Method and apparatus for reconstruction of 3D image volumes from projection images
The invention provides improvements in reconstructive imaging of the type in which a volume is reconstructed from a series of measured projection images (or other two-dimensional representations) by utilizing the capabilities of graphics processing units (GPUs). In one aspect, the invention configures a GPU to reconstruct a volume by initializing an estimated density distribution of that volume to arbitrary values in a three-dimensional voxel-based matrix and, then, determining the actual density distribution iteratively by, for each of the measured projections, (a) forward-projecting the estimated volume computationally and comparing the forward-projection with the measured projection, (b) generating a correction term for each pixel in the forward-projection based on that comparison, and (c) back-projecting the correction term for each pixel in the forward-projection onto all voxels of the volume that were mapped into that pixel in the forward-projection.
1. An apparatus for computed tomography of the type that reconstructs density distribution of a volume from a plurality of measured projection images, comprising
a graphics processing unit (GPU) including a plurality of programmable vertex shaders that are coupled to a plurality of programmable pixel shaders,
the vertex shaders and the pixel shaders being adapted to generate, for at least one measured projection image, a respective forward-projection image of an estimated density distribution assigned to the volume and to generate one or more correction terms based on comparison of one or more pixels in the forward-projection image with respective pixels in that measured projection image.
2. The apparatus of claim 1 , the further wherein the volume is represented as a plurality of slices.
3. An apparatus for computed tomography of the type that reconstructs density distribution of a volume from a plurality of measured projection images, comprising
a graphics processing unit (GPU) including a plurality of programmable vertex shaders that are coupled to a plurality of programmable pixel shaders,
the vertex shaders and the pixel shaders being adapted to generate for at least one measured projection image a respective forward-projection image of an estimated density distribution assigned to the volume and to generate one or more correction terms based on comparison of one or more pixels in the forward-projection image with respective pixels in that measured projection image;
wherein the volume is represented as a plurality of slices, and
wherein one or more of the vertex shaders are configured to map to each pixel in the forward-projection image a plurality of voxels that lie substantially at vertices of one or more selected polygonal portions of the slices.
4. The apparatus of claim 3 , wherein the one or more vertex shaders treat the forward-projection image as a “window” and each of the polygonal portions as a “model” being projected onto the window.
5. The apparatus of claim 3 , wherein one or more of the pixel shaders compute an intensity for each pixel in the forward-projection image as a summation of the projections of the voxels mapped to that pixel.
6. The apparatus of claim 5 , wherein at least one of the pixel shaders computes multiple forward-projection steps along a ray, which extends through the volume to a pixel in the forward-projection image, prior to computing corresponding steps for another ray.
7. The apparatus of claim 4 , wherein at least one of the pixel shaders generates correction terms for one or more pixels in the forward-projection image based on comparison of the intensities of those pixels with intensities of the respective pixels in the measured projection image.
8. The apparatus of claim 4 , wherein at least one of pixel shaders back-projects the correction term corresponding to each pixel in the forward-projection image to voxels in the volume that are mapped to that pixel.
9. The apparatus of claim 8 , wherein the one or more pixel shaders generate an updated density distribution for the volume as a weighted sum of the estimated density distribution at each voxel and the back-projected correction term corresponding to that voxel.
10. The apparatus of claim 1 , wherein the GPU classifies the measured projection images into two groups characterized by substantially orthogonal projection directions.
11. The apparatus of claim 10 , wherein the GPU processes the measured projection images in one group prior to processing the measured projection images in the other group.
12. The apparatus of claim 11 , wherein the GPU processes the measured projections in at least one of the groups according to a quasi-random sequence.
13. The apparatus of claim 3 , wherein the reconstruction volume comprises an intersection of cone beams corresponding to the measured projection images.
14. The apparatus of claim 8 , wherein the at least one pixel shader back-projecting the correction term utilizes a windowing function to weight the correction term along one or more back-projection rays.
15. The apparatus of claim 14 , wherein one of the pixel shaders computes the weights applied to the back-projected correction term.
16. The apparatus of claim 15 , wherein the weights are computed via lookup in a 1-D texture.