Analytical Reconstruction of Periodically Deformed Objects in Time-resolved CT

Time-resolved CT is an advanced measurement technique that has been widely used to observe dynamic objects, including periodically varying structures such as hearts, lungs, or hearing structures. To reconstruct these objects from CT projections, a common approach is to divide the projections into several collections based on their motion phases and perform reconstruction within each collection, assuming they originate from a static object. This describes the gating-based method, which is the standard approach for time-periodic reconstruction. However, the gating-based reconstruction algorithm only utilizes a limited subset of projections within each collection and ignores the correlation between different collections, leading to inefficient use of the radiation dose. To address this issue, we propose two analytical reconstruction pipelines in this paper, and validate them with experimental data captured using tomographic synchrotron microscopy. We demonstrate that our approaches significantly reduce random noise in the reconstructed images without blurring the sharp features of the observed objects. Equivalently, our methods can achieve the same reconstruction quality as gating-based methods but with a lower radiation dose. Our code is available at github.com/PeriodRecon.

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.