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Purpose: Today's standard imaging technique in interventional radiology is the single- or biplane x-ray fluoroscopy which delivers 2D projection images as a function of time (2D+T). This state-of-the-art technology, however, suffers from its projective nature and is limited by the superposition of the patient's anatomy. Temporally resolved tomographic volumes (3D+T) would significantly improve the visualization of complex structures. A continuous tomographic data acquisition, if carried out with today's technology, would yield an excessive patient dose. Recently the authors proposed a method that enables tomographic fluoroscopy at the same dose level as projective fluoroscopy which means that if scanning time of an intervention guided by projective fluoroscopy is the same as that of an intervention guided by tomographic fluoroscopy, almost the same dose is administered to the patient. The purpose of this work is to extend authors' previous work and allow for patient motion during the intervention. Methods: The authors propose the running prior technique for adaptation of a prior image. This adaptation is realized by a combination of registration and projection replacement. In a first step the prior is deformed to the current position via affine and deformable registration. Then the information from outdated projections is replaced by newly acquired projections using forward and backprojection steps. The thus adapted volume is the running prior. The proposed method is validated by simulated as well as measured data. To investigate motion during intervention a moving head phantom was simulated. Realin vivo data of a pig are acquired by a prototype CT system consisting of a flat detector and a continuously rotating clinical gantry. Results: With the running prior technique it is possible to correct for motion without additional dose. For an application in intervention guidance both steps of the running prior technique, registration and replacement, are necessary. Reconstructed volumes based on the running prior show high image quality without introducing new artifacts and the interventional materials are displayed at the correct position. Conclusions: The running prior improves the robustness of low dose 3D+T intervention guidance toward intended or unintended patient motion.