[论文解读] 3D Field of Junctions: A Noise-Robust, Training-Free Structural Prior for Volumetric Inverse Problems

Namhoon Kim, Narges Moeini+2 more|arXiv (Cornell University)|Mar 2, 2026

Advanced Electron Microscopy Techniques and Applications被引用 0

一句话总结

介绍一种训练-free的3D Junctions场（3D FoJ）表示，用于去噪和正则化低信噪比体积的多种逆问题，具备无幻觉风险，且可作为直接的近端先验。

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.

研究动机与目标

• 在多种模态下的极端噪声环境中，推动对3D体积的鲁棒去噪与重建。
• 提出一个训练-free、显式的3D结构先验，保留3D体积的边缘和角点。
• 开发一个高效的基于补丁的3D FoJ模型，使其能够与近端梯度方法结合用于逆问题。
• 展示该方法在低剂量CT、cryo-ET和带噪点云上的有效性。
• 突出可扩展性和作为体积问题的直接正则化器的潜力。

提出的方法

• 通过将每个体积补丁表示为三条相交平面，将补丁分割为3D楔区，在每个区域内赋予恒定值，从而将Field of Junctions扩展到3D。
• 通过优化补丁级的连接参数与区域值，利用一个目标函数在局部拟合、边界对齐和跨补丁强度一致性之间取得平衡。
• 使用可微的软指示符和可微的边界映射，实现两阶段的基于梯度的优化：局部初始化和全局联合细化。
• 采用近端梯度框架解决以3D FoJ作为正则化项的逆问题，数据保真度的梯度步长更新后再进行FoJ为基础的近端步。
• 实现多GPU并行化以处理高分辨率体积和补丁。

Figure 1 : Our 3D Field of Junctions (3D FoJ) is an effective volumetric denoiser across diverse inverse problems: low-dose computed tomography ( top row ), cryogenic electron tomography ( middle row ), and point cloud denoising ( bottom row ). Our cryo-ET experiment uses real data for which noisele

实验结果

研究问题

• RQ1 训练-free的3D结构先验是否能在极端噪声下在多种体积中保持清晰的3D边界？
• RQ2 在体积逆问题中，3D FoJ作为去噪和正则化相比传统和神经方法的表现如何？
• RQ3 3D FoJ先验在低SNR的CT、cryo-ET和激光雷达样点云中是否保持几何保真？
• RQ4 补丁大小、平面数量（M）和平滑参数对重建质量与效率有什么影响？
• RQ5 该方法能否作为其他噪声体积逆问题的直接正则化器（除断层成像外）？

主要发现

• 3D FoJ在低-SNR CT数据集的2D投影上实现了更高的MS-SSIM，在体积上的3D PSNR也高于基线。
• 对于低剂量CT，光子计数水平P50、P100、P1000，3D FoJ在投影指标和体积指标上均优于R2-Gaussian、Filter2Noise和3D-TV。
• 在cryo-ET中，3D FoJ在降噪与对比度增强之间取得平衡，定性保留了细微结构细节，优于SC-Net、NMSG和NLM。
• 在点云去噪方面，3D FoJ在各种噪声条件下提供具有竞争力的Chamer距离表现，且对离群和扩散噪声具有鲁棒性。
• 总体而言，3D FoJ提供鲁棒的、训练-free去噪，并作为噪声3D逆问题的有效正则化器。

Figure 4 : Comparison of unseen projection views synthesized from reconstructed 3D volumes (top) and slice views of reconstructed 3D volumes (bottom) for the engine dataset under low-SNR ( P50 ) conditions.