# NAF: Neural Attenuation Fields for Sparse-View CBCT Reconstruction

arXiv: https://arxiv.org/abs/2209.14540 · HTML: https://mlsanity.com/paper/2209.14540/

## Key facts

- Cited by 108 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 29 Sep 2022.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [X2CT-GAN: Reconstructing CT from Biplanar X-Rays with Generative Adversarial Networks](https://mlsanity.com/paper/1905.06902/) (2019)
- [IREM: High-Resolution Magnetic Resonance (MR) Image Reconstruction via Implicit Neural Representation](https://mlsanity.com/paper/2106.15097/) (2021)
- [Lose The Views: Limited Angle CT Reconstruction via Implicit Sinogram Completion](https://mlsanity.com/paper/1711.10388/) (2017)
- [End-To-End Convolutional Neural Network for 3D Reconstruction of Knee Bones From Bi-Planar X-Ray Images](https://mlsanity.com/paper/2004.00871/) (2020)
- [Improving Generalizability in Limited-Angle CT Reconstruction with Sinogram Extrapolation](https://mlsanity.com/paper/2103.05255/) (2021)
- [LEARN: Learned Experts' Assessment-based Reconstruction Network for Sparse-data CT](https://mlsanity.com/paper/1707.09636/) (2017)

## Built on by (most cited first, 30 of 108)

- [Structure-Aware Sparse-View X-ray 3D Reconstruction](https://mlsanity.com/paper/2311.10959/) (2023)
- [R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction](https://mlsanity.com/paper/2405.20693/) (2024)
- [Radiative Gaussian Splatting for Efficient X-ray Novel View Synthesis](https://mlsanity.com/paper/2403.04116/) (2024)
- [Learning Deep Intensity Field for Extremely Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2303.06681/) (2023)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [3DGR-CT: Sparse-View CT Reconstruction with a 3D Gaussian Representation](https://mlsanity.com/paper/2312.15676/) (2023)
- [SNAF: Sparse-view CBCT Reconstruction with Neural Attenuation Fields](https://mlsanity.com/paper/2211.17048/) (2022)
- [DDGS-CT: Direction-Disentangled Gaussian Splatting for Realistic Volume Rendering](https://mlsanity.com/paper/2406.02518/) (2024)
- [Learning 3D Gaussians for Extremely Sparse-View Cone-Beam CT Reconstruction](https://mlsanity.com/paper/2407.01090/) (2024)
- [DPER: Diffusion Prior Driven Neural Representation for Limited Angle and Sparse View CT Reconstruction](https://mlsanity.com/paper/2404.17890/) (2024)
- [C^2RV: Cross-Regional and Cross-View Learning for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2406.03902/) (2024)
- [Geometry-Aware Attenuation Learning for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2303.14739/) (2023)
- [How to Train Neural Field Representations: A Comprehensive Study and Benchmark](https://mlsanity.com/paper/2312.10531/) (2023)
- [Volumetrically Consistent 3D Gaussian Rasterization](https://mlsanity.com/paper/2412.03378/) (2024)
- [Fit Pixels, Get Labels: Meta-learned Implicit Networks for Image Segmentation](https://mlsanity.com/paper/2510.04021/) (2025)
- [Unsupervised Polychromatic Neural Representation for CT Metal Artifact Reduction](https://mlsanity.com/paper/2306.15203/) (2023)
- [Implicit Neural Representations for Robust Joint Sparse-View CT Reconstruction](https://mlsanity.com/paper/2405.02509/) (2024)
- [CT Reconstruction from Few Planar X-rays with Application towards Low-resource Radiotherapy](https://mlsanity.com/paper/2308.02100/) (2023)
- [DIFR3CT: Latent Diffusion for Probabilistic 3D CT Reconstruction from Few Planar X-Rays](https://mlsanity.com/paper/2408.15118/) (2024)
- [Neural Radiance Fields in Medical Imaging: A Survey](https://mlsanity.com/paper/2402.17797/) (2024)
- [TOGS: Gaussian Splatting with Temporal Opacity Offset for Real-Time 4D DSA Rendering](https://mlsanity.com/paper/2403.19586/) (2024)
- [NeRF-US: Removing Ultrasound Imaging Artifacts from Neural Radiance Fields in the Wild](https://mlsanity.com/paper/2408.10258/) (2024)
- [3DGR-CAR: Coronary artery reconstruction from ultra-sparse 2D X-ray views with a 3D Gaussians representation](https://mlsanity.com/paper/2410.00404/) (2024)
- [MedFuncta: A Unified Framework for Learning Efficient Medical Neural Fields](https://mlsanity.com/paper/2502.14401/) (2025)
- [Glimpse: Generalized Locality for Scalable and Robust CT](https://mlsanity.com/paper/2401.00816/) (2024)
- [DeepCA: Deep Learning-based 3D Coronary Artery Tree Reconstruction from Two 2D Non-simultaneous X-ray Angiography Projections](https://mlsanity.com/paper/2407.14616/) (2024)
- [Discretized Gaussian Representation for Tomographic Reconstruction](https://mlsanity.com/paper/2411.04844/) (2024)
- [X-LRM: X-ray Large Reconstruction Model for Extremely Sparse-View Computed Tomography Recovery in One Second](https://mlsanity.com/paper/2503.06382/) (2025)
- [X2-Gaussian: 4D Radiative Gaussian Splatting for Continuous-time Tomographic Reconstruction](https://mlsanity.com/paper/2503.21779/) (2025)
- [X-GRM: Large Gaussian Reconstruction Model for Sparse-view X-rays to Computed Tomography](https://mlsanity.com/paper/2505.15235/) (2025)

## Abstract (arXiv)

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.