Installation designed for reconstructing a three-dimensional image of an object defined by values assumed by a function (f) on points of the object, the function being a property of a conical radiation having a focal point (S) and passing through the object, said installation comprising a bidimensional array (5) of radiation detectors (6) oriented toward the focal point, and means (4, 7) for moving the detector array (5) along two trajectories around the object (1) at different distances from said object, wherein radiation received by the detectors passes through an area of interest of the object and, the reconstructed image relates to the area of interest of the object during a first of said two trajectories, and radiation received by the detectors passes through the entire object during a second of said two trajectories, the installation further comprising means for acquiring sums of the function on rays between the focal point and the detectors and performing an inversion algorithm calculating summations of the function on planes passing through the object.