Influence of imaging geometry on noise texture in quantitative in-line X-ray phase-contrast imaging

Quantitative in-line X-ray phase-contrast imaging methods seek to reconstruct separate images that depict an object's projected absorption and refractive properties. An understanding of the statistical properties of the reconstructed images can facilitate the identification of optimal imaging parameters for specific diagnostic tasks. However, the statistical properties of quantitative X-ray phase-contrast imaging remain largely unexplored. In this work, we derive analytic expressions that describe the second-order statistics of the reconstructed absorption and phase images. Concepts from statistical decision theory are applied to demonstrate how the statistical properties of images corresponding to distinct imaging geometries can influence signal detectability.