# Gradient-Based Geometry Learning for Fan-Beam CT Reconstruction

arXiv: https://arxiv.org/abs/2212.02177 · HTML: https://mlsanity.com/paper/2212.02177/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 5 Dec 2022.

## Builds on (most cited first, 8 of 8)

- [TorchRadon: Fast Differentiable Routines for Computed Tomography](https://mlsanity.com/paper/2009.14788/) (2020)
- [PYRO-NN: Python Reconstruction Operators in Neural Networks](https://mlsanity.com/paper/1904.13342/) (2019)
- [Generalizing Spatial Transformers to Projective Geometry with Applications to 2D/3D Registration](https://mlsanity.com/paper/2003.10987/) (2020)
- [Near-Exact Recovery for Tomographic Inverse Problems via Deep Learning](https://mlsanity.com/paper/2206.07050/) (2022)
- [NeAT: Neural Adaptive Tomography](https://mlsanity.com/paper/2202.02171/) (2022)
- [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)
- [Appearance Learning for Image-based Motion Estimation in Tomography](https://mlsanity.com/paper/2006.10390/) (2020)

## Built on by (most cited first, 8 of 8)

- [A gradient-based approach to fast and accurate head motion compensation in cone-beam CT](https://mlsanity.com/paper/2401.09283/) (2024)
- [Optimizing CT Scan Geometries With and Without Gradients](https://mlsanity.com/paper/2302.06251/) (2023)
- [Segmentation-Guided Knee Radiograph Generation using Conditional Diffusion Models](https://mlsanity.com/paper/2404.03541/) (2024)
- [Differentiable Score-Based Likelihoods: Learning CT Motion Compensation From Clean Images](https://mlsanity.com/paper/2404.14747/) (2024)
- [Exploring Epipolar Consistency Conditions for Rigid Motion Compensation in In-vivo X-ray Microscopy](https://mlsanity.com/paper/2303.00449/) (2023)
- [On the Influence of Smoothness Constraints in Computed Tomography Motion Compensation](https://mlsanity.com/paper/2405.19079/) (2024)
- [Revisiting Pose Sensitivity in Splat-based Computed Tomography under Sparse-view Reconstruction](https://mlsanity.com/paper/2608.04752/) (2026)
- [Differentiable Jitter Correction using Deep Learning-based Image Quality Metric for Phase-Contrast Micro-CT](https://mlsanity.com/paper/2608.27034/) (2026)

## Abstract (arXiv)

Incorporating computed tomography (CT) reconstruction operators into differentiable pipelines has proven beneficial in many applications. Such approaches usually focus on the projection data and keep the acquisition geometry fixed. However, precise knowledge of the acquisition geometry is essential for high quality reconstruction results. In this paper, the differentiable formulation of fan-beam CT reconstruction is extended to the acquisition geometry. This allows to propagate gradient information from a loss function on the reconstructed image into the geometry parameters. As a proof-of-concept experiment, this idea is applied to rigid motion compensation. The cost function is parameterized by a trained neural network which regresses an image quality metric from the motion affected reconstruction alone. Using the proposed method, we are the first to optimize such an autofocus-inspired algorithm based on analytical gradients. The algorithm achieves a reduction in MSE by 35.5 % and an improvement in SSIM by 12.6 % over the motion affected reconstruction. Next to motion compensation, we see further use cases of our differentiable method for scanner calibration or hybrid techniques employing deep models.