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Proton therapy treatment for lungs remains challenging as images enabling the detection of inter- and intra-fractional motion, which could be used for proton dose adaptation, are not readily available. 4D computed tomography (4DCT) provides high image quality but is rarely available in-room, while in-room 4D cone beam computed tomography (4DCBCT) suffers from image quality limitations stemming mostly from scatter detection. This study investigated the feasibility of using virtual 4D computed tomography (4DvCT) as a prior for a phase-per-phase scatter correction algorithm yielding a 4D scatter corrected cone beam computed tomography image (4DCBCTcor), which can be used for proton dose calculation. 4DCT and 4DCBCT scans of a porcine lung phantom, which generated reproducible ventilation, were acquired with matching breathing patterns. Diffeomorphic Morphons, a deformable image registration algorithm, was used to register the mid-position 4DCT to the mid-position 4DCBCT and yield a 4DvCT. The 4DCBCT was reconstructed using motion-aware reconstruction based on spatial and temporal regularization (MA-ROOSTER). Successively for each phase, digitally reconstructed radiographs of the 4DvCT, simulated without scatter, were exploited to correct scatter in the corresponding CBCT projections. The 4DCBCTcor was then reconstructed with MA-ROOSTER using the corrected CBCT projections and the same settings and deformation vector fields as those already used for reconstructing the 4DCBCT. The 4DCBCTcor and the 4DvCT were evaluated phase-by-phase, performing proton dose calculations and comparison to those of a ground truth 4DCT by means of dose-volume-histograms (DVH) and gamma pass-rates (PR). For accumulated doses, DVH parameters deviated by at most 1.7% in the 4DvCT and 2.0% in the 4DCBCTcor case. The gamma PR for a (2%, 2 mm) criterion with 10% threshold were at least 93.2% (4DvCT) and 94.2% (4DCBCTcor), respectively. The 4DCBCTcor technique enabled accurate proton dose calculation, which indicates the potential for applicability to clinical 4DCBCT scans. [ABSTRACT FROM AUTHOR]