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).