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.