This paper presents the first application of the novel ANET Compact Neutron Collimator to a tomographic study. The ANET collimator consists of a structure were collimating and absorbing channels are alternated in a chessboard-like geometry. It is characterised by an elevated collimation power within a limited length and presents a scalable structure both in length and in field of view. The first tomography with this collimator has been performed at the Paul Scherrer Institute, at the BOA beamline, on two small objects chosen for their different scattering properties: an iron fibula, circa X century, and an Afghan lapis lazuli. The result of the tomographic reconstruction is described in this paper.