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Purpose: Projections acquired with continuous gantry rotation may suffer from blurring effects, depending on the rotation speed and the exposure time of each projection. This leads to blurred reconstructions if conventional reconstruction algorithms are applied. In this paper, the authors propose a reconstruction method for fast acquisitions based on a continuously moving and continuously emitting x-ray source. They study the trade-off between total acquisition time and reconstruction quality and compare with conventional reconstructions using projections acquired with a stepwise moving x-ray source. Methods: The authors introduce the algebraic reconstruction technique with angular integration concept, which models the angular integration due to the relative motion of the x-ray source during the projection. Results: Compared to conventional reconstruction from projections acquired with pulsed x-ray emission, the proposed method results in substantially improved reconstruction quality around the center of rotation. Outside this region, the proposed method results in improved radial resolution and a decreased tangential resolution. For a fixed reconstruction quality of this region of interest, the proposed method enables a lower number of projections and thus a faster acquisition. Conclusions: The modeling of the continuous gantry rotation in the proposed method substantially improves the reconstruction quality in a region of interest around the rotation center. The proposed method shows potential for fast region of interest tomography. [ABSTRACT FROM AUTHOR]