Department of Engineering Physics, Tsinghua University, Haidian District, Beijing, People's Republic of China. Key Laboratory of Particle & Radiation Imaging (Tsinghua University) of Ministry of Education, Haidian District, Beijing, People's Republic of China.
Phys Med Biol. 2019 Jun 12;64(12):125010. doi: 10.1088/1361-6560/ab0d5a.
The cosine-model analysis (CMA) method and the small angle x-ray scattering (SAXS) method are two major types of information retrieval algorithms, commonly utilized in x-ray phase-contrast imaging with a grating interferometer. However, there are significant differences between the two methods in algorithm implementation, and the existing literature has not completely revealed their intrinsic relationship. In this paper, we theoretically derive and experimentally verify the intrinsic connections between CMA and SAXS, and it is seen that SAXS can be interpreted well by the cosine-model assumption of CMA. To validate our analysis of the scattering distribution when applying the cosine model to the convolution used in SAXS, we applied a deconvolution process into CMA before using the Fourier transform to get the three contrasts. Furthermore, the principal component analysis (PCA) is introduced in this work, and two PCA-based retrieval algorithms are presented in order to simplify the iteration process of deconvolution in SAXS or to obtain absorption and dark-field signals instead of the Fourier transform in CMA. Applying a quantitative structural similarity (SSIM) index and a profile analysis to the results of an ex vivo mammography, it is proved that retrieved images via CMA and SAXS are consistent with each other (SSIM values are 1.0000, 0.9845 and 0.9767 respectively), and that the extra deconvolution process applied into CMA shows a good performance and our analytical analysis of the scattering distribution is valid when applying the cosine model to the convolution used in SAXS. Besides, it is concluded that PCA shows almost the same performance with the Fourier transform (SSIM values are 1.0000 for both absorption and dark-field images), and the simplified SAXS-analogous method works well with higher efficiency in computation and better stability relative to the original SAXS, while maintaining the similar level of image quality (SSIM values are 1.0000, 0.9839 and 0.9781 respectively).
余弦模型分析（CMA）方法和小角 X 射线散射（SAXS）方法是光栅型干涉仪 X 射线相衬成像中两种主要的信息检索算法。然而，这两种方法在算法实现上存在显著差异，现有文献并未完全揭示它们之间的内在关系。本文从理论上推导出 CMA 和 SAXS 之间的内在联系，并通过实验进行了验证，结果表明，SAXS 可以很好地用 CMA 的余弦模型假设来解释。为了验证我们对在 SAXS 中应用余弦模型时卷积的散射分布的分析，我们在使用傅里叶变换获得三个对比度之前，先对 CMA 进行反卷积处理。此外，本文还引入了主成分分析（PCA），提出了两种基于 PCA 的检索算法，以便简化 SAXS 中的反卷积迭代过程，或者在 CMA 中获得吸收和暗场信号而不是傅里叶变换。通过对离体乳腺 X 光图像进行定量结构相似性（SSIM）指数和轮廓分析，证明了通过 CMA 和 SAXS 检索得到的图像是一致的（SSIM 值分别为 1.0000、0.9845 和 0.9767），并且应用于 CMA 中的卷积的额外反卷积过程具有良好的性能，当在 SAXS 中应用余弦模型时，对散射分布的分析是有效的。此外，结果表明 PCA 与傅里叶变换具有几乎相同的性能（吸收和暗场图像的 SSIM 值均为 1.0000），简化后的 SAXS 类似方法在计算效率方面具有更高的效率和更好的稳定性，同时保持了类似的图像质量水平（SSIM 值分别为 1.0000、0.9839 和 0.9781）。
