Source-linked AI summary
NAF: Neural Attenuation Fields for Sparse-View CBCT Reconstruction
Ruyi Zha, Yanhao Zhang, Hongdong Li
TL;DR
Sparse-view CBCT must recover 3D attenuation fields from insufficient projections while avoiding the data and computational demands of existing methods. NAF learns the field as an implicit neural representation, synthesizes projections for self-supervision, and uses hash encoding to capture details efficiently. It achieves better results than baselines on human-organ and phantom datasets while requiring reasonably short computation time.
Problem
Sparse-view CBCT reconstructs a volumetric attenuation field from dozens of projections, but insufficient views cause artifacts and existing learning-based methods often require extensive training datasets.
Method
NAF trains a fully connected network that maps encoded 3D coordinates to attenuation coefficients, synthesizes projections through X-ray attenuation, and minimizes projection error using hash encoding.
Results
NAF achieves significantly better results than other baselines on human-organ and phantom datasets with reasonably short computation time.
Takeaways & Limitations
NAF provides a self-supervised sparse-view CBCT solution that needs no external datasets or structural prior beyond the subject’s projections.
Abstract
from arXiv · showhide
This paper proposes a novel and fast self-supervised solution for sparse-view CBCT reconstruction (Cone Beam Computed Tomography) that requires no external training data. Specifically, the desired attenuation coefficients are represented as a continuous function of 3D spatial coordinates, parameterized by a fully-connected deep neural network. We synthesize projections discretely and train the network by minimizing the error between real and synthesized projections. A learning-based encoder entailing hash coding is adopted to help the network capture high-frequency details. This encoder outperforms the commonly used frequency-domain encoder in terms of having higher performance and efficiency, because it exploits the smoothness and sparsity of human organs. Experiments have been conducted on both human organ and phantom datasets. The proposed method achieves state-of-the-art accuracy and spends reasonably short computation time.
1 Introduction
Sparse-view CBCT reconstructs a 3D attenuation field from far fewer projections than conventional CBCT, making artifacts and computational cost central challenges. NAF addresses these challenges with a self-supervised implicit neural representation that uses hash encoding and achieves strong accuracy with relatively short computation time.
- Problem: Sparse-view CBCT uses dozens of projections to recover a volumetric attenuation field, whereas traditional CBCT uses hundreds of images.The roughly 10× reduction in views produces notable artifacts and increases reconstruction difficulty.
- Prior approaches: Existing analytical, iterative, and learning-based approaches trade off sparse-view robustness, computation, memory, training data, or cross-application generalization.Analytical methods handle ideal settings but poorly address ill-posed sparse views; iterative methods are costly, while many learning-based methods require extensive datasets.
- Method: NAF represents the attenuation coefficient field as an implicit neural representation and trains an MLP to minimize error between real and synthesized projections.The network maps encoded 3D coordinates to attenuation coefficients and synthesizes projections by modeling attenuation along ray trajectories.
- Method: NAF adopts hash encoding instead of frequency-domain encoding to learn high-frequency details with a faster, more compact representation.The method is motivated by the smoothness and piecewise homogeneity of human organs, which make dense frequency encoding redundant.
- Results: The method reconstructs detailed CT models within 10-40 minutes, a computation time described as comparable to iterative methods.The paper presents this efficiency alongside its accuracy as supporting feasibility for clinical CT applications.
- Contribution: NAF requires neither external datasets nor structural priors beyond projections of the subject.This self-supervised setup trains directly from the acquired projections rather than relying on a separately trained CT model.
2 Method
NAF reconstructs sparse-view CBCT by learning a continuous attenuation field, synthesizing projections from sampled rays, and optimizing against real projections. Its hash encoder exploits organ sparsity and smoothness to provide compact features for the neural field.
- Pipeline: NAF samples points along scanner-defined X-ray paths, encodes their coordinates, predicts attenuation coefficients with an MLP, and synthesizes projections from those predictions.The pipeline then queries the trained network at voxel coordinates to form the final discrete CT model.
- Position encoding: Because spectral bias favors low-frequency details, NAF introduces position encoding to map 3D coordinates into a higher-dimensional feature space.The paper motivates encoding as a way to ease learning of spatial detail.
- Position encoding: Human organs’ approximately uniform media and smooth shapes make dense frequency encoding redundant except near edges.The paper uses these structural properties to motivate a sparse, learning-based alternative.
- Hash encoding: Hash encoding represents bounded space with multiresolution voxel grids, trainable lookup-table features, neighboring-corner queries, and interpolation.Features from all resolution levels are concatenated into the encoder output.
- Hash encoding: Hash encoding produces 32-dimensional outputs with competitive feature quality, enabling a more compact subsequent network than frequency encoding.The paper attributes this to hash collisions matching organ sparsity and trainable selection of relevant frequency content.
- Optimization: NAF updates the hash encoder and attenuation network by minimizing the L2 difference between real and synthesized projections over ray batches.The loss compares Ir and Is for each ray while jointly optimizing both parameter sets.
3 Experiments
Experiments on human-organ and phantom CT datasets compare NAF with analytical, iterative, and frequency-encoding learning-based baselines. NAF achieves the strongest reconstruction quality across slices and view settings while requiring substantially less training time than IntraTomo3D.
- Experimental settings: Experiments use five human-organ and phantom CT datasets, including chest, jaw, foot, abdomen, and aorta data.Human-organ projections are generated with TIGRE using 50 projections, 3% noise, and a 180° range.
- Experimental settings: NAF is compared with FDK, SART, ASD-POCS, and the frequency-encoding deep-learning method IntraTomo3D.The baselines represent analytical, iterative, and learning-based reconstruction approaches.
- Quantitative results: NAF achieves the best PSNR and SSIM results across both human-organ and phantom datasets.On the abdomen dataset, NAF’s PSNR is 3.07 dB higher than SART, the second-best method.
- Qualitative results: NAF produces the most detailed reconstructions, clearest edges, and fewest artifacts, outperforming other methods across all abdomen slices.FDK shows artifacts, SART loses details, ASD-POCS smears structures, and IntraTomo3D slightly blurs media boundaries.
- View-count analysis: NAF performs better than other methods under most tested view counts, while reconstruction quality generally increases as the number of input views rises.The view-count comparison is conducted on the abdomen dataset.
- Running time: NAF is 3× faster than IntraTomo3D and has running time similar to iterative methods.IntraTomo3D requires more than one hour to train, whereas NAF benefits from a compact network design.
4 Conclusion
The paper concludes that NAF reconstructs sparse-view CBCT volumes by fitting a neural attenuation field to projection errors. Across human-organ and phantom datasets, it provides better results than baselines while maintaining reasonably short computation time.
- Conclusion: NAF trains a fully connected neural network that maps 3D spatial coordinates to attenuation coefficients and minimizes synthesized-versus-real projection error.Projections are synthesized by attenuating incident X-rays according to predicted coefficients.
- Conclusion: Hash encoding replaces frequency encoding to extract features for tomographic reconstruction.The conclusion identifies frequency encoding as computationally inefficient for this task.
- Conclusion: Experiments on human-organ and phantom datasets show significantly better results than baselines with reasonably short computation time.The conclusion presents this as the principal empirical outcome of the method.