# Data-Driven Filter Design in FBP: Transforming CT Reconstruction with Trainable Fourier Series

arXiv: https://arxiv.org/abs/2401.16039 · HTML: https://mlsanity.com/paper/2401.16039/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 12 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 4 of 4)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PYRO-NN: Python Reconstruction Operators in Neural Networks](https://mlsanity.com/paper/1904.13342/) (2019)
- [Gradient Variance Loss for Structure-Enhanced Image Super-Resolution](https://mlsanity.com/paper/2202.00997/) (2022)

## Built on by (most cited first, 6 of 6)

- [BIMCV-R: A Landmark Dataset for 3D CT Text-Image Retrieval](https://mlsanity.com/paper/2403.15992/) (2024)
- [Graphical Structural Learning of rs-fMRI data in Heavy Smokers](https://mlsanity.com/paper/2409.08395/) (2024)
- [DRACO: Differentiable Reconstruction for Arbitrary CBCT Orbits](https://mlsanity.com/paper/2410.14900/) (2024)
- [EAGLE: An Edge-Aware Gradient Localization Enhanced Loss for CT Image Reconstruction](https://mlsanity.com/paper/2403.10695/) (2024)
- [Learning Wavelet-Sparse FDK for 3D Cone-Beam CT Reconstruction](https://mlsanity.com/paper/2505.13579/) (2025)
- [An update to PYRO-NN: A Python Library for Differentiable CT Operators](https://mlsanity.com/paper/2511.08427/) (2025)

## Abstract (arXiv)

In this study, we introduce a Fourier series-based trainable filter for computed tomography (CT) reconstruction within the filtered backprojection (FBP) framework. This method overcomes the limitation in noise reduction by optimizing Fourier series coefficients to construct the filter, maintaining computational efficiency with minimal increment for the trainable parameters compared to other deep learning frameworks. Additionally, we propose Gaussian edge-enhanced (GEE) loss function that prioritizes the L1 norm of high-frequency magnitudes, effectively countering the blurring problems prevalent in mean squared error (MSE) approaches. The model's foundation in the FBP algorithm ensures excellent interpretability, as it relies on a data-driven filter with all other parameters derived through rigorous mathematical procedures. Designed as a plug-and-play solution, our Fourier series-based filter can be easily integrated into existing CT reconstruction models, making it an adaptable tool for a wide range of practical applications. Code and data are available at https://github.com/sypsyp97/Trainable-Fourier-Series.