Projection matrix acquisition for cone-beam computed tomography iterative reconstruction

Projection matrix is an essential and time-consuming part in computed tomography (CT) iterative reconstruction. In this article a novel calculation algorithm of three-dimensional (3D) projection matrix is proposed to quickly acquire the matrix for cone-beam CT (CBCT). The CT data needed to be reconstructed is considered as consisting of the three orthogonal sets of equally spaced and parallel planes, rather than the individual voxels. After getting the intersections the rays with the surfaces of the voxels, the coordinate points and vertex is compared to obtain the index value that the ray traversed. Without considering ray-slope to voxel, it just need comparing the position of two points. Finally, the computer simulation is used to verify the effectiveness of the algorithm.

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