An apparatus (1) for performing tomosynthesis and/or mammography of a breast of a patient, comprises: an X-ray detector device (2), designed to receive and detect X-rays in a first, detection plane (3) at least one X-ray source (4), which can be activated individually and which is positioned in such a way that it emits a corresponding X-ray beam (F) towards the first, detection plane (3) a region (R2) for positioning the breast (M) through which the beam (F) from the source (4) passes a processing and control unit (6), connected to the X-ray source (4) for activating it and connected to the detector device (2) for receiving a signal (s1) relating to the X-rays which passed through the breast (M) and were detected by the detector device (2), the unit (6) being designed to derive from the signal (s1) at least one radiographic image representative of the internal structure of the breast (M) of the patient a grille (7) for removing diffuse radiation, interposed between the source (4) and the detector device (2) to receive the X-rays which passed through the breast, the grille (7) for removing diffuse radiation comprising a plurality of plates (26) which are positioned opposite the chest (TO) of the patient when the breast (M) is positioned in the positioning region (R2), and which are angled in such a way that they converge towards the same region (R1) proximal to the X-ray source (4).
