General Cone-Beam Reconstruction With the Algebraic Reconstruction Technique
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
Here are the publications that describe these contributions:
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 .
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 .
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 .
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
Here is a talk on cone-beam ART
that I gave at the University of Pennsylvania in May 2000.
 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,
 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.
 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.
 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
 K. Mueller and R. Yagel, "Rapid
3D cone-beam reconstruction with ART utilizing texture mapping graphics
hardware," presented at IEEE Medical Imaging Conference 1998.
 K. Mueller and R. Yagel, "Rapid 3D cone-beam reconstruction
with the Algebraic Reconstruction Technique (ART) by utilizing texture
mapping hardware," (in review) 1999.
 K. Mueller and R. Yagel, "On
the use of graphics hardware to accelerate algebraic reconstruction methods,"
presented at the 1999 SPIE Medical Imaging Conference.
 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.
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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