1. A method for correcting artifacts in an x-ray projection of an object, comprising: passing x-ray radiation of a primary x-ray source through a modulator field having a repetitive pattern of modulator field areas with different x-ray radiation attenuation, the modulator field producing amplitude-modulated radiation, which is passed through the object to produce an amplitude-modulated projection that is recorded by a detector; performing a moving operation to move the x-ray source, the object and the detector relative to the modulator field, from first relative positions to second relative positions, the moving operation reciprocally interchanging modulator field areas having a relatively small x-ray radiation attenuation coefficient with modulator field areas having a relatively large x-ray radiation attenuation coefficient such that first and second original amplitude-modulated projections of the object are generated in the first and second relative positions, respectively; calculating first and second scatter images associated with the first and second original amplitude-modulated projections, respectively; and using the first and second scatter images to remove scatter contained in the first and second original amplitude-modulated projections.