Superiorization versus regularization: A comparison of algorithms for solving image reconstruction problems with applications in computed tomography

Abstract

A system matrix can be built in order to account for the refractions in an optical computed tomography (CT) system. In order to utilize this system matrix, iterative methods are employed to solve the image reconstruction problem. The purpose of this study is to compare potential iterative algorithms to solve this image reconstruction problem. Comparisons examine both solution time and the quality of the reconstructed image. While our work is motivated by optical CT, the results can be extended more generally to CT. Methods: A collection of 21 algorithms for solving the image reconstruction problem were evaluated. Specifically, algorithms using (i) superiorization techniques and (ii) regularization to avoid overfitting were compared. Multiple test problems are investigated using 18 different image phantoms, parallel-beam and fan-beam system matrices, and varying noise levels. Comparison of the algorithms is done using performance profiles on three different performance measures. Results:The results for both the synthetic and clinical test problems show that there is not one single algorithm outperforming all others, but instead a set of top algorithms that give the best values on the performance profiles. When qualitative analyses such as reliance on stopping conditions, number of input parameters, and run time are also considered, FISTA-TV shows slight advantages over the other top algorithms. Conclusions: There is a set of top algorithms that all show good results in the performance profiles with a mix of superiorized and regularized model algorithms. As to which of these top algorithms outperforms the rest is undetermined and further research needs to be investigated.

Iterative image reconstruction algorithm analysis for optical CT radiochromic gel dosimetry

“…The reconstruction algorithms that were investigated were the top 6 performing algorithms set forth by Guenter et al [41] with the addition of the Landweber [32] algorithm to be used as a baseline for comparison. These algorithms are summarized in table 1.…”

“…In contrast, SIRT algorithms use all the equations at the same time in one iteration, hence being termed simultaneous. Guenter et al [41] evaluated a collection 21 SIRT algorithms in terms of solution error, total variation and run time. The analysis was intended to compare a large number of algorithms on a large number of test problems with varying image properties and noise levels to determine the top-performing algorithms.…”

“…The work of Guenter et al [41] analyzed three categories of iterative algorithms: base, superiorized, and regularized. Each category takes a different approach to finding the indirect solution to tomography problems.…”

Commissioning of a solid tank design for fan-beam optical CT based 3D radiation dosimetry

“…The system matrix used in the iterative reconstructing algorithm is built in-house and based on the ray-tracing simulator created for the scanner design optimization (Ogilvy et al 2020). In 2021, Guenter et al identified several viable algorithms for CT imaging (Guenter et al 2022). Of those, the FISTA has high performance when a stopping condition is unknown, and can be run to higher number of iterations without fear of over-iterating.…”

Preliminary commissioning of a prototype solid tank optical CT scanner for 3D radiation dosimetry

“…clinical test problems by Guenter et al in 2021, and FISTA-TV was a top performer in both solution quality and low runtime[14].…”