Motion-Enabled Tomography via Gaussian Mixture Models
This work addresses the challenge of reconstructing moving objects in tomography, offering a method with closed-form ray transforms and exact gradients, though validation is limited to simulated 2D data.
The paper proposes a parametric spatiotemporal model using Gaussian Mixture Models (GMM) for computerized tomography of moving objects, enabling accurate reconstruction of a 5-Gaussian GMM with intersecting trajectories in simulated 2D experiments.
Recovering physical properties of objects in motion is a core task across scientific and industrial applications. When the relative motion between the object and the sensing apparatus provides sufficient angular coverage, Computerized Tomography offers a powerful means of reconstruction. For such scenarios, we propose a parametric spatiotemporal model applied to Gaussian Mixture Models (GMM), in which each constituent Gaussian is parameterized by its own angular velocity, projectile motion, and geometry. GMM are a suitable means of reconstruction because they (i) admit accurate approximations in object space and (ii) have a closed form expression under the ray transform; enabling efficient forward predictions and exact gradient computations in data space. By decoupling the reconstruction problem into two sub-inverse problems, we characterize solutions as minimizers of task-specific objective functions that are derived and solved by utilizing the properties of (ii). The resulting algorithm we provide is applicable to objects in Euclidean space of arbitrary dimension. We validate the method on a simulated 2D problem, achieving accurate reconstruction of a 5-Gaussian GMM with intersecting trajectories. This also provides a foundation for further experimentation in settings with noisy data, 3D objects, and non-rigid body dynamics.