Gradient-based rigid motion correction in CBCT via Lie algebra-constrained registration

Low-frame-rate flat-panel detector and gantry design limit Cone-beam computed tomography (CBCT) scanning speed, increasing susceptibility to patient motion during prolonged scanning. Rigid motion invalidates the predetermined imaging geometry, leading to degraded image quality. To ensure diagnostic reliability and support downstream tasks, accurate motion estimation and subsequent motion-compensated reconstruction are essential. This work presents a general rigid motion correction framework for CBCT using differentiable 3D–2D registration. We introduce a Lie group manifold-constrained motion modeling approach that conforms to the definition of rigid transformation and analytically derive the gradient of the CBCT forward projection operator with respect to rigid motion parameters. Furthermore, we identify the spatial deviation relationship between motion-corrupted and ground truth images, proposing a motion estimation constraint to enhance convergence. Experimental comparisons with state-of-the-art methods demonstrate that our method achieves superior motion estimation and image restoration. It effectively recovers anatomical details and substantially reduces rigid motion artifacts, even under severe motion conditions.