# Self-Supervised Coordinate Projection Network for Sparse-View Computed Tomography

arXiv: https://arxiv.org/abs/2209.05483 · HTML: https://mlsanity.com/paper/2209.05483/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 51 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [Low-Dose CT with a Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)](https://mlsanity.com/paper/1702.00288/) (2017)
- [DeRF: Decomposed Radiance Fields](https://mlsanity.com/paper/2011.12490/) (2020)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [Deep-neural-network based sinogram synthesis for sparse-view CT image reconstruction](https://mlsanity.com/paper/1803.00694/) (2018)
- [Joint Implicit Image Function for Guided Depth Super-Resolution](https://mlsanity.com/paper/2107.08717/) (2021)
- [UncertaINR: Uncertainty Quantification of End-to-End Implicit Neural Representations for Computed Tomography](https://mlsanity.com/paper/2202.10847/) (2022)
- [Joint Image Reconstruction and Segmentation Using the Potts Model](https://mlsanity.com/paper/1405.5850/) (2014)

## Built on by (most cited first, 30 of 31)

- [DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction](https://mlsanity.com/paper/2211.12340/) (2022)
- [Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction](https://mlsanity.com/paper/2301.00127/) (2022)
- [CuNeRF: Cube-Based Neural Radiance Field for Zero-Shot Medical Image Arbitrary-Scale Super Resolution](https://mlsanity.com/paper/2303.16242/) (2023)
- [DPER: Diffusion Prior Driven Neural Representation for Limited Angle and Sparse View CT Reconstruction](https://mlsanity.com/paper/2404.17890/) (2024)
- [Geometry-Aware Attenuation Learning for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2303.14739/) (2023)
- [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)
- [Joint Rigid Motion Correction and Sparse-View CT via Self-Calibrating Neural Field](https://mlsanity.com/paper/2210.12731/) (2022)
- [TiAVox: Time-aware Attenuation Voxels for Sparse-view 4D DSA Reconstruction](https://mlsanity.com/paper/2309.02318/) (2023)
- [ReLUs Are Sufficient for Learning Implicit Neural Representations](https://mlsanity.com/paper/2406.02529/) (2024)
- [Highly Accelerated MRI via Implicit Neural Representation Guided Posterior Sampling of Diffusion Models](https://mlsanity.com/paper/2407.02744/) (2024)
- [Physics-Inspired Generative Models in Medical Imaging: A Review](https://mlsanity.com/paper/2407.10856/) (2024)
- [Unsupervised Multi-Parameter Inverse Solving for Reducing Ring Artifacts in 3D X-Ray CBCT](https://mlsanity.com/paper/2412.05853/) (2024)
- [4DRGS: 4D Radiative Gaussian Splatting for Efficient 3D Vessel Reconstruction from Sparse-View Dynamic DSA Images](https://mlsanity.com/paper/2412.12919/) (2024)
- [AC-IND: Sparse CT reconstruction based on attenuation coefficient estimation and implicit neural distribution](https://mlsanity.com/paper/2409.07171/) (2024)
- [Unsupervised Self-Prior Embedding Neural Representation for Iterative Sparse-View CT Reconstruction](https://mlsanity.com/paper/2502.05445/) (2025)
- [DM4CT: Benchmarking Diffusion Models for Computed Tomography Reconstruction](https://mlsanity.com/paper/2602.18589/) (2026)
- [Diff-INR: Generative Regularization for Electrical Impedance Tomography](https://mlsanity.com/paper/2409.04494/) (2024)
- [Evaluating the Posterior Sampling Ability of Plug&Play Diffusion Methods in Sparse-View CT](https://mlsanity.com/paper/2410.21301/) (2024)
- [Disentangled Learning Improves Implicit Neural Representations for Medical Reconstruction](https://mlsanity.com/paper/2605.04234/) (2026)
- [Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow](https://mlsanity.com/paper/2406.01299/) (2024)
- [JSolver: Joint Spectrum Estimation and Multi-Material Decomposition from Single-Energy CT Projections](https://mlsanity.com/paper/2505.08123/) (2025)
- [Accelerating multiparametric quantitative MRI using self-supervised scan-specific implicit neural representation with model reinforcement](https://mlsanity.com/paper/2508.00891/) (2025)
- [APRF: Anti-Aliasing Projection Representation Field for Inverse Problem in Imaging](https://mlsanity.com/paper/2307.05270/) (2023)
- [CoCPF: Coordinate-based Continuous Projection Field for Ill-Posed Inverse Problem in Imaging](https://mlsanity.com/paper/2406.14976/) (2024)
- [Coordinate-Based Neural Representation Enabling Zero-Shot Learning for 3D Multiparametric Quantitative MRI](https://mlsanity.com/paper/2410.01577/) (2024)
- [Resolution Enhancement of Under-sampled Photoacoustic Microscopy Images using Implicit Neural Representations](https://mlsanity.com/paper/2410.19786/) (2024)
- [Low-Rank Augmented Implicit Neural Representation for Unsupervised High-Dimensional Quantitative MRI Reconstruction](https://mlsanity.com/paper/2506.09100/) (2025)
- [Diffusion Model Regularized Implicit Neural Representation for CT Metal Artifact Reduction](https://mlsanity.com/paper/2512.08999/) (2025)
- [XDen-1K: A Density Field Dataset of Real-World Objects](https://mlsanity.com/paper/2512.10668/) (2025)

## Abstract (arXiv)

In the present work, we propose a Self-supervised COordinate Projection nEtwork (SCOPE) to reconstruct the artifacts-free CT image from a single SV sinogram by solving the inverse tomography imaging problem. Compared with recent related works that solve similar problems using implicit neural representation network (INR), our essential contribution is an effective and simple re-projection strategy that pushes the tomography image reconstruction quality over supervised deep learning CT reconstruction works. The proposed strategy is inspired by the simple relationship between linear algebra and inverse problems. To solve the under-determined linear equation system, we first introduce INR to constrain the solution space via image continuity prior and achieve a rough solution. And secondly, we propose to generate a dense view sinogram that improves the rank of the linear equation system and produces a more stable CT image solution space. Our experiment results demonstrate that the re-projection strategy significantly improves the image reconstruction quality (+3 dB for PSNR at least). Besides, we integrate the recent hash encoding into our SCOPE model, which greatly accelerates the model training. Finally, we evaluate SCOPE in parallel and fan X-ray beam SVCT reconstruction tasks. Experimental results indicate that the proposed SCOPE model outperforms two latest INR-based methods and two well-popular supervised DL methods quantitatively and qualitatively.