Noise properties and task-based evaluation of diffraction-enhanced imaging

Diffraction-enhanced imaging (DEI) is an emerging x-ray imaging method that simultaneously yields x-ray attenuation and refraction images and holds great promise for soft-tissue imaging. The DEI has been mainly studied using synchrotron sources, but efforts have been made to transition the technology to more practical implementations using conventional x-ray sources. The main technical challenge of this transition lies in the relatively lower x-ray flux obtained from conventional sources, leading to photon-limited data contaminated by Poisson noise. Several issues that must be understood in order to design and optimize DEI imaging systems with respect to noise performance are addressed. Specifically, we: (a) develop equations describing the noise properties of DEI images, (b) derive the conditions under which the DEI algorithm is statistically optimal,