数据驱动的滤波器设计用于灵活且抗噪的断层成像
Data-Driven Filter Design for Flexible and Noise-Robust Tomographic Imaging
AI总结：
本文提出了一种数据驱动的方法，通过学习FBP滤波器和投影权重来提高断层成像的鲁棒性和抗噪能力，同时保持计算效率。
摘要：
尽管滤波反投影（FBP）仍然是快速断层重建的首选方法，但在存在噪声、采样不完整或非标准扫描几何的情况下，其性能会明显下降。我们提出了一种数据驱动的方法，直接从训练数据中学习FBP滤波器和投影权重，旨在在不牺牲计算效率的情况下提高鲁棒性。所得的重建结果能自然适应噪声水平和获取几何结构，同时保持经典反投影的速度和简便性。所提出的方法可以表征为线性逆算子的正则化优化问题，这使我们能够建立所学解的存在性、唯一性和稳定性。从频谱角度看，所学滤波器充当数据自适应的增益函数，明确平衡噪声放大和偏倚，在很大程度上类似于正则化的伪逆。在2D和3D实验中，不同案例研究均显示出比传统FBP和FDK有持续改进。最后，我们展示在合成层状显微镜数据上训练的滤波器能够很好地推广到实际测量中，提供与先进迭代方法相当的图像质量，而无需高计算成本。
英文摘要：
While filtered back projection (FBP) is still the method of choice for fast tomographic reconstruction, its performance degrades noticeably in the presence of noise, incomplete sampling, or non-standard scan geometries. We propose a data-driven approach for learning FBP filters and projection weights directly from training data, with the goal of improving robustness without sacrificing computational efficiency. The resulting reconstructions adapt naturally to the noise level and acquisition geometry, while retaining the speed and simplicity of classical back-projection. The proposed method can be formulated as a regularized optimization problem for a linear inverse operator, which allows us to establish existence, uniqueness, and stability of the learned solution. From a spectral viewpoint, the learned filters act as data-adaptive gain functions that explicitly balance noise amplification and bias, in close analogy to a regularized pseudo-inverse. Experiments in both 2D and 3D show consistent improvements over conventional FBP and FDK in different case studies. Finally, we show that filters trained on synthetic laminography data generalize well to real-world measurements, delivering image quality comparable to advanced iterative methods without the high computational cost.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
