3D Cone-Beam Reconstruction With ART

General Cone-Beam Reconstruction With the Algebraic Reconstruction Technique (ART)

Cone-beam computed tomography (CT) is an emerging imaging technology. It provides all projections needed for three-dimensional (3D) reconstruction in a single spin of the X- ray source-detector pair. This facilitates fast, low-dose data acquisition, which is required for the imaging of rapidly moving objects, such as the human heart, as well as for intra-operative CT applications. In these scenarios, the number of projections is usually sparse. Current cone-beam reconstruction algorithms mainly employ the Filtered-Backprojection (FBP) approach, which has difficulties when the projection set is limited. In this work, a different class of reconstruction algorithm is studied: the algebraic reconstruction methods. Algebraic reconstruction starts from an initial guess for the reconstructed object and then performs a sequence of iterative grid projections and correction backprojections until the reconstruction has converged. Algebraic methods have reportedly a number of advantages over FBP, such as better noise tolerance and the better handling of sparse and non-uniformly distributed projection datasets. So far, the main repellant for using algebraic methods in routine clinical situations was their slow speed. This work provides solutions for this pressing problem. Furthermore, it also applies, for the first time, algebraic methods in the context of general low-contrast cone-beam tomography. This new context poses several challenges, both for reconstruction quality and speed.

The contributions of this work are as follows (see numbered publications listed below)

Strong aliasing artifacts occur when standard algebraic methods are applied for cone angles exceeding 20 degs. By using the new concept of depth-adaptive basis function kernels, these aliasing artifacts can be eliminated [1].
A comprehensive study is conducted on how various parameters, such as grid initialization, relaxation coefficient, the number of iterations, and correction method (ART or Simultaneous ART (SART)) influence cone-beam reconstruction quality and speed.
A new algorithm, the Weighted Distance Scheme, is proposed that optimally arranges the order in which the grid projections are performed. This new algorithm reduces the number of iterations and also improves reconstruction quality. We find that three iterations are sufficient to obtain good reconstruction quality in the general case [3].
An accurate and efficient projection algorithm is described that reduces the cost of ART considerably, almost to the cost of FBP. It introduces a fast incremental projection scheme and by caches projection computations for their reuse in the subsequent backprojection [2][4].
A new hardware-accelerated scheme for algebraic methods is described that utilizes readily available off-the-shelf texture mapping graphics hardware and enables a reconstruction to be performed in less than 2 minutes at good quality. This corresponds to a speedup of 75 with respect to software solutions [5]-[7].

Here are the publications that describe these contributions:

[1] K. Mueller, R. Yagel, and J.J. Wheller, "Anti-Aliased 3D Cone-Beam Reconstruction Of Low-Contrast Objects With Algebraic Methods," IEEE Transactions on Medical Imaging, vol. 18, no. 6, pp. 519-537, 1999.
[2] K. Mueller, R. Yagel, and J.J. Wheller, "Fast implementations of algebraic methods for the 3D reconstruction from cone-beam data," IEEE Transactions on Medical Imaging, vol. 18, no. 6, pp. 538-547, 1999.
[3] K. Mueller, R. Yagel, and J.F. Cornhill, "The weighted distance scheme: a globally optimizing projection ordering method for the Algebraic Reconstruction Technique (ART)," IEEE Transactions on Medical Imaging, vol. 16, no. 2, pp. 223-230, April 1997.
[4] K. Mueller, R. Yagel, and J.J. Wheller " A fast and accurate projection algorithm for the Algebraic Reconstruction Technique (ART)," Proceedings of the 1998 SPIE Medical Imaging Conference (won Honorary Mention)
[5] K. Mueller and R. Yagel, "Rapid 3D cone-beam reconstruction with ART utilizing texture mapping graphics hardware," presented at IEEE Medical Imaging Conference 1998.
[6] K. Mueller and R. Yagel, "Rapid 3D cone-beam reconstruction with the Algebraic Reconstruction Technique (ART) by utilizing texture mapping hardware," (in review) 1999.
[7] K. Mueller and R. Yagel, "On the use of graphics hardware to accelerate algebraic reconstruction methods," presented at the 1999 SPIE Medical Imaging Conference.
[8] K. Mueller, R. Yagel, and J.F. Cornhill, "Accelerating the anti-aliased Algebraic Reconstruction Technique (ART) by table-based voxel backward projection," Proceedings EMBS'95 (The Annual International Conference of the IEEE Engineering in Medicine and Biology Society), pp. 579-580, 1995.

Here is a talk on cone-beam ART that I gave at the University of Pennsylvania in May 2000.

Finally, here is my dissertation that embraces all this material, some in more detail, some in less: "Fast and Accurate Three-Dimensional Reconstruction from Cone-Beam Projection Data Using Algebraic Methods"

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