Noise propagation in x-ray phase-contrast imaging and computed tomography

Three phase-retrieval algorithms, based on the transport-of-intensity equation and on the contrast transfer function for propagation-based imaging, and on the linearized geometrical optics approximation for analyser-based imaging, are investigated. The algorithms are compared in terms of their effect on propagation of noise from projection images to the corresponding phase-retrieved images and further to the computed tomography (CT) images/slices of a monomorphous object reconstructed using filtered backprojection algorithm. The comparison is carried out in terms of an integral noise characteristic, the variance, as well as in terms of a simple figure-of-merit, i.e. signal-to-noise ratio per unit dose. A gain factor is introduced that quantitatively characterizes the effect of phase retrieval on the variance of noise in the reconstructed projection images and in the axial slices of the object. Simple analytical expressions are derived for the gain factor and the signal-to-noise ratio, which indicate that the application of phase-retrieval algorithms can increase these parameters by up to two orders of magnitude compared to raw projection images and conventional CT, thus allowing significant improvement in the image quality and/or reduction of the x-ray dose delivered to the patient.