School of Physics and Astronomy, Monash University, Monash, VIC, 3800, Australia.
Japan Synchrotron Radiation Research Institute (JASRI)/SPring-8, Sayo, Hyogo, 679-5198, Japan.
Sci Rep. 2022 Nov 2;12(1):18469. doi: 10.1038/s41598-022-19940-9.
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 of 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 tissues, 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%.
光学中使用一个或多个强度测量值进行的不适定相位恢复问题，在使用电磁或物质波时有多种应用。由于其计算效率高，许多相位恢复算法都在像素阵列上使用离散傅里叶变换进行计算。然而，这些算法的数学基础通常是使用连续数学来构建的，这可能会导致重建图像的空间分辨率下降。在此，我们研究了如何使用离散数学重新推导基于传播的相衬 X 射线成像的相位恢复算法，并为单材料和多材料物体以及光谱图像分解提供更精确的恢复。我们通过使用具有一系列成像系统点扩散函数 (PSF) 的探测器对塑料体模和生物组织进行计算机断层扫描 (CT) 重建的空间分辨率实验测量来验证这一理论。我们证明，如果 PSF 大幅抑制了高频空间频率，则利用离散推导的潜在改进是有限的。然而，对于具有单个像素 PSF 的探测器（例如直接、光子计数 X 射线探测器），可以获得显著提高的空间分辨率，这里的示例高达 17%。
