OX-NeRF: 3D X-ray Tomography Reconstruction from Sparse Views Using Implicit Neural Representation

1. Introduction

• At ten or fewer projections, the inverse problem has a large null space, making classical reconstruction unreliable.Fewer projections can result from dose limits or from high-rate acquisition of objects that evolve within microseconds.Source: §1 · p. 1
• OX-NeRF trains one model across related scenes, combining shared convolutional features with a separate multi-resolution hash encoding for each scene.The fused features predict attenuation, and self-supervision compares ray-integrated predictions with measured projections.Source: §1 · p. 1
• Across four datasets, OX-NeRF achieves the highest 3D reconstruction accuracy among existing self-supervised radiance-field methods at every count from four to ten projections.The evaluation is restricted to the ultra-sparse regime.Source: §1 · p. 1

2.1. Computed Tomography

• At extreme sparsity, analytical methods produce streaks and hand-designed iterative regularizers are insufficient; supervised deep methods require representative labelled volumes.Analytical resolution is tied to projection count, while iterative regularizers suppress artifacts at moderate sparsity.Source: §2.1 · p. 2

2.2. Radiance fields

• X-ray NeRF and Gaussian-splatting methods optimize attenuation representations against measured projections without requiring volumetric ground truth.Prior methods fit one scene at a time and had not been evaluated in the ultra-sparse domain.Source: §2.2 · p. 2

2.3. Generalisable Radiance Fields

• Generalisable radiance fields share learned features across scenes; OX-NeRF adds an optimized per-scene spatial representation alongside its cross-scene encoder.This separates transferable priors from scene-specific geometry, unlike ONIX, whose prior is held entirely in shared weights.Source: §2.3 · p. 2

3.1. X-ray image formation

• Under the weak-interaction and projection approximations, the refractive index describes matter’s interaction with radiation, with β representing attenuation and δ representing phase shift.For attenuation projections, only the β term contributes.Source: §3.1 · pp. 2–3
• A detector pixel records a projection related to the field along its ray: attenuation accumulates along the ray, and reconstruction seeks the underlying 3D field.Every point along the ray contributes; the sampled field is the 3D reconstruction.Source: §3.1 · pp. 2–3
• Figure 1 pairs a shared convolutional encoder with the active scene’s hash grid; fused features predict attenuation, which is integrated along rays and compared with measurements by mean squared error.Only the hash grids are scene-specific.Source: Figure 1 · p. 3

3.2. Acquisition geometry

• Acquisition geometry maps each detector pixel to a ray with an origin and direction; parallel-beam and cone-beam acquisitions differ in how those coordinates are determined.The same transformations map a 3D point to its detector position for a projection.Source: §3.2 · p. 3

4.1. Pipeline

• The shared encoder, fusion module, and MLP learn set-wide features while each scene’s hash encoding stores scene-specific structure, with updates from each scene’s loss reaching shared components and only its own encoding.Each scene supplies source projections for feature extraction and target projections for the loss.Source: §4.1 · pp. 3–4

4.2. Ray Sampling

• Residual-guided sampling draws more rays from pixels with larger rendered-versus-measured errors, while a uniform component preserves supervision in better-rendered regions.Error maps refresh every τ epochs for the next B scenes in a fixed cyclic order; scenes not yet reached in the cycle draw rays uniformly.Source: §4.2 · p. 4

4.3. Feature Extraction and Fusion

• A shared ResNet-34 encoder supplies image features, while each scene’s multi-resolution hash grid supplies spatial features; the fusion module concatenates them and applies a learned linear map.Image features are read at each point’s projected position, and hash-grid features are queried at its 3D coordinates.Source: §4.3 · p. 4

4.4. Attenuation Prediction and Aggregation

• A four-layer MLP predicts attenuation per source projection, and learned geometry-aware weights combine those estimates into one value for the point.Every projection is rendered from the same aggregated field, and updates score all target projections of a scene together.Source: §4.4 · pp. 4–5

5.1. Datasets

• The four evaluation datasets comprise parallel-beam Ellipsoids and Shells, plus cone-beam Lung CT and Voids.Shells and Voids are datasets introduced by this work; Shells contains fine structures of voids and membranes, while Voids contains many small voids.Source: §5.1 · p. 5

5.2. Implementation and Baseline Methods

• Four self-supervised radiance-field baselines were compared, with CombiNeRF adapted to X-ray transmission and ONIX extended to cone-beam geometry.ONIX and OX-NeRF trained across 50 scenes and used the same four evenly spaced source projections; the other methods trained on individual scenes.Source: §5.2 · p. 5

5.3. Evaluation Setup

• Evaluation scored held-out projections with 2D SSIM and reconstructed volumes with 3D PSNR and 3D SSIM, using the same metric definitions across methods.A single least-squares gain was applied before scoring to account for each method's volume-length unit.Source: §5.3 · p. 5, Table 2 · p. 6

5.4. Novel View Synthesis and 3D Reconstruction

• OX-NeRF achieves the highest 3D SSIM in every setting and the highest 3D PSNR in all but one.At ten views, its reconstructions show finer detail and fewer artifacts than baselines, which exhibit streaks and diffuse haze.Source: Table 2 · p. 6, §5.4 · p. 6, Figure 3 · p. 7
• OX-NeRF renders the most faithful held-out projections in 11 of 12 settings, with a less pronounced advantage as the view budget rises toward ten.Projection quality improves for every method as views increase; by ten views, nearly every method renders excellent projections.Source: §5.4 · p. 6, Table 2 · p. 6, Figure 2 · p. 6

5.5. Ablation

• The convolutional encoder improves on either point encoder alone, hash grids beat sinusoidal encoding in all but one configuration, and residual-guided selection improves 3D SSIM in every configuration.The hash-grid exception is the gradient-guided, encoder-free configuration; taken together, the cross-scene encoder and per-scene hash grid account for most improvement and are strongest in combination.Source: §5.5 · pp. 6–7
• Reconstruction quality rises sharply as the scene set grows to 50 and more gradually beyond, while gains from larger hash tables continue through log2 T = 14 before leveling off.Each scene keeps its own table resident during training, so hash-grid memory scales with the number of scenes and table size.Source: §5.5 · p. 7

5.6. Increasing Views

• On Lung CT, OX-NeRF leads R2-Gaussian at 15 views, is on par at 20, and is overtaken by 25 views.With the chosen experimental settings, OX-NeRF peaks at over 90 GB of VRAM.Source: §5.6 · p. 8, Table 4 · p. 8

• In scenes with ten projections or fewer, OX-NeRF improves 3D reconstruction accuracy over existing self-supervised methods on both parallel- and cone-beam data.Source: §6 · p. 8
• Whether reconstruction gains continue with more capable hardware remains open because scene count and hash-table size were capped by memory.Source: §6 · p. 8
• Other proposed directions are anatomical priors in shared components and cross-scene X-ray Gaussian splatting, whose combination has not yet been attempted.Source: §6 · p. 8
• A time-domain extension would replace scene sets with temporally ordered sequences, potentially using motion across frames to resolve geometry ambiguous within one frame.Source: §6 · p. 8