[en] A new technique for digital mammography based on the use of a collimator and an anti-scatter grid coupled with a mosaic detector has been studied with a Monte Carlo program. The simulation, with a low-energy spectrum X-ray beam and a breast phantom, provides a quantitative assessment of the capability of the method to reduce the physical background of the image due to scattering in the body, without introducing image artifacts. With minor modifications to the existing X-ray facilities, the method could also be applied to area detectors. To verify the results of the simulation, an experimental setup based on a CCD camera coupled via a fiber optic plate to a CsI(Tl) scintillator is under test