基于离散数学的传播基图像精确相位恢复
Precise phase retrieval for propagation-based images using discrete mathematics
摘要：
光学中相位恢复的不适定问题，使用一个或多个强度测量，具有使用电磁波或物质波的大量应用。由于离散傅里叶变换计算效率高，许多相位恢复算法都是在像素阵列上计算的。然而，支撑这些算法的数学通常使用连续数学来公式化，这可能导致重建图像中的空间分辨率的损失。在这里，我们研究如何传播为基础的相位衬度X射线成像的相位恢复算法可以使用离散数学重新推导，并导致更精确的检索单和多材料的对象和光谱图像分解。我们验证了这一理论，通过实验测量的空间分辨率，使用计算机断层扫描（CT）重建塑料幻影和生物组织，使用探测器的成像系统点扩散函数（PSF）的范围。我们证明，如果PSF基本上抑制高空间频率，从利用离散推导的潜在改善是有限的。然而，使用以单像素PSF为特征的探测器（例如，直接光子计数X射线探测器），可以获得空间分辨率的显著改善，在这里被证明高达17%。
英文摘要：
The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete Fourier transforms due to their high computational efficiency. However, the mathematics underpinning these algorithms is typically formulated using continuous mathematics, which can result in a loss in spatial resolution in the reconstructed images. Herein we investigate how phase retrieval algorithms for propagation-based phase-contrast X-ray imaging can be rederived using discrete mathematics and result in more precise retrieval for single- and multi-material objects and for spectral image decomposition. We validate this theory through experimental measurements of spatial resolution using computed tomography (CT) reconstructions of plastic phantoms and biological tissue, using detectors with a range of imaging system point spread functions (PSFs). We demonstrate that if the PSF substantially suppresses high spatial frequencies, the potential improvement from utilising the discrete derivation is limited. However, with detectors characterised by a single pixel PSF (e.g. direct, photon-counting X-ray detectors), a significant improvement in spatial resolution can be obtained, demonstrated here at up to 17%.
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