# Ultra Low-Parameter Denoising: Trainable Bilateral Filter Layers in Computed Tomography

arXiv: https://arxiv.org/abs/2201.10345 · HTML: https://mlsanity.com/paper/2201.10345/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 46 references that are in the map.
- First posted on arXiv 25 Jan 2022.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Adversarial Examples: Attacks and Defenses for Deep Learning](https://mlsanity.com/paper/1712.07107/) (2017)
- [Low-Dose CT with a Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)](https://mlsanity.com/paper/1702.00288/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Low Dose CT Image Denoising Using a Generative Adversarial Network with Wasserstein Distance and Perceptual Loss](https://mlsanity.com/paper/1708.00961/) (2017)
- [A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstruction](https://mlsanity.com/paper/1610.09736/) (2016)
- [Quadratic Autoencoder (Q-AE) for Low-dose CT Denoising](https://mlsanity.com/paper/1901.05593/) (2019)
- [Learning with Known Operators reduces Maximum Training Error Bounds](https://mlsanity.com/paper/1907.01992/) (2019)
- [PYRO-NN: Python Reconstruction Operators in Neural Networks](https://mlsanity.com/paper/1904.13342/) (2019)
- [Precision Learning: Towards Use of Known Operators in Neural Networks](https://mlsanity.com/paper/1712.00374/) (2017)
- [JBFnet -- Low Dose CT Denoising by Trainable Joint Bilateral Filtering](https://mlsanity.com/paper/2007.04754/) (2020)

## Built on by (most cited first, 9 of 9)

- [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)
- [Trainable Joint Bilateral Filters for Enhanced Prediction Stability in Low-dose CT](https://mlsanity.com/paper/2207.07368/) (2022)
- [Noise2Contrast: Multi-Contrast Fusion Enables Self-Supervised Tomographic Image Denoising](https://mlsanity.com/paper/2212.04832/) (2022)
- [Comparison Study: Glacier Calving Front Delineation in Synthetic Aperture Radar Images With Deep Learning](https://mlsanity.com/paper/2501.05281/) (2025)
- [Filter2Noise: A Framework for Interpretable and Zero-Shot Low-Dose CT Image Denoising](https://mlsanity.com/paper/2504.13519/) (2025)
- [Geometric Constraints Enable Self-Supervised Sinogram Inpainting in Sparse-View Tomography](https://mlsanity.com/paper/2302.06436/) (2023)
- [Segmentation-Guided Knee Radiograph Generation using Conditional Diffusion Models](https://mlsanity.com/paper/2404.03541/) (2024)
- [Agentic Autoresearch for CT Reconstruction](https://mlsanity.com/paper/2607.22824/) (2026)

## Abstract (arXiv)

Computed tomography is widely used as an imaging tool to visualize three-dimensional structures with expressive bone-soft tissue contrast. However, CT resolution and radiation dose are tightly entangled, highlighting the importance of low-dose CT combined with sophisticated denoising algorithms. Most data-driven denoising techniques are based on deep neural networks and, therefore, contain hundreds of thousands of trainable parameters, making them incomprehensible and prone to prediction failures. Developing understandable and robust denoising algorithms achieving state-of-the-art performance helps to minimize radiation dose while maintaining data integrity. This work presents an open-source CT denoising framework based on the idea of bilateral filtering. We propose a bilateral filter that can be incorporated into a deep learning pipeline and optimized in a purely data-driven way by calculating the gradient flow toward its hyperparameters and its input. Denoising in pure image-to-image pipelines and across different domains such as raw detector data and reconstructed volume, using a differentiable backprojection layer, is demonstrated. Although only using three spatial parameters and one range parameter per filter layer, the proposed denoising pipelines can compete with deep state-of-the-art denoising architectures with several hundred thousand parameters. Competitive denoising performance is achieved on x-ray microscope bone data (0.7053 and 33.10) and the 2016 Low Dose CT Grand Challenge dataset (0.9674 and 43.07) in terms of SSIM and PSNR. Due to the extremely low number of trainable parameters with well-defined effect, prediction reliance and data integrity is guaranteed at any time in the proposed pipelines, in contrast to most other deep learning-based denoising architectures.