1 research outputs found
Distributed Computation of Linear Inverse Problems with Application to Computed Tomography
The inversion of linear systems is a fundamental step in many inverse
problems. Computational challenges exist when trying to invert large linear
systems, where limited computing resources mean that only part of the system
can be kept in computer memory at any one time. We are here motivated by
tomographic inversion problems that often lead to linear inverse problems. In
state of the art x-ray systems, even a standard scan can produce 4 million
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 utilise
modern graphics processing unit (GPU) based computing architectures,
combinations of iterative reconstruction algorithms and parallel computing
schemes are increasingly applied. Although both row and column action methods
have been proposed to utilise parallel computing architectures, individual
computations in current methods need to know either the entire set of
observations or the entire set of estimated x-ray absorptions, which can be
prohibitive in many realistic big data applications. We present a fully
parallelizable computed tomography (CT) image reconstruction algorithm that
works with arbitrary partial subsets of the data and the reconstructed volume.
We further develop a non-homogeneously randomised selection criteria which
guarantees that sub-matrices of the system matrix are selected more frequently
if they are dense, thus maximising information flow through the algorithm. A
grouped version of the algorithm is also proposed to further improve
convergence speed and performance. Algorithm performance is verified
experimentally.Comment: 13 pages, 17 figures, journa