On the crucial impact of the coupling projector-backprojector in iterative tomographic reconstruction

TL;DR

This paper demonstrates that the matching between forward and backprojectors significantly influences the quality and convergence of iterative tomographic reconstruction algorithms, surpassing other factors like operator accuracy or constraints.

Contribution

It highlights the importance of the coupling between projector and backprojector, an aspect previously overlooked, and shows its critical impact on reconstruction performance.

Findings

Matching projector and backprojector improves reconstruction quality.

Coupling affects convergence more than operator accuracy.

Physical constraints and stopping criteria are less influential.

Abstract

The performance of an iterative reconstruction algorithm for X-ray tomography is strongly determined by the features of the used forward and backprojector. For this reason, a large number of studies has focused on the to design of projectors with increasingly higher accuracy and speed. To what extent the accuracy of an iterative algorithm is affected by the mathematical affinity and the similarity between the actual implementation of the forward and backprojection, referred here as "coupling projector-backprojector", has been an overlooked aspect so far. The experimental study presented here shows that the reconstruction quality and the convergence of an iterative algorithm greatly rely on a good matching between the implementation of the tomographic operators. In comparison, other aspects like the accuracy of the standalone operators, the usage of physical constraints or the choice of stopping criteria may even play a less relevant role.