# Precision Learning: Towards Use of Known Operators in Neural Networks

arXiv: https://arxiv.org/abs/1712.00374 · HTML: https://mlsanity.com/paper/1712.00374/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2017.

## Built on by (most cited first, 7 of 7)

- [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)
- [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)
- [Synthetic Data in Radiological Imaging: Current State and Future Outlook](https://mlsanity.com/paper/2407.01561/) (2024)
- [Trainable Joint Bilateral Filters for Enhanced Prediction Stability in Low-dose CT](https://mlsanity.com/paper/2207.07368/) (2022)
- [Robust partial Fourier reconstruction for diffusion-weighted imaging using a recurrent convolutional neural network](https://mlsanity.com/paper/2105.09378/) (2021)
- [Beating the Style Detector: Three Hours of Agentic Research on the AI-Text Arms Race](https://mlsanity.com/paper/2605.02620/) (2026)

## Abstract (arXiv)

In this paper, we consider the use of prior knowledge within neural networks. In particular, we investigate the effect of a known transform within the mapping from input data space to the output domain. We demonstrate that use of known transforms is able to change maximal error bounds. In order to explore the effect further, we consider the problem of X-ray material decomposition as an example to incorporate additional prior knowledge. We demonstrate that inclusion of a non-linear function known from the physical properties of the system is able to reduce prediction errors therewith improving prediction quality from SSIM values of 0.54 to 0.88. This approach is applicable to a wide set of applications in physics and signal processing that provide prior knowledge on such transforms. Also maximal error estimation and network understanding could be facilitated within the context of precision learning.