Noise analysis for diffraction enhanced imaging

Herein we present a quantitative noise analysis of diffraction enhanced imaging (DEI), an X-ray imaging method that produces absorption and refraction images, with inherent immunity to wide-angle scatter. DEI produces remarkable images, but requires an X-ray source of very high power; therefore, it has principally been confined to synchrotron studies. Clinical systems currently under development using conventional X-ray sources will be photon-limited. Therefore, it is important that the noise properties of DEI be understood. Herein, we show that the original formulation of DEI, given by Chapman, et al, is the maximum-likelihood solution of the image-estimation problem for the case of Poisson noise. We derive the mean, covariance and signal-to-noise ratio of the images produced by this method, which sheds light on the effect of system parameters on the computed images. We will use these results in future work to derive reconstruction methods that are more optimal in the presence of noise than the original DEI formulation.