An x-ray imaging apparatus, comprising: a rotating x-ray source for emitting a radiation beam; an x-ray detector positioned to receive radiation from the x-ray source; a beamformer configured to adjust a shape of the radiation beam emitted by the x-ray source, such that a primary region of the x-ray detector is directly exposed to the radiation beam and at least one shadow region (512, 514) of the x-ray detector is blocked from direct exposure to the radiation beam by the beamformer; a data processing system configured to: receive measured projection data in the primary region and measured scatter data in the at least one shadow region (512, 514); and determine an estimated scatter in the primary region during a current rotation of the x-ray source based on the measured scatter data in the at least one shadow region (512, 514) during at least one of a previous rotation of the x-ray source or a next rotation of the x-ray source; wherein coverage of the at least one shadow region (512, 514) during at least one of the previous rotation or the next rotation overlaps the primary region during the current rotation at a common azimuth angle projecting into a same plane, or overlaps the primary region during the current rotation at the same azimuth angle projecting onto the same plane. a rotating x-ray source for emitting a radiation beam; an x-ray detector positioned to receive radiation from the x-ray source; a beamformer configured to adjust a shape of the radiation beam emitted by the x-ray source, such that a primary region of the x-ray detector is directly exposed to the radiation beam and at least one shadow region (512, 514) of the x-ray detector is blocked from direct exposure to the radiation beam by the beamformer; a data processing system configured to: receive measured projection data in the primary region and measured scatter data in the at least one shadow region (512, 514); and determine an estimated scatter in the primary region during a current rotation of the x-ray source based on the measured scatter data in the at least one shadow region (512, 514) during at least one of a previous rotation of the x-ray source or a next rotation of the x-ray source; wherein coverage of the at least one shadow region (512, 514) during at least one of the previous rotation or the next rotation overlaps the primary region during the current rotation at a common azimuth angle projecting into a same plane, or overlaps the primary region during the current rotation at the same azimuth angle projecting onto the same plane. receive measured projection data in the primary region and measured scatter data in the at least one shadow region (512, 514); and determine an estimated scatter in the primary region during a current rotation of the x-ray source based on the measured scatter data in the at least one shadow region (512, 514) during at least one of a previous rotation of the x-ray source or a next rotation of the x-ray source; wherein coverage of the at least one shadow region (512, 514) during at least one of the previous rotation or the next rotation overlaps the primary region during the current rotation at a common azimuth angle projecting into a same plane, or overlaps the primary region during the current rotation at the same azimuth angle projecting onto the same plane.