Fast backprojection/reprojection with hexagonal segmentation of image

• US 7,215,731 B1
• Filed: 11/30/2005
• Issued: 05/08/2007
• Est. Priority Date: 11/30/2005
• Status: Expired due to Fees

• Current Assignee: General Electric Company
• Original Assignee: General Electric Company
• Inventors: Basu, Samit Kumar, DeMan, Bruno Kristiaan Bernard
• Primary Examiner(s): Ullah; Akm E.
• Assistant Examiner(s): COCHRAN, ANTHONY K
• Application Number:
  US11/164,625
• Time in Patent Office: 524 Days
• Field of Search: 378/4, 378/15, 378/901, 382/128, 382/131
• US Class Current: 378/4
• CPC Class Codes: G06T 11/006 Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods
• CPC Class Codes: G06T 2211/421 Filtered back projection [FBP]
• CPC Class Codes: Y10S 378/901 Computer tomography program or processor

Abstract

A reprojection/backprojection technique and apparatus for carrying out such a technique provides a hierarchical solution to speeding-up reprojection and backprojection of tomographic images. In the context of reprojection, a tomographic image is divided into a series of subimages. Each subimage is shifted to the origin, projected at a reduced number of views, and then up-sampled and shifted back (in the sinogram space). The resulting sinograms are then combined to provide a single sinogram. This process is applied one or more times recursively. In the context of backprojection, the above steps are transposed such that a sinogram is divided into a series of subsinograms. The subsinograms are then shifted and decimated by a given decimation factor. The decimated subsinograms are then backprojected onto hexagonal tiles whereupon the tiles are composited into a final image.

Claims

1. A tomographic imaging apparatus, comprising:

a scanner for acquiring tomographic data of an object; and

a computer programmed to;

generate a sinogram from tomographic data acquired by the scanner;

segment the sinogram into a plurality of subsinograms;

backproject each of the plurality of subsinograms onto a respective hexagonal tile; and

combine the hexagonal tiles to form a composite image of the object.

2. The apparatus of claim 1, wherein the scanner is a CT scanner.

3. The apparatus of claim 1, wherein the computer is further programmed to segment the sinogram in a recursive manner until each subsinogram corresponds to an image that is one image element in size.

4. The apparatus of claim 1, wherein the computer is further programmed to segment the sinogram into seven subsinograms and backproject the seven subsinograms onto seven hexagonal tiles.

5. The apparatus of claim 1, wherein the computer is further programmed to:

radially shift each subsinogram to a reference origin; and

decimate each subsinogram by a given decimation factor.

6. The apparatus of claim 5, wherein the decimation factor is 2.65.

7. The apparatus of claim 1, wherein the computer is further programmed to resample the composite image having hexagonally-shaped image elements onto a square pixel grid to form a final image.

8. A process of reconstructing a tomographic image, comprising:

subdividing a sinogram into a series of subsinograms;

backprojecting each of the subsinograms onto a respective hexagonal tile;

combining the hexagonal tiles to form an electronic image; and

displaying the electronic image.

9. The process of claim 8, wherein the series of subsinograms includes seven sinograms.

10. The process of claim 9, wherein each subsinogram corresponds to a hexagonal image element of the electronic image.

11. The process of claim 8, wherein the series of subsinograms are generated from recursively subdividing the sinogram.

12. The process of claim 8, further comprising the step of acquiring raw data with a CT scanner and generating the sinogram from the raw data.

13. The process of claim 8, further comprising the step of decimating each subsinogram by a decimation factor.

14. The process of claim 13, wherein the decimation factor is 2.65.

15. The process of claim 8, wherein the step of backprojecting is carried out with N²log_2.65N operations, wherein N equals number of views of acquired data and where N×

N approximates a number of samples in a corresponding square image.

16. A computer readable storage medium having a computer program stored thereon for image reprojection and representing a set of instructions that when executed by a computer causes the computer to:

divide a tomographic image of 7ⁿ samples into a plurality of subimages, each containing 7<sup>n−

1</sup> samples;

generate a subsinogram for each subimage, each subsinogram corresponding to N/2.65 views;

up-sample each subsinogram such that each subsinogram corresponds to N views; and

combine the up-sampled subsinograms to form a sinogram.

17. The computer readable storage medium of claim 16, wherein the computer is further caused to perform the act of dividing in a recursive manner.

18. The computer readable storage medium of claim 16, wherein the computer is further caused to radially shift each upsampled subsinogram prior to the act of combining.

19. The computer readable storage medium of claim 16, wherein the computer is further caused to initially divide the tomographic image into seven subimages and recursively divide each of the seven subimages until each subimage corresponds to a single hexagonal tile.

20. The computer readable storage medium of claim 16 incorporated into a CT scanner.