<title>Use of graphics hardware to accelerate algebraic reconstruction methods</title>

Abstract

The Algebraic Reconstruction Technique (ART) reconstructs a 2D or 3D object from its projections. It has, in certain scenarios, many advantages over the more popular Filtered Backprojection approaches and has also recently been shown to perform well for 3D cone-beam reconstruction. However, so far, ART's slow speed has prohibited its routine use in clinical applications. Currently, a software implementation requires several hours for a 3D reconstruction, even on modest reconstruction grid sizes. Although one solution to combat these problems would be the time-consuming design of expensive custom accelerator boards, we would rather like to resort to existing and widely available hardware for our purposes. In this sense, we find that ART's main operations, i.e., volume projections and image backprojections, can be performed very rapidly on standard 2D texture mapping hardware, resident in many graphics workstations and PC graphics boards. In this paper, we discuss the use of this hardware in two volume decomposition modes: voxel and slice. Although we find that the speedups obtained in the voxel mode are respectable, the speedups obtained in the slice-mode are tremendous. Here, a quality cone-beam reconstruction on a 128 3 grid can be obtained in less than 2 minutes, which corresponds to a speedup of over 70. Since our rapid ART reconstruction algorithm can be run on the same workstations that are typically used for the viewing of clinical datasets, it is immediately available for routine parallel-and cone-beam CT.

Volumetric backprojection

“…For that reason, many bits of fixed precision are required to store each voxel. Tests [15] have shown that 16 bits of scalar data are required to provide a 1% percent contrast sensitivity in reconstruction. With this much precision in the hardware, hardware accelerated medical reconstruction is practical.…”

Rapid 3-D cone-beam reconstruction with the simultaneous algebraic reconstruction technique (SART) using 2-D texture mapping hardware

“…The less discretized integration of the splatting methods yields more accurate weight factors and, as a consequence, more accurate projections/backprojections. Although it is possible to simulate the splatting approach in hardware, using polygon-mounted, voxel-weighted texture maps for each voxel's kernel footprint, this approach tends to be rather slow, since the granularity of this approach (on the order of voxels) is too small to be efficient [18]. We now describe an approach with higher granularity (on the order of volume slices) that offers more promise.…”

Compressed sensing inspired rapid algebraic reconstruction technique for computed tomography

“…al. has put forwarded to stop ART after 3 iterations, making a compromise between time and efficiency [2]. To meet these challenges we propose a compressed sensing based iterative reconstruction methodology that produces better reconstruction with comparatively less number of iterations.…”