Abstract
The inversion of linear systems is fundamental in computed tomography (CT) reconstruction. Computational challenges arise when trying to invert large linear systems, as limited computing resources mean that only a part of the system can be kept in computer memory at any one time. In linear tomographic inversion problems, such as X-ray tomography, even a standard scan can produce millions of individual measurements and the reconstruction of X-ray attenuation profiles typically requires the estimation of a million attenuation coefficients. To deal with the large data sets encountered in real applications and to efficiently utilize modern graphics processing unit based computing architectures, combinations of iterative reconstruction algorithms and parallel computing schemes are increasingly applied. Whilst different parallel methods have been proposed, individual computations currently need to access either the entire set of observations or estimated X-ray absorptions, which can be prohibitive in many realistic applications. We present a fully parallelizable CT image reconstruction algorithm where each computation node works on arbitrary partial subsets of the data and the reconstructed volume. We further develop a nonhomogeneously randomized selection criterion which guarantees that submatrices of the system matrix are selected more frequently if they are dense, thus maximizing information flow through the algorithm. We compare our algorithm with block alternating direction method of multipliers and show that our method is significantly faster for CT reconstruction.
Highlights
I N TRANSMISSION computed tomography (CT), standard scan trajectories, such as rotation based or helical trajectories, allow the use of efficient analytical reconstruction techniques such as the filtered backprojection algorithm (FBP) [1], [2] and the Feldkamp Davis Kress (FDK) [3], [4] method
coordinate-wise stochastic gradient descent (CSGD) was designed for a distributed reconstruction of cone beam CT data under arbitrary scan trajectories
Whilst the method does not converge to the least squares solution, the solution is found empirically to be comparable in quality to those found with other common tomographic reconstruction algorithms, such as Simultaneous Iterative Reconstruction Technique (SIRT) and component averaging (CAV), but at a significant computational advantage
Summary
Abstract—The inversion of linear systems is fundamental in computed tomography (CT) reconstruction. Computational challenges arise when trying to invert large linear systems, as limited computing resources mean that only a part of the system can be kept in computer memory at any one time. In linear tomographic inversion problems, such as X-ray tomography, even a standard scan can produce millions of individual measurements and the reconstruction of X-ray attenuation profiles typically requires the estimation of a million attenuation coefficients. To deal with the large data sets encountered in real applications and to efficiently utilize modern graphics processing unit based computing architectures, combinations of iterative reconstruction algorithms and parallel computing schemes are increasingly applied. Whilst different parallel methods have been proposed, individual computations currently need to access either the entire set of observations or estimated X-ray absorptions, which can be prohibitive in many realistic applications.
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