层析重建中级联滤波-插值调制的统一频域模型

中文摘要 AI 辅助

在线性逆问题（如层析成像）中，从投影重建图像的质量关键取决于频域滤波与空间域插值之间的协同交互。然而，迄今为止，仍缺乏一个能够定量描述这两个组件如何在频域中级联交互并最终决定图像质量的物理模型。在此，我们提出一个统一的频域模型，将滤波反投影（FBP）算法中滤波与插值的联合效应概念化为一个级联调制过程。该模型表明，有效重建频谱由原始投影数据依次经滤波器和插值核的频率响应调制而决定。全面的数值模拟和同步辐射CT实验验证了该模型，证实了其在理想和噪声条件下解释经典滤波-插值对性能排序的能力。该模型成功预测了关键性能特征，包括空间分辨率和结构保真度，从而阐明了特定组合有效性背后的物理原理。这项工作为分析线性逆问题中的级联系统建立了可推广的理论基础，将计算成像中算法选择的做法从经验主义转向基于物理学的原则性范式。

英文摘要

The fidelity of image reconstruction from projections in linear inverse problems, such as tomography, is critically dependent on the synergistic interaction between frequency-domain filtering and spatial-domain interpolation. However, a physical model that can quantitatively describe how these two components cascade interact in the frequency domain and ultimately determine image quality is still lacking to this day. Here, we introduce a unified frequency-domain model that conceptualizes the combined effect of filtering and interpolation in the filtered backprojection (FBP) algorithm as a cascaded modulation process. This model demonstrates that the effective reconstruction spectrum is determined by the original projection data being sequentially modulated by the frequency responses of the filter and the interpolation kernel. Comprehensive numerical simulations and synchrotron radiation CT experiments validate the model, confirming its power to explain the performance hierarchy of classical filter-interpolation pairs under both ideal and noisy conditions. The model successfully predicts key performance characteristics, including spatial resolution and structural fidelity, thereby elucidating the physical principles behind the efficacy of specific combinations. This work establishes a generalizable theoretical foundation for analyzing cascaded systems in linear inverse problems, moving the practice of algorithm selection in computational imaging from empiricism to a principled, physics-based paradigm.

发表机构

• Shandong Normal University（山东师范大学）

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