Abstract: Objective. In particle therapy (PT), several methods are being investigated to help reduce range margins and identify deviations from the original treatment plan, such as prompt-gamma imaging with Compton cameras (CC). To reconstruct the images, the Origin Ensemble (OE) algorithm is commonly used. In the context of PT, artifacts and strong noise often affect CC images. To improve the ability of OE to identify range shifts, and also to enhance image quality, we propose to regularize OE using beam a-priori knowledge (beam prior). Approach. We implemented the beam prior to OE using the class of Gibbs' distribution functions. For evaluation, Monte-Carlo simulations of centered and off-center beams with therapeutic energies impinging on a PMMA target were conducted in GATE. To introduce range shifts, air layers were introduced into the target. In addition, the effect of a bone layer, closer to a realistic scenario, was investigated. OE with the beam prior (BP-OE) and conventional OE (reference) were compared using the spill-over-ratio (SOR) as well as shifts in the distal falloff in projections using cubic splines with Chebyshev nodes. Main results. BP-OE improved the shift estimates by up to 11% compared to conventional OE for centered and up to 250% with off-centered beams. BP-OE decreased the image noise level, improving the SOR significantly by up to 96%. Significance. BP-OE applied to CC data can improve shift estimations compared to conventional OE. The developed Gibbs-based regularization framework also allows further prior functions to be included into OE, for instance, smoothing or edge-preserving priors. BP-OE could be extended to PET-based range verification or multiple-beam scenarios.