3D Field of Junctions: A Noise-Robust, Training-Free Structural Prior for Volumetric Inverse Problems

Volume denoising is a foundational problem in computa-tional imaging, as many 3D imaging inverse problems face high levels ofmeasurement noise. Inspired by the strong 2D image denoising propertiesof Field of Junctions (ICCV 2021), we propose a novel, fully volumetric3D Field of Junctions (3D FoJ) representation that optimizes a junctionof 3D wedges that best explain each 3D patch of a full volume, while en-couraging consistency between overlapping patches. In addition to directvolume denoising, we leverage our 3D FoJ representation as a structuralprior that: (i) requires no training data, and thus precludes the risk of hal-lucination, (ii) preserves and enhances sharp edge and corner structuresin 3D, even under low signal to noise ratio (SNR), and (iii) can be used asa drop-in denoising representation via projected or proximal gradient de-scent for any volumetric inverse problem with low SNR. We demonstratesuccessful volume reconstruction and denoising with 3D FoJ across threediverse 3D imaging tasks with low-SNR measurements: low-dose X-raycomputed tomography (CT), cryogenic electron tomography (cryo-ET),and denoising point clouds such as those from lidar in adverse weather.Across these challenging low-SNR volumetric imaging problems, 3D FoJoutperforms the evaluated classical denoisers, untrained neural denois-ers, and denoisers trained only on noisy examples. Code is available athttps://github.com/voilalab/3D-Field-of-Junctions.