[Paper Review] 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 Applications0 citations

TL;DR

Introduces a training-free 3D Field of Junctions (3D FoJ) representation that denoises and regularizes low-SNR volumes for diverse inverse problems, without hallucination risk, and works as a drop-in proximal prior.

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.

Motivation & Objective

• Motivate robust denoising and reconstruction of 3D volumes under severe noise across diverse modalities.
• Propose a training-free, explicit 3D structural prior that preserves edges and corners in 3D volumes.
• Develop an efficient patch-based 3D FoJ model that integrates with proximal gradient methods for inverse problems.
• Demonstrate the method's effectiveness on low-dose CT, cryo-ET, and noisy point clouds.
• Highlight scalability and potential as a drop-in regularizer for volumetric problems.

Proposed method

• Extend Field of Junctions to 3D by representing each volumetric patch with three intersecting planes that partition the patch into 3D wedges with constant values in each region.
• Optimize patch-wise junction parameters and region values to balance data fidelity with inter-patch consistency via an objective that enforces local fit, boundary alignment, and cross-patch intensity coherence.
• Use differentiable soft indicators and a differentiable boundary map to enable gradient-based optimization in two stages: local initialization and global joint refinement.
• Adopt a proximal gradient framework to solve inverse problems where the 3D FoJ serves as a regularizer, yielding x updates via a gradient step on data fidelity followed by a FoJ-based proximal step.
• Enable multi-GPU parallelism for processing high-resolution volumes and patches.

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

Experimental results

Research questions

• RQ1 Can a training-free 3D structural prior preserve sharp 3D boundaries under extreme noise across diverse volumes?
• RQ2 How does 3D FoJ perform as a denoiser and as a regularizer in volumetric inverse problems compared to classical and neural methods?
• RQ3 Does the 3D FoJ prior maintain geometric fidelity in low-SNR CT, cryo-ET, and lidar-like point clouds?
• RQ4 What is the impact of patch size, number of planes (M), and smoothing parameters on reconstruction quality and efficiency?
• RQ5 Can the method generalize as a drop-in regularizer for various noisy volumetric inverses beyond tomography?

Key findings

• 3D FoJ achieves higher MS-SSIM on 2D projections and higher 3D PSNR on volumes than baselines across low-SNR CT datasets.
• For low-dose CT with photon-count levels P50, P100, P1000, 3D FoJ outperforms R2-Gaussian, Filter2Noise, and 3D-TV in both projection-based and volumetric metrics.
• In cryo-ET, 3D FoJ qualitatively preserves fine structural details with balanced denoising and contrast enhancement compared to SC-Net, NMSG, and NLM.
• In point cloud denoising, 3D FoJ delivers competitive Chamfer Distance performance under various noise regimes, showing robustness to outlier and spread noise.
• Overall, 3D FoJ provides robust, training-free denoising and acts as an effective regularizer for noisy 3D inverse problems.

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.