DYRECT Computed Tomography: DYnamic Reconstruction of Events on a Continuous Timescale

TL;DR

DYRECT addresses the limited temporal resolution and heavy data burden of 4D μCT by introducing an event-based, projection-level reconstruction that represents local attenuation evolution with three voxel-wise parameters: $\mu_A$, $\mu_B$, and $t^*$. Integrating a SIRT-like iterative scheme with a dynamic forward operator $\tilde{A}$, DYRECT directly estimates transition times from raw projections, enabling continuous-time description of dynamics with far fewer parameters than frame-based sequences. Validation on synthetic porous-media flow data and an experimental bubble coalescence dataset shows mean transition-time errors around $0.088$ rotations, i.e., less than a tenth of the time required for conventional frames, signaling substantial temporal gains. The approach opens a new path for high-temporal-resolution dynamic CT in opaque materials, with potential improvements from spatial regularization and extensions to multi-step dynamics. Overall, DYRECT demonstrates that projection-level event modeling can dramatically enhance temporal resolution while maintaining data efficiency in 4D CT imaging.

Abstract

Time-resolved high-resolution X-ray Computed Tomography (4D $μ$CT) is an imaging technique that offers insight into the evolution of dynamic processes inside materials that are opaque to visible light. Conventional tomographic reconstruction techniques are based on recording a sequence of 3D images that represent the sample state at different moments in time. This frame-based approach limits the temporal resolution compared to dynamic radiography experiments due to the time needed to make CT scans. Moreover, it leads to an inflation of the amount of data and thus to costly post-processing computations to quantify the dynamic behaviour from the sequence of time frames, hereby often ignoring the temporal correlations of the sample structure. Our proposed 4D $μ$CT reconstruction technique, named DYRECT, estimates individual attenuation evolution profiles for each position in the sample. This leads to a novel memory-efficient event-based representation of the sample, using as little as three image volumes: its initial attenuation, its final attenuation and the transition times. This third volume represents local events on a continuous timescale instead of the discrete global time frames. We propose a method to iteratively reconstruct the transition times and the attenuation volumes. The dynamic reconstruction technique was validated on synthetic ground truth data and experimental data, and was found to effectively pinpoint the transition times in the synthetic dataset with a time resolution corresponding to less than a tenth of the amount of projections required to reconstruct traditional $μ$CT time frames.

Figures (8)

• Figure 1: Schematic comparison between the proposed event-based reconstruction (DYRECT) and conventional frame-based reconstruction techniques. DYRECT describes events with fine temporal resolution at the projection level, using a single volume of local transition times. This mitigates temporal blurring associated with the longer frame sequence of coarse-resolution time step volumes.
• Figure 2: Illustrative update of the transition time $t_j^*$ of a single voxel $j$. The dashed blue line indicates the prior estimate $\mu_j(t)$ of the voxel, based on the three parameters $t_j^{*(it-1)} = 768$, $\mu_{A,j}^{(it-1)} = 0.6\,\mathrm{cm}^{-1}$, and $\mu_{B,j}^{(it-1)}= 0.9\,\mathrm{cm}^{-1}$. The full line is the virtual corrected attenuation curve $\mu_\mathrm{step}(t;\varepsilon_j)+\delta_j(t)$, by addition of the correction terms below, shown as the dotted line. The blue area at the bottom, between projection index $t = 400$ (ground truth) and $768$ (current estimate) indicates that the attenuation for those projections should be increased. Since the projections between $t = 0$ and $400$ have zero correction terms, this growing trend indicates that not$\mu_{A,j}$ should be updated, but that the final higher attenuation phase should start earlier by shifting $t_j^*$ to a lower projection time.
• Figure 3: Horizontal and vertical cross-sections (a) of bubble coalescence experiment at the initial rupture moment, reconstructed using the DYRECT technique. The overlay images (b) show the transition times $t^*$ of the indicated regions of interest. The temporal cross-sections (c) of a DYRECT reconstruction were compared to those made with a SART reconstruction. The estimated time of rupture during the bubble coalescence is indicated by $t^*_r$ .
• Figure 4: The reconstructed time of bubble coalescence $t^*_r$ corresponds to the time determined independently using the sinogram event detection technique. These difference projections (c) and sinograms (d) with the diverging colour map show the sample changes in the detector domain.
• Figure 5: Tracking the selected features in the sinogram domain (red, cyan, green and yellow ellipses) reveals their evolution at a higher temporal resolution than possible with reconstruction techniques that define global time windows. The study indicated that the alignment of the dynamic internal features with respect to the optical axis may affect the accuracy. When the wall aligns with the optical axis, the (red and cyan) tracks in the sinogram domain overlap which causes ambiguity in the event localisation along the viewing direction.