Image reconstruction in phase-contrast tomography exploiting the second-order statistical properties of the projection data.

X-ray phase-contrast tomography (PCT) methods seek to quantitatively reconstruct separate images that depict an object's absorption and refractive contrasts. Most PCT reconstruction algorithms generally operate by explicitly or implicitly performing the decoupling of the projected absorption and phase properties at each tomographic view angle by use of a phase-retrieval formula. However, the presence of zero-frequency singularity in the Fourier-based phase retrieval formulas will lead to a strong noise amplification in the projection estimate and the subsequent refractive image obtained using conventional algorithms like filtered backprojection (FBP). Tomographic reconstruction by use of statistical methods can account for the noise model and a priori information, and thereby can produce images with better quality over conventional filtered backprojection algorithms. In this work, we demonstrate an iterative image reconstruction method that exploits the second-order statistical properties of the projection data can mitigate noise amplification in PCT. The autocovariance function of the reconstructed refractive images was empirically computed and shows smaller and shorter noise correlation compared to those obtained using the FBP and unweighted penalized least-squares methods. Concepts from statistical decision theory are applied to demonstrate that the statistical properties of images produced by our method can improve signal detectability.