# Resolution-Agnostic Neural Operators for Multi-Rate Sparse-View CT

arXiv: https://arxiv.org/abs/2512.12236 · HTML: https://mlsanity.com/paper/2512.12236/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 62 references that are in the map.
- First posted on arXiv 13 Dec 2025.

## Builds on (most cited first, 30 of 33)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [The KiTS19 Challenge Data: 300 Kidney Tumor Cases with Clinical Context, CT Semantic Segmentations, and Surgical Outcomes](https://mlsanity.com/paper/1904.00445/) (2019)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction](https://mlsanity.com/paper/2211.12340/) (2022)
- [DuDoNet: Dual Domain Network for CT Metal Artifact Reduction](https://mlsanity.com/paper/1907.00273/) (2019)
- [Neural Operators with Localized Integral and Differential Kernels](https://mlsanity.com/paper/2402.16845/) (2024)
- [TransCT: Dual-path Transformer for Low Dose Computed Tomography](https://mlsanity.com/paper/2103.00634/) (2021)
- [Scalable and Equivariant Spherical CNNs by Discrete-Continuous (DISCO) Convolutions](https://mlsanity.com/paper/2209.13603/) (2022)
- [InDuDoNet: An Interpretable Dual Domain Network for CT Metal Artifact Reduction](https://mlsanity.com/paper/2109.05298/) (2021)
- [FreeSeed: Frequency-band-aware and Self-guided Network for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2307.05890/) (2023)
- [Low-dose CT denoising with convolutional neural network](https://mlsanity.com/paper/1610.00321/) (2016)
- [Learning to Distill Global Representation for Sparse-View CT](https://mlsanity.com/paper/2308.08463/) (2023)
- [DiffusionBlend: Learning 3D Image Prior through Position-aware Diffusion Score Blending for 3D Computed Tomography Reconstruction](https://mlsanity.com/paper/2406.10211/) (2024)
- [Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning](https://mlsanity.com/paper/2506.10973/) (2025)
- [Deep Back Projection for Sparse-View CT Reconstruction](https://mlsanity.com/paper/1807.02370/) (2018)
- [Improving Generalizability in Limited-Angle CT Reconstruction with Sinogram Extrapolation](https://mlsanity.com/paper/2103.05255/) (2021)
- [A Unified Model for Compressed Sensing MRI Across Undersampling Patterns](https://mlsanity.com/paper/2410.16290/) (2024)
- [QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2402.17951/) (2024)
- [Coarse Graining with Neural Operators for Simulating Chaotic Systems](https://mlsanity.com/paper/2408.05177/) (2024)

## Abstract (arXiv)

Sparse-view Computed Tomography (CT) reconstructs images from a limited number of X-ray projections to reduce radiation and scanning time, which is an ill-posed inverse problem. Existing methods achieve high-fidelity reconstructions but overfit to a fixed acquisition setup, failing to generalize well across sampling rates. For example, convolutional neural networks (CNNs) use the same kernels across resolutions, leading to artifacts when data resolution changes. This is a critical limitation in clinical practice, where acquisition sampling settings vary across organs and diagnostic protocols. We propose Computed Tomography neural Operator (CTO), the first neural operator (NO) framework for CT reconstruction. CTO extends learning from fixed discretized grids to continuous function space, enabling a single model to generalize across measurement sampling rates without retraining. We also propose new NO architectural designs for CT: (i) a dual-domain NO architecture in both sinogram and image spaces, capturing complementary spatial-frequency information, and (ii) rotation-equivariant DIScrete-COntinuous convolutions (DISCO) that exploit the rotational structure inherent in tomographic acquisition. Empirically, CTO outperforms CNNs (> 3.4dB PSNR gain) and other baselines in multi-resolution settings across multiple CT datasets. Compared to state-of-the-art diffusion methods, CTO has 500x faster inference with an average 3dB gain. CTO further demonstrates strong out-of-distribution robustness, maintaining gains under cross-dataset transfer and noisy sinogram conditions. Ablation studies also validate each design choice. CTO establishes neural operators as a principled and practical paradigm for flexible, discretization-agnostic CT reconstruction. Our code is available at https://github.com/neuraloperator/sparse_ct.