# PYRO-NN: Python Reconstruction Operators in Neural Networks

arXiv: https://arxiv.org/abs/1904.13342 · HTML: https://mlsanity.com/paper/1904.13342/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2019.

## Built on by (most cited first, 24 of 24)

- [Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Future](https://mlsanity.com/paper/2108.04543/) (2021)
- [Ultra Low-Parameter Denoising: Trainable Bilateral Filter Layers in Computed Tomography](https://mlsanity.com/paper/2201.10345/) (2022)
- [On the Benefit of Dual-domain Denoising in a Self-supervised Low-dose CT Setting](https://mlsanity.com/paper/2211.01111/) (2022)
- [Gradient-Based Geometry Learning for Fan-Beam CT Reconstruction](https://mlsanity.com/paper/2212.02177/) (2022)
- [WNet: A data-driven dual-domain denoising model for sparse-view computed tomography with a trainable reconstruction layer](https://mlsanity.com/paper/2207.00400/) (2022)
- [Data-Driven Filter Design in FBP: Transforming CT Reconstruction with Trainable Fourier Series](https://mlsanity.com/paper/2401.16039/) (2024)
- [Deep Learning Computed Tomography based on the Defrise and Clack Algorithm](https://mlsanity.com/paper/2403.00426/) (2024)
- [DRACO: Differentiable Reconstruction for Arbitrary CBCT Orbits](https://mlsanity.com/paper/2410.14900/) (2024)
- [Data Models for Dataset Drift Controls in Machine Learning With Optical Images](https://mlsanity.com/paper/2211.02578/) (2022)
- [A gradient-based approach to fast and accurate head motion compensation in cone-beam CT](https://mlsanity.com/paper/2401.09283/) (2024)
- [EAGLE: An Edge-Aware Gradient Localization Enhanced Loss for CT Image Reconstruction](https://mlsanity.com/paper/2403.10695/) (2024)
- [Artifact Reduction in 3D and 4D Cone-beam Computed Tomography Images with Deep Learning -- A Review](https://mlsanity.com/paper/2403.18565/) (2024)
- [Learned Cone-Beam CT Reconstruction Using Neural Ordinary Differential Equations](https://mlsanity.com/paper/2201.07562/) (2022)
- [Optimizing CT Scan Geometries With and Without Gradients](https://mlsanity.com/paper/2302.06251/) (2023)
- [Geometric Constraints Enable Self-Supervised Sinogram Inpainting in Sparse-View Tomography](https://mlsanity.com/paper/2302.06436/) (2023)
- [A 2D Sinogram-Based Approach to Defect Localization in Computed Tomography](https://mlsanity.com/paper/2401.16104/) (2024)
- [Compressibility Analysis for the differentiable shift-variant Filtered Backprojection Model](https://mlsanity.com/paper/2501.11586/) (2025)
- [Learning Wavelet-Sparse FDK for 3D Cone-Beam CT Reconstruction](https://mlsanity.com/paper/2505.13579/) (2025)
- [A Deep Risk Estimator for Known Operator Learning](https://mlsanity.com/paper/2605.08517/) (2026)
- [On the Influence of Smoothness Constraints in Computed Tomography Motion Compensation](https://mlsanity.com/paper/2405.19079/) (2024)
- [An update to PYRO-NN: A Python Library for Differentiable CT Operators](https://mlsanity.com/paper/2511.08427/) (2025)
- [Robustness and Stability Analysis of Differentiable Shift-Variant FBP for Cone-Beam CT under Challenging Acquisition Settings](https://mlsanity.com/paper/2607.09828/) (2026)
- [GB-SVFBP: Gaussian-Based Shift-Variant FBP neural network](https://mlsanity.com/paper/2607.11584/) (2026)
- [Agentic Autoresearch for CT Reconstruction](https://mlsanity.com/paper/2607.22824/) (2026)

## Abstract (arXiv)

Purpose: Recently, several attempts were conducted to transfer deep learning to medical image reconstruction. An increasingly number of publications follow the concept of embedding the CT reconstruction as a known operator into a neural network. However, most of the approaches presented lack an efficient CT reconstruction framework fully integrated into deep learning environments. As a result, many approaches are forced to use workarounds for mathematically unambiguously solvable problems. Methods: PYRO-NN is a generalized framework to embed known operators into the prevalent deep learning framework Tensorflow. The current status includes state-of-the-art parallel-, fan- and cone-beam projectors and back-projectors accelerated with CUDA provided as Tensorflow layers. On top, the framework provides a high level Python API to conduct FBP and iterative reconstruction experiments with data from real CT systems. Results: The framework provides all necessary algorithms and tools to design end-to-end neural network pipelines with integrated CT reconstruction algorithms. The high level Python API allows a simple use of the layers as known from Tensorflow. To demonstrate the capabilities of the layers, the framework comes with three baseline experiments showing a cone-beam short scan FDK reconstruction, a CT reconstruction filter learning setup, and a TV regularized iterative reconstruction. All algorithms and tools are referenced to a scientific publication and are compared to existing non deep learning reconstruction frameworks. The framework is available as open-source software at urlhttps://github.com/csyben/PYRO-NN. Conclusions: PYRO-NN comes with the prevalent deep learning framework Tensorflow and allows to setup end-to-end trainable neural networks in the medical image reconstruction context. We believe that the framework will be a step towards reproducible research