In interventional radiology, 3D reconstruction of devices such as needles would 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. We thus investigate the interest 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 on simulations of limited-angle acquisitions. It is shown to allow good reconstruction of the needles from a small angular coverage, even if the anatomical background cannot be recovered.
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