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

TL;DR

This paper introduces a training-free 3D structural prior called 3D Field of Junctions (FoJ) that enhances denoising and reconstruction in volumetric inverse problems, especially under low SNR conditions.

Contribution

The paper proposes a novel 3D FoJ representation that is noise-robust, training-free, and applicable as a structural prior for various volumetric inverse problems.

Findings

Outperforms classical and neural methods in low-SNR 3D imaging tasks

Effectively preserves edges and corners in noisy volumetric data

Demonstrates success across CT, cryo-ET, and lidar point cloud denoising

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.