Data-Driven Filter Design in FBP: Transforming CT Reconstruction with
  Trainable Fourier Series
Yipeng Sun Linda-Sophie Schneider Fuxin Fan Mareike Thies Mingxuan Gu Siyuan Mei Yuzhong Zhou Siming Bayer Andreas Maier
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,
inherent in conventional FBP methods, by optimizing Fourier series coefficients
to construct the filter. This method enables robust performance across
different resolution scales and maintains 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 a versatile tool
for a wide range of practical applications. Our research presents a robust and
scalable method that expands the utility of FBP in both medical and scientific
imaging.