TY - JOUR
T1 - Alternating minimization algorithm with automatic relevance determination for transmission tomography under poisson noise
AU - Kaganovsky, Yan
AU - Han, Shaobo
AU - Degirmenci, Soysal
AU - Politte, David G.
AU - Brady, David J.
AU - O’Sullivan, Joseph A.
AU - Carin, Lawrence
N1 - Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015/9/30
Y1 - 2015/9/30
N2 - We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer’s law. The algorithm promotes solutions that are sparse in the pixel/voxel– difference domain by introducing additional latent variables, one for each pixel/voxel, and then learning these variables from the data using a hierarchical Bayesian model. Importantly, the proposed AM algorithm is free of any tuning parameters with image quality comparable to standard penalized likelihood methods. Our algorithm exploits optimization transfer principles which reduce the problem into parallel one-dimensional optimization tasks (one for each pixel/voxel), making the algorithm feasible for large-scale problems. This approach considerably reduces the computational bottleneck of ARD associated with the posterior variances. Positivity constraints inherent in transmission tomography problems are also enforced. We demonstrate the performance of the proposed algorithm for x-ray computed tomography using synthetic and real-world datasets. The algorithm is shown to have much better performance than prior ARD algorithms based on approximate Gaussian noise models, even for high photon flux. Sample code is available from http://www.yankaganovsky. com/#!code/c24bp.
AB - We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer’s law. The algorithm promotes solutions that are sparse in the pixel/voxel– difference domain by introducing additional latent variables, one for each pixel/voxel, and then learning these variables from the data using a hierarchical Bayesian model. Importantly, the proposed AM algorithm is free of any tuning parameters with image quality comparable to standard penalized likelihood methods. Our algorithm exploits optimization transfer principles which reduce the problem into parallel one-dimensional optimization tasks (one for each pixel/voxel), making the algorithm feasible for large-scale problems. This approach considerably reduces the computational bottleneck of ARD associated with the posterior variances. Positivity constraints inherent in transmission tomography problems are also enforced. We demonstrate the performance of the proposed algorithm for x-ray computed tomography using synthetic and real-world datasets. The algorithm is shown to have much better performance than prior ARD algorithms based on approximate Gaussian noise models, even for high photon flux. Sample code is available from http://www.yankaganovsky. com/#!code/c24bp.
KW - Alternating minimization
KW - Automatic relevance determination
KW - Optimization transfer
KW - Poisson noise
KW - Transmission tomography
KW - X-ray CT
UR - http://www.scopus.com/inward/record.url?scp=84943574790&partnerID=8YFLogxK
U2 - 10.1137/141000038
DO - 10.1137/141000038
M3 - Article
AN - SCOPUS:84943574790
VL - 8
SP - 2087
EP - 2132
JO - SIAM Journal on Imaging Sciences
JF - SIAM Journal on Imaging Sciences
SN - 1936-4954
IS - 3
ER -