用于滤波反投影重建的优化滤波函数
Optimized filter functions for filtered back projection reconstructions
AI总结：
针对医疗CT中需减少扫描时间与辐射剂量、提升FBP重建质量的需求，本文解析推导了可最小化重建误差的闭式优化滤波函数，无需训练数据，易实现且经模拟与真实CT数据实验验证。
摘要：
滤波反投影（filtered back projection, FBP）方法是X射线计算机断层扫描（computerized tomography, CT）中广泛使用的重建技术，在临床诊断中尤为重要。为减少医疗CT场景下的扫描时间和辐射剂量，提升FBP方法的重建质量至关重要。为此，本文聚焦于对所采用的滤波函数进行解析优化。我们推导了一个滤波函数公式，该公式可在给定无限含噪测量数据的情况下，最小化FBP重建结果与真实目标函数之差的期望平方$\n\textrm{L}^2$-范数。此外，我们将推导得到的滤波器适配到有限测量数据的场景。所得滤波函数具有闭式表达式，无需训练数据集，因此提供了一种易于实现、开箱即用的解决方案。我们的理论发现得到了基于模拟CT数据和真实CT数据的数值实验的支持。
英文摘要：
The method of filtered back projection (FBP) is a widely used reconstruction technique in X-ray computerized tomography (CT), which is particularly important in clinical diagnostics. To reduce scanning times and radiation doses in medical CT settings, enhancing the reconstruction quality of the FBP method is essential. To this end, this paper focuses on analytically optimizing the applied filter function. We derive a formula for the filter that minimizes the expected squared $\mathrm{L}^2$-norm of the difference between the FBP reconstruction, given infinite noisy measurement data, and the true target function. Additionally, we adapt our derived filter to the case of finitely many measurements. The resulting filter functions have a closed-form representation, do not require a training dataset, and, thus, provide an easy-to-implement, out-of-the-box solution. Our theoretical findings are supported by numerical experiments based on both simulated and real CT data.
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。
