Comparison of optimization techniques for regularized statistical reconstruction in X-ray tomography

Abstract

Numerical efficiency and convergence are matters of importance for regularized statistical reconstruction in X-ray tomography. We propose a performance comparison of four numerical methods that fall into two categories: first, variants of the SPS framework, a modern take on expectation-maximization-type algorithms, that benefit from acceleration through ordered subset strategies and were developed specifically for tomographic reconstruction; second, Hessian-free general-purpose nonlinear solvers with bound constraints, used to minimize directly the regularized objective function. The comparison is established on a common target for the noise-to-resolution trade-off of the reconstructed images. The experiments show that while the ordered-subsets separable paraboloidal surrogate iteration variant is the fastest to reach the target, its nonconvergent nature precludes the use of a rigorous stopping rule. Conversely, the other three methods are convergent and can be stopped using a common criterion related to the noise-to-resolution target. Among convergent techniques, general purpose solvers achieve the highest efficiency.