In interventional radiology, 3D reconstruction of devices such as needles can increase the precision of procedures. Doing so with CBCT is time-consuming and increases the X-ray dose. Needles being sparse, a compressed-sensing reconstruction approach seems viable. In this paper, we thus investigate the benefits of directional total variation as an adequate prior for anisotropic devices. We introduce a decomposition method that allows several a priori directions to be considered at once as well as excludes the anatomical background that is not sparse. The capacity of the method is illustrated in simulations of limited-angle acquisitions. It allows good reconstruction of the needles from a small angular coverage, even if it cannot recover the anatomical background.