneous algebraic reconstruction technique, simultaneous iterative reconstruction technique, least-squares QR method, expectation maximization, ordered subset convex method, or ordered subset expectation maximization, and

wherein the plurality of radiation measurements does not satisfy a volumetric reconstruction requirement.

9. The system of claim 8 , further comprising a plurality of radiation source-detector pairs, each radiation source-detector pair in the plurality of radiation source-detector pairs being operable to obtain at least one radiation measurement of the object.

10. The system of claim 8 , wherein the plurality of radiation source-detector pairs is arranged so that at least 75 percent of the voxels of the object are imaged from at least 180 angles.

11. The system of claim 8 , wherein the plurality of radiation source-detector pairs is arranged so that all the voxels of the object are imaged from at least 180 angles.

12. The system of claim 8 , further comprising a plurality of steered e-beams impinging on a target.

13. The system of claim 12 , wherein the e-beams are not arranged symmetrically about the target.

14. The system of claim 8 , wherein the volumetric reconstruction requirement is a requirement selected from the group consisting of a Tuy condition, a pi-line condition, a Nyquist condition, and a non-truncation condition.

15. The system of claim 8 , wherein the direct reconstruction method comprises filtered back projection, direct Fourier reconstruction, analytic cone beam method, or approximate cone beam method.

16. The system of claim 8 comprising at least one processor configured to perform at least one iteration by:

calculating, for each iteration, an error value; and

performing another iteration of the iterative reconstruction method if the error value is above a threshold amount.

17. The system of claim 8 , wherein a volume of each voxel in the second volumetric image is less than or equal to five cubic millimeters.

18. The system of claim 8 , wherein the second volumetric image is computed in less than three seconds.

19. At least one computer-readable medium storing processor-executable instructions that when executed by at least one processor perform a method for deriving a full-volume volumetric image of an object being imaged, the method comprising:

calculating a first volumetric image of the object using a direct reconstruction method from a plurality of radiation measurements of the object taken from different directions, wherein calculating the first volumetric image comprises calculating a value for each voxel in the first volumetric image; and

performing at least one iteration of an iterative reconstruction method to compute a second volumetric image of the object, wherein the iterative reconstruction method is initialized with the first volumetric image of the object, wherein the second volumetric image comprises a corresponding voxel for each voxel in the first volumetric image, and wherein performing the at least one iteration comprises calculating a value for each voxel in the second volumetric image,

wherein the iterative reconstruction method comprises ordered subset maximum likelihood, algebraic reconstruction technique, simultaneous algebraic reconstruction technique, simultaneous iterative reconstruction technique, least-squares QR method, expectation maximization, ordered subset convex method, or ordered subset expectation maximization,

wherein the plurality of radiation measurements does not satisfy a volumetric reconstruction requirement.

20. The at least one computer-readable medium of claim 19 , wherein performing at least one iteration comprises performing an iteration of the iterative reconstruction method one, two, three, four, five, six, seven, eight, nine or ten times.

21. The at least one computer-readable medium of claim 19 , wherein the direct reconstruction method comprises filtered back projection, direct Fourier reconstruction, analytic cone beam method, or approximate cone beam method.

22. The at least one computer-readable medium of claim 19 , wherein calculating the first volumetric image of the object using a direct reconstruction method further comprises using a plurality of different direct reconstruction methods to produce a plurality of volumetric images and selecting the first volumetric image from the plurality of volumetric images based on an error criterion.

23. The at least one computer-readable medium of claim 19 , wherein performing at least one iteration comprises:

calculating, for each iteration, an error value; and

performing another iteration of the iterative reconstruction method if the error value is above a threshold amount.

24. The at least one computer-readable medium of claim 19 , wherein the volumetric reconstruction requirement is a requirement selected from the group consisting of a Tuy condition, a pi-line condition, a Nyquist condition, and a non-truncation condition.

25. The at least one computer-readable medium of claim 19 , wherein a volume of each voxel in the second volumetric image is less than or equal to five cubic millimeters.

26. A system for deriving a full-volume volumetric image of an object comprising at least one processor configured to:

calculate a first volumetric image of the object using a direct reconstruction method from a plurality of radiation measurements of the object taken from different directions, wherein the at least one processor is configured to calculate the first volumetric image by calculating a value for each voxel in the first volumetric image; and;

perform at least one iteration of an iterative reconstruction method at least in part by calculating a measure of error in the projection image domain between the first volumetric image and the plurality of radiation measurements and updating the first volumetric image based on a quantity depending only on the calculated measure of error to compute a second volumetric image of the object, wherein the second volumetric image comprises a corresponding voxel for each voxel in the first volumetric image, and wherein computing the second volumetric image comprises calculating a value for each voxel in the second volumetric image,

wherein the iterative reconstruction method comprises ordered subset maximum likelihood, algebraic reconstruction technique, simultaneous algebraic reconstruction technique, simultaneous iterative reconstruction technique, least-squares QR method, expectation maximization, ordered subset convex method, or ordered subset expectation maximization, and

wherein the plurality of radiation measurements does not satisfy a volumetric reconstruction requirement.

27. The system of claim 26 , further comprising a plurality of radiation source-detector pairs, each radiation source-detector pair in the plurality of radiation source-detector pairs being operable to obtain at least one radiation measurement of the object.

28. The system of claim 27 , wherein the plurality of radiation source-detector pairs is arranged so that at least 75 percent of the voxels of the object are imaged from at least 180 angles.

29. The system of claim 26 , wherein calculating the measure of error in the projection image domain comprises comparing a forward projection of the second volumetric image of the object to the plurality of radiation measurements.

30. The system of claim 26 , wherein the volumetric reconstruction requirement is a requirement selected from the group consisting of a Tuy condition, a pi-line condition, a Nyquist condition, and a non-truncation condition.

31. The system of claim 26 , wherein a volume of each voxel in the second volumetric image is less than or equal to five cubic millimeters.