Stochastic First-Order Minimization Techniques Using Jensen Surrogates for X-Ray Transmission Tomography

TL;DR

This paper introduces two Jensen surrogate-based incremental algorithms for X-ray CT image reconstruction, demonstrating that the stochastic variant outperforms existing methods, including gradient descent, especially in later iterations.

Contribution

The paper proposes novel stochastic and ordered-subsets incremental methods using Jensen surrogates for X-ray CT, addressing convergence issues in traditional algorithms.

Findings

Stochastic Jensen surrogate method outperforms other algorithms.

Proposed methods accelerate convergence in X-ray CT reconstruction.

Measured data confirms improved performance of the stochastic approach.

Abstract

Image reconstruction in X-ray transmission tomography has been an important research field for decades. In light of data volume increasing faster than processor speeds, one needs accelerated iterative algorithms to solve the optimization problem in the X-ray CT application. Incremental methods, in which a subset of data is being used at each iteration to accelerate the computations, have been getting more popular lately in the machine learning and mathematical optimization fields. The most popular member of this family of algorithms in the X-ray CT field is ordered-subsets. Even though it performs well in earlier iterations, the lack of convergence in later iterations is a known phenomenon. In this paper, we propose two incremental methods that use Jensen surrogates for the X-ray CT application, one stochastic and one ordered-subsets type. Using measured data, we show that the stochastic variant we propose outperforms other algorithms, including the gradient descent counterparts.