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

• URL: http://arxiv.org/abs/2401.16039v2
• Date: Fri, 25 Oct 2024 10:18:00 GMT
• Title: Data-Driven Filter Design in FBP: Transforming CT Reconstruction with Trainable Fourier Series
• Authors: Yipeng Sun, Linda-Sophie Schneider, Fuxin Fan, Mareike Thies, Mingxuan Gu, Siyuan Mei, Yuzhong Zhou, Siming Bayer, Andreas Maier,
• Abstract summary: We introduce a 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. Our filter can be easily integrated into existing CT reconstruction models, making it an adaptable tool for a wide range of practical applications.
• Score: 3.6508148866314163
• License:
• 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.

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