⚡ electrical engineering

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

This paper introduces CTO, the first neural operator framework for sparse-view CT reconstruction that leverages continuous function spaces, dual-domain processing, and rotation-equivariant convolutions to achieve superior resolution-agnostic generalization and significantly faster inference compared to existing CNN and diffusion-based methods.

Original authors: Aujasvit Datta, Jiayun Wang, Asad Aali, Anima Anandkumar

Published 2026-08-10

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CC BY 4.0

Original authors: Aujasvit Datta, Jiayun Wang, Asad Aali, Anima Anandkumar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to solve a giant, 3D jigsaw puzzle, but someone has secretly removed most of the pieces. In the world of medical imaging, this is exactly what happens during a Computed Tomography (CT) scan. A CT scanner takes X-rays from different angles to build a picture of what's happening inside your body. Usually, it takes hundreds of these "snapshots" to create a clear image. But taking so many shots means more radiation for the patient and a longer time in the machine. To keep people safe and scans fast, doctors sometimes use "sparse-view" CT, where they take far fewer snapshots. The problem is that with so few pieces, the puzzle is broken; the computer has to guess what the missing parts look like, often resulting in blurry or ghostly images that are hard to read.

For years, scientists have tried to teach computers to fix these broken puzzles using Artificial Intelligence. Think of these AI models like a student who studies hard for a specific test. If the student only practices with puzzles that have 18 missing pieces, they get really good at that one specific test. But if you hand them a puzzle with only 9 missing pieces, or one with 36, they get confused and make mistakes. They are "overfit," meaning they memorized the specific rules of one setup but can't adapt to a new one. This is a huge problem in real hospitals, where different body parts and different machines require different numbers of snapshots. The big question is: Can we build an AI that doesn't just memorize one puzzle size, but learns the rules of the puzzle itself, so it can solve any version, big or small, without needing to relearn everything?

This is the story of a new invention called CTO (Computed Tomography neural Operator), created by a team of researchers. Instead of teaching the AI to look at a fixed grid of pixels like a standard camera, CTO teaches the AI to see the world as a smooth, continuous flow of information, like a river rather than a series of stepping stones. In the language of math, this is called a "neural operator." While old AI models are like a photographer who can only take photos at one specific zoom level, CTO is like a magical lens that can zoom in or out instantly without losing any sharpness.

The researchers found that by using this "continuous" approach, CTO can handle any number of X-ray snapshots, whether the scanner takes 9, 18, 36, or 72 views. It doesn't need to be retrained for each new setting. To make this work, they designed two special tools. First, they created a "dual-domain" system that looks at the raw data (the sinogram, which is like the raw sound waves of the X-rays) and the final picture at the same time, catching clues that other methods miss. Second, they invented a special kind of math trick called DISCO (Discrete–Continuous) convolution. Imagine trying to paint a circle on a wall. A normal AI tries to paint it by placing individual square tiles, which looks jagged if you zoom in. DISCO, however, paints with a continuous brush that flows smoothly, so the circle looks perfect no matter how close you look.

The results are quite impressive. In their tests, CTO didn't just work; it outperformed the best existing AI models. When compared to standard AI networks, CTO produced clearer images with a quality boost of more than 3.4 dB (a technical measure of image clarity). It even beat the latest "diffusion" models—which are like AI artists that slowly paint an image from scratch—by 3 dB, but with a massive bonus: CTO is 500 times faster at making the final image. This speed is crucial because doctors can't wait minutes for a scan to finish; they need answers in seconds.

The paper also shows that CTO is incredibly tough. Even when the data is noisy or the scanner settings change completely (like moving from an abdomen scan to a kidney scan), CTO keeps performing well without needing a new lesson. The researchers proved this by testing it on different datasets and showing that it doesn't get confused by "out-of-distribution" challenges. They also checked that their "continuous" math actually converges, meaning as the image gets higher resolution, the errors get smaller and smaller, eventually disappearing.

In short, this paper suggests that we can stop building a new AI for every single type of CT scan setting. Instead, we can build one smart, flexible "operator" that understands the physics of X-rays so well that it can adapt to any situation on the fly. It's a shift from memorizing specific answers to understanding the underlying language of the puzzle, promising faster, safer, and clearer medical scans for everyone.

Technical Summary: Resolution-Agnostic Neural Operators for Multi-Rate Sparse-View CT

1. Problem Statement

Sparse-View Computed Tomography (SVCT) aims to reconstruct high-fidelity images from a limited number of X-ray projections to reduce radiation exposure and scanning time. This constitutes an ill-posed inverse problem, as the number of measurements is insufficient to uniquely determine the underlying attenuation map.

While deep learning methods, particularly Convolutional Neural Networks (CNNs) and unrolled optimization networks, have significantly improved reconstruction quality over classical methods like Filtered Back Projection (FBP) and compressed sensing, they suffer from a critical limitation: resolution and sampling rate dependence. Existing models are typically trained on a fixed discretization of the acquisition setup (e.g., a specific number of projection angles or a fixed image resolution). Consequently, a model trained for one sampling rate fails to generalize to others, often producing severe artifacts when the input resolution or view count changes. In clinical practice, where acquisition settings vary across organs and protocols, maintaining separate models for each configuration is unscalable and impractical.

2. Methodology: The CTO Framework

The authors propose Computed Tomography neural Operator (CTO), the first framework to apply Neural Operators (NOs) to sparse-view CT reconstruction. Unlike standard neural networks that learn mappings between fixed discrete grids, NOs learn mappings between infinite-dimensional function spaces. This allows CTO to generalize across different measurement sampling rates and image resolutions without retraining.

Core Architectural Components

CTO follows an unrolled network design, mimicking iterative optimization algorithms but replacing the learned regularization steps with neural operators. The framework consists of two primary domains:

Sinogram-Space Operator ( $NO_s$ ):
- Function Space: Operates on the sinogram $p(\theta, r)$ in polar coordinates (angle $\theta$ , detector position $r$ ), the natural domain of CT measurements.
- Dual-Branch Design: Inspired by Filtered Back Projection (FBP), $NO_s$ $N O_{s}$ employs two parallel U-shaped DISCO blocks:
  - Spatial Branch ( $NO_{s,spatial}$ ): Captures local, geometry-aware correlations in the $(\theta, r)$ domain.
  - Frequency Branch ( $NO_{s,freq}$ ): Applies a 1D Fourier transform along the detector axis ( $r$ ) to model long-range angular–radial dependencies, effectively learning a data-driven frequency prior similar to the ramp filter in FBP.
- Rotation-Equivariance: To respect the physical symmetries of CT (where object rotation corresponds to a shift in the sinogram's angular axis), the architecture utilizes circular padding along the $\theta$ axis with a flip along the $r$ axis. This ensures the network is equivariant to rotations, handling the $\pi$ -periodicity and flip identity inherent in parallel-beam geometry.
Image-Space Operator ( $NO_i$ ):
- Function Space: Operates on the 2D Cartesian image grid.
- Refinement: Takes the intermediate reconstruction from the sinogram domain and refines spatial features, recovering high-frequency details and ensuring structural consistency.

The DISCO Mechanism

Both operators rely on Discrete–Continuous (DISCO) convolutions as their fundamental building block.

Continuous Kernels: Unlike CNNs that use fixed discrete kernels, DISCO defines convolution kernels as continuous functions in the function space.
Resolution Agnosticism: These continuous kernels are discretized only at the resolution of the specific input data. This allows the same model parameters to be applied to inputs of varying resolutions (e.g., different numbers of views or detector bins) while maintaining a consistent receptive field relative to the physical domain.
Convergence: DISCO is proven to be discretization-convergent, meaning the approximation error is bounded across resolutions and converges to zero as resolution increases.

3. Key Contributions

First Application of Neural Operators to SVCT: CTO is the first framework to utilize Neural Operators for sparse-view CT, enabling a single model to generalize across measurement sampling rates and image resolutions without retraining.
Joint Spatial-Frequency Sinogram Learning: The authors introduce a dual-domain operator in the sinogram space that respects CT rotational geometry and acquisition physics, combining spatial processing with frequency-domain learning inspired by FBP.
Inherent Resolution and Rotation Agnosticism: By learning in function space via DISCO operators, CTO achieves consistent reconstructions across varying conditions. The design is inherently rotation-equivariant through specific padding schemes in the sinogram domain, improving robustness to varying acquisition angles.
Unified Function-Space Formulation: Instead of learning separate discrete models for each sampling rate, CTO learns a single continuous operator from which different discretizations can be sampled, enabling multi-rate reconstruction and cross-discretization consistency.

4. Experimental Results

The authors evaluated CTO on the AAPM Low-Dose Abdominal CT and Kidney CT datasets, comparing it against learning-free methods (FBP, SART), single-pass deep learning models (DuDoTrans, GloReDi), unrolled networks (Learned Primal-Dual, LEARN, RegFormer), and diffusion-based methods (DPS, ALD).

Multi-Rate Performance: CTO was trained on a single model using multi-rate data (9, 18, 36, and 72 views). It consistently outperformed all baselines across all sampling rates.
- On the Kidney dataset, CTO achieved an average 4 dB PSNR gain over the unrolled CNN baseline, 3 dB over diffusion methods, and 5 dB over transformer-based methods.
- On the Abdomen dataset, CTO showed a 3 dB PSNR gain over the unrolled CNN baseline and 6 dB over diffusion and transformer baselines.
Zero-Shot Super-Resolution: CTO demonstrated strong generalization to higher resolutions without fine-tuning. When tested on 512×512 images (trained on 256×256), CTO maintained sharp details, whereas CNN baselines suffered from blurring and aliasing, yielding a 3 dB PSNR gain over the CNN baseline.
Efficiency: Compared to state-of-the-art diffusion methods, CTO offers 500× faster inference while achieving comparable or superior reconstruction quality (average 3 dB gain). Unlike diffusion models, CTO does not require rate-specific hyperparameter tuning.
Robustness: CTO demonstrated strong out-of-distribution (OOD) robustness, maintaining performance gains under cross-dataset transfer (Kidney to AAPM) and in the presence of noisy sinogram data.

5. Significance and Claims

The paper positions CTO as a principled and practical paradigm for flexible CT reconstruction. Its primary significance lies in overcoming the "discretization binding" that plagues current deep learning approaches. By shifting from discrete grid-based learning to function-space learning, CTO addresses the critical clinical need for a unified model that can adapt to varying acquisition protocols (different organs, scan speeds, and resolutions) without the overhead of training and maintaining multiple specialized models.

The authors claim that CTO establishes Neural Operators as a viable alternative to traditional CNNs and diffusion models for computational imaging, offering a unique combination of high fidelity, resolution agnosticism, and computational efficiency. The work suggests that future clinical applications could benefit from a single, scalable model capable of handling the diverse and dynamic nature of CT acquisition settings.