# Deriving Neural Network Architectures using Precision Learning: Parallel-to-fan beam Conversion

arXiv: https://arxiv.org/abs/1807.03057 · HTML: https://mlsanity.com/paper/1807.03057/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2018.

## Built on by (most cited first, 3 of 3)

- [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)
- [Data-driven Modeling in Metrology -- A Short Introduction, Current Developments and Future Perspectives](https://mlsanity.com/paper/2406.16659/) (2024)
- [Robustness and Stability Analysis of Differentiable Shift-Variant FBP for Cone-Beam CT under Challenging Acquisition Settings](https://mlsanity.com/paper/2607.09828/) (2026)

## Abstract (arXiv)

In this paper, we derive a neural network architecture based on an analytical formulation of the parallel-to-fan beam conversion problem following the concept of precision learning. The network allows to learn the unknown operators in this conversion in a data-driven manner avoiding interpolation and potential loss of resolution. Integration of known operators results in a small number of trainable parameters that can be estimated from synthetic data only. The concept is evaluated in the context of Hybrid MRI/X-ray imaging where transformation of the parallel-beam MRI projections to fan-beam X-ray projections is required. The proposed method is compared to a traditional rebinning method. The results demonstrate that the proposed method is superior to ray-by-ray interpolation and is able to deliver sharper images using the same amount of parallel-beam input projections which is crucial for interventional applications. We believe that this approach forms a basis for further work uniting deep learning, signal processing, physics, and traditional pattern recognition.