Adaptive Dual Velocity Field Learning along Reconstruction Trajectories for Insufficient-Angle CT

Diffusion models and flow-based generative models, most notably flow matching (FM), have recently delivered strong performance in computed tomography (CT) reconstruction. However, for the same scanning system whose acquisition geometry varies in the number of projection angles or in the angular range, existing methods still require retraining a dedicated model for each configuration and thus offer limited cross-geometry adaptability. Moreover, we observe that the quantity learned during intermediate sampling—the noise predictor ${ϵ}_{\theta }$ or score function in diffusion or the velocity field in flow models—is essentially independent of the current state along the sampling trajectory: in linear FM, for instance, the conditional velocity is a constant determined only by the two endpoints, $\mathbf{v}={\mathbf{x}}_1-{\mathbf{x}}_0$. Such a position-independent field is fundamentally implausible for the intrinsically nonlinear transport from projection data to images. In this paper, we therefore organize reconstructions obtained under different numbers of projections as an ordered reconstruction trajectory, and learn along this trajectory a dual velocity field consisting of a current (geometry-transition) velocity that describes the local evolution between successive angle settings and a target velocity that points toward the clean image. An adaptive velocity-learning mechanism further conditions the transport on the current state and its position along the trajectory, and the two velocities drive a progressive two-stage reconstruction network. A single trained model thereby generalizes across sparse- and limited-angle settings without retraining, achieving high-precision quantitative imaging on LoDoInd, Mayo, and PCB benchmarks.