Alternating Minimization Algorithm with Automatic Relevance Determination for Transmission Tomography under Poisson Noise

TL;DR

This paper introduces a globally convergent alternating minimization algorithm with automatic relevance determination for transmission tomography under Poisson noise, promoting sparse solutions and reducing computational complexity.

Contribution

It extends ARD to Poisson noise models, introduces a parameter-free AM algorithm, and exploits optimization transfer for large-scale image reconstruction.

Findings

Outperforms prior ARD algorithms with Gaussian noise assumptions

Effective in high photon flux scenarios

Reduces computational bottleneck in ARD methods

Abstract

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-differences 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 1D 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.