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

TL;DR

This paper presents a novel trainable Fourier series-based filter for CT reconstruction within the FBP framework, enhancing noise reduction and interpretability while maintaining computational efficiency and adaptability.

Contribution

It introduces a Fourier series-based trainable filter and a Gaussian edge-enhanced loss function, improving CT image quality with minimal added complexity.

Findings

Effective noise reduction in CT images

Maintains computational efficiency and interpretability

Easy to integrate into existing CT reconstruction workflows

Abstract

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 $L_1$ 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.