Reprojection and backprojection methods and algorithms for implementation thereof

#The present invention relates generally to the processes of reprojection-backprojection, and more specifically, to reprojection-backprojection techniques/algorithms that includes new interpolation and data access schemes that result in better speed, lower artifacts, lower noise and higher spatial resolution than existing techniques.

#In computed tomography, the operation that transforms an N-Dimension image into an N-Dimension set of line integrals is called the forward projection or reprojection. The most evident example of this operation is the physical process that generates an X-ray image of an object. After logarithmic conversion, an X-ray image is well approximated as the line integral projection of the distribution of the object's linear attenuation coefficient. In practice, a forward projector is required for tomographic simulations or when performing iterative reconstruction.

#The transpose operation is called backprojection. This is used in filtered backprojection and in iterative reconstruction, which form the bulk of today's reconstruction algorithms.

#FIG. 1 is a schematic representation of a ray-driven reprojection-backprojection with linear interpolation wherein, for every row or column intersected by the projection line, linear interpolation is performed between the two adjacent pixels.

#FIG. 2 is a schematic representation of a pixel-driven reprojection-backprojection with linear interpolation wherein a line connecting source and image pixel determines an intersection with the detector array and wherein linear interpolation is performed between the two adjacent detector bins.

#FIG. 3 is a depiction of a ray-driven backprojection of a uniform view showing the result wherein high-frequency artifacts are introduced because some pixels are updated more frequently than their neighbors.

#In order to better understand the embodiments of the present invention a more detailed explanation of the above prior art techniques is deemed appropriate. In FIGS. 1, 2, 6 and 7 the grid depicts a pixel image reconstruction grid which is fixed in a three dimensional coordinate system, onto which pixels are mapped in accordance with data acquired in response to a ray being projected from the source to the detector both (schematically shown). Each of the squares in these grids depicts a pixel.

#As noted above, a drawback encountered with both the ray-driven and the pixel-driven method is that they introduce high-frequency artifacts, one in the backprojection and another in the reprojection. FIG. 3 shows an example of a ray-driven backprojection of one uniform view. The interference pattern is due to the fact that some pixels are updated more frequently than other pixels. The artifact problem is worse when the pixel size is small compared to the detector bin size, and vanishes when the pixel size is large compared to the detector bin size.

#FIG. 4 graphically shows one sinogram line of a pixel-driven projection of a uniform disk. By way of example, in Computed Tomography, a measured data set (sinogram) is made up of a large number of views (projections). Each view corresponds to a measurement with the entire detector array, so each view in turn consists of a large number of detector bins (projection lines). A typical sinogram consists of 1500 views/projections of 1000 detector bins/projection lines.