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

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.

Improving analytical tomographic reconstructions through consistency conditions

This work introduces and characterizes a fast parameterless filter based on the Helgason-Ludwig consistency conditions, used to improve the accuracy of analytical reconstructions of tomographic undersampled datasets. The filter, acting in the Radon domain, extrapolates intermediate projections between those existing. The resulting sinogram, doubled in views, is then reconstructed by a standard analytical method. Experiments with simulated data prove that the peak-signal-to-noise ratio of the results computed by filtered backprojection is improved up to 5-6 dB, if the filter is used prior to reconstruction.