Fast backprojection/reprojection with hexagonal segmentation of image
View Patent ↗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.
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 N 2 log 2.65 N 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 7 n samples into a plurality of subimages, each containing 7 n−1 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.