Volume denoising is a foundational problem in computational imaging, as many 3D imaging inverse problems face high levels of measurement noise. Inspired by the strong 2D image denoising properties of Field of Junctions (ICCV 2021), we propose a novel, fully volumetric 3D Field of Junctions (3D FoJ) representation that optimizes a junction of 3D wedges that best explain each 3D patch of a full volume, while encouraging consistency between overlapping patches. In addition to direct volume denoising, we leverage our 3D FoJ representation as a structural prior that: (i) requires no training data, and thus precludes the risk of hallucination, (ii) preserves and enhances sharp edge and corner structures in 3D, even under low signal to noise ratio (SNR), and (iii) can be used as a drop-in denoising representation via projected or proximal gradient descent for any volumetric inverse problem with low SNR. We demonstrate successful volume reconstruction and denoising with 3D FoJ across three diverse 3D imaging tasks with low-SNR measurements: low-dose X-ray computed 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 FoJ outperforms a mixture of classical and neural methods.

翻译：体积去噪是计算成像中的一个基础问题，因为许多三维成像逆问题都面临高水平的测量噪声。受二维图像去噪方法“交会场”（ICCV 2021）强大性能的启发，我们提出了一种新颖的、完全体积化的三维交会场表示方法。该方法优化一个由三维楔形块构成的交会结构，以最佳地解释整个体积中每个三维块，同时鼓励重叠块之间的一致性。除了直接用于体积去噪外，我们还利用我们的三维交会场表示作为一种结构先验，该先验具有以下特点：（i）无需训练数据，从而避免了产生幻觉的风险；（ii）即使在低信噪比条件下，也能保持并增强三维中的锐利边缘和角点结构；（iii）可通过投影梯度下降或邻近梯度下降，作为一种即插即用的去噪表示，用于任何低信噪比的体积逆问题。我们在三种不同的低信噪比测量三维成像任务中，成功展示了使用三维交会场进行体积重建和去噪的效果：低剂量X射线计算机断层扫描、冷冻电子断层扫描，以及点云去噪（例如恶劣天气下的激光雷达点云）。在这些具有挑战性的低信噪比体积成像问题中，三维交会场的性能优于一系列经典方法与神经方法的混合。