Abstract
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.
Abstract (translated)
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向问题是高度测量噪声的。受图像领域节点（ICCV 2021）在二维图像去噪方面的强大性能启发，我们提出了一种全新的、完全体素化的3D图像节点场（3D FoJ）表示方法。这种表示法优化了一个最佳解释全体积中每个三维补丁的3D楔形连接点，并鼓励重叠补丁之间的一致性。除了直接进行体积去噪之外，我们的3D FoJ表示还可以作为结构先验：(i) 不需要训练数据，从而消除了幻觉的风险；(ii) 即使在低信噪比（SNR）条件下也能保持并增强三维中的锐边和角点结构；(iii) 可以通过投影或近似梯度下降用于任何具有低SNR的体素逆向问题去噪。我们在三个不同且测量信噪比较低的3D成像任务中成功展示了3D FoJ的体积重建与降噪：低剂量X射线计算机断层扫描（CT）、冷冻电子断层扫描（cryo-ET）以及恶劣天气下激光雷达点云的去噪。在这些具有挑战性的低SNR体素成像问题上，3D FoJ的表现超过了经典方法和神经网络方法的混合使用。
URL
https://arxiv.org/abs/2603.02149
