Sparse View Tomographic Reconstruction of Elongated Objects using Learned Primal-Dual Networks

TL;DR

This work tackles sparse-view tomographic reconstruction for elongated objects (wood logs) scanned on a conveyor, where each 2D slice lacks sufficient information for 3D recovery. It proposes a 2.5D Learned Primal-Dual (LPD) method that accumulates information from neighboring slices via memory-enabled CNN updates, bridging 2D and 3D reconstructions. The approach is evaluated on a wood-CT dataset, showing that with as few as five source positions the 2.5D LPD yields reconstructions preserving knots, heartwood, and sapwood, and achieves knot-segmentation performance within roughly 15% of full CT-based segmentation. This method offers a practical, cost-efficient pathway for industrial sawmills to obtain meaningful 3D interior information from sparse X-ray scans, potentially improving yield and wood quality assessment; future work includes log rotation during acquisition and joint reconstruction/segmentation. $y = \mathcal{A}(x) + e$, where $\mathcal{A}$ is the forward (ray) operator and $e$ models noise, and the learned reconstruction $\mathcal{R}_{\theta}$ aims to satisfy $\mathcal{A}(\mathcal{R}_{\theta}(y)) \approx y$, integrating data fidelity with learned priors in a memory-enhanced, unrolled optimization framework.$

Abstract

In the wood industry, logs are commonly quality screened by discrete X-ray scans on a moving conveyor belt from a few source positions. Typically, the measurements are obtained in a single two-dimensional (2D) plane (a "slice") by a sequential scanning geometry. The data from each slice alone does not carry sufficient information for a three-dimensional tomographic reconstruction in which biological features of interest in the log are well preserved. In the present work, we propose a learned iterative reconstruction method based on the Learned Primal-Dual neural network, suited for sequential scanning geometries. Our method accumulates information between neighbouring slices, instead of only accounting for single slices during reconstruction. Evaluations were performed by training U-Nets on segmentation of knots (branches), which are crucial features in wood processing. Our quantitative and qualitative evaluations show that with as few as five source positions our method yields reconstructions of logs that are sufficiently accurate to identify biological features like knots (branches), heartwood and sapwood.

Figures (9)

• Figure 1: Overview of the experimental workflow and dataset structure.
• Figure 2: Reconstructions of a log slice with knots, using $3$ consecutive slices and varying number of source positions.
• Figure 3: Reconstructions of a log slice without knots, using $3$ consecutive slices and varying number of source positions.
• Figure 4: Average PSNR (of all slices from 3 entire test logs) for 2.5D LPD for different number of consecutive slices and different number of source positions per slice. "Last" and "middle" corresponds to two different strategies where last and middle slice is being reconstructed.
• Figure 5: Reconstructions of log using $5$ consecutive slices and different number of source positions - sample where knots start appearing. "Last" and "middle" corresponds to two different strategies where last and middle slice is being reconstructed.