Cramér-Rao lower bound in differential phase contrast imaging and its application in the optimization of data acquisition systems

Abstract

Unlike conventional x-ray absorption imaging, x-ray differential phase contrast imaging (DPCI) uses a phase retrieval algorithm to obtain x-ray phase information from a group of x-ray intensity measurements. As a result, the noise performance of DPCI is expected to differ from that of x-ray absorption imaging. Given the total number of x-ray photons used in imaging, lower noise variance in estimated phase contrast images suggests superior dose efficiency, which is one of the most desirable feature in x-ray imaging. When an algorithm is used to retrieve the phase information, it is important to understand what the lowest possible noise variance would be and whether the algorithm used to retrieve the phase information yields the lowest possible noise variance. To address these questions for differential phase contrast imaging, we studied the noise performance of DPC imaging using the powerful Cramer-Rao lower bound (CRLB) in statistical signal estimation method. Results demonstrated that the noise variances in DPCI images obtained by the algorithmic phase retrieval are always higher than the CRLB, which implies a possible sub-optimality of current phase estimation method. The results also call for the need to apply statistical signal estimation theory to DPCI in order to further improve its noise performance and dose efficiency.