Accelerating the Anti-aliased Algebraic Reconstruction Technique (ART) by . . .

Accelerating the Anti-aliased Algebraic Reconstruction Technique 2 enables us to transform ART into a backward-viewing algorithm in which voxels are projected individually onto the projection plane where their effects accumulate to form the projection image. Similarly to the PKLUT's used in [3], voxel footprints can be implemented as high-resolution 1D voxel projection tables (2D for cubic voxels), one for each projection angle ϕ, where each table entry represents the result of a linear integration of h(u,v) orthogonal to the projection plane of P ϕ. In the projection phase, for a particular projection angle ϕ, we compute for each grid voxel v j the projection Proj(v j) of v j 's center, and subsequently the extent Ext(Proj(v j)) of the voxel projection table on the projection plane. We then index the table for all pixels that fall within Ext(Proj(v j)) to obtain v j 's contribution to these pixels. Note that most of the projection calculations can be performed as incremental operations. SART's grid update equation [1] can then be implemented as follows: We associate two buffers with the projection plane: buffer B r accumulating ray sum and buffer B w accumulating the weights as voxels are projected. Buffer B o is the aquired projection image. After all voxels have been processed , the correction image buffer B c is computed as: where λ, 0<λ≤1.0 is a relaxation factor [1]. In the reprojection phase, the correction buffer B c is distributed back onto the reconstruction grid. As in the projection phase, for each voxel v j we compute Proj(v j) and Ext(Proj(v j)). The correction term for v j is then computed as the weighted sum of all correction terms affecting v j : where I is the set of elements of buffer B c for which Ext(Proj(v j)) is the corresponding set of projection pixels. This value is then added to v j. Our discussion so far was limited to the parallel beam case, however, our approach is easily extended to fan-and cone beam data with one modification: One has to scale each voxel footprint according to the perspective distortion. P 0 P 4 5 u v h(u,v) v j v k x y Proj(v j) Ext(Proj(v j)) Fig. 1. Voxels v j and v k leave identical, though spatially offset, footprints on projection planes P 0 and P 45. In P 45 , the composite footprint is depicted as …