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.

该研究引入一种基于傅里叶级数的可训练滤波器，用于在过滤反投影 (FBP) 框架中进行计算机断层扫描 (CT) 重建。该方法通过优化傅里叶级数系数来构建滤波器，克服了传统 FBP 方法中噪声减少的限制。该方法在不同分辨率尺度下具有稳健的性能，并且与其他深度学习框架相比，对可训练参数的增量极小，保持了计算效率。此外，我们提出了高斯边缘增强 (GEE) 损失函数，该函数优先考虑高频幅度的 $L_1$ 范数，有效对抗了均方误差 (MSE) 方法中普遍存在的模糊问题。该模型基于 FBP 算法，保证了卓越的可解释性，因为它依赖于通过严格的数学程序导出的数据驱动滤波器的所有其他参数。我们的傅里叶级数滤波器设计为即插即用的解决方案，可以轻松集成到现有的 CT 重建模型中，成为广泛实际应用的多功能工具。我们的研究提出了一种强大且可伸缩的方法，扩展了 FBP 在医学和科学成像中的应用价值。