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Alternating minimization algorithm with automatic relevance determination for transmission tomography under Poisson noise. (English) Zbl 1330.94009

Summary: 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.yan-kaganovsky.com/\#!code/c24bp.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65F22 Ill-posedness and regularization problems in numerical linear algebra
65K10 Numerical optimization and variational techniques
65J22 Numerical solution to inverse problems in abstract spaces
90C25 Convex programming
90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming

Software:

PRMLT; Matlab; spBayes; VARD
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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