Weighted least-squares image reconstruction in phase-contrast tomography

X-ray phase-contrast tomography (PCT) methods seek to quantitatively reconstruct separate images that depict an object's absorption and refractive properties. 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, followed by the inversion of X-ray transform. 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. We proposed a weighted least-squares method that takes into account the second-order statistical properties of the projected phase images and aims to minimize the objective function by employing a conjugate-gradient (CG) method. A computer-simulation study was carried out to investigate and evaluate the developed method.