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The X-ray in-line phase-contrast imaging technique requires that the light source provides a spatially coherent X-ray beam typically generated by a microfocus X-ray tube in most laboratories. However, its small focal spot limits the lightness. An arrayed X-ray point source can overcome this drawback and provide an adequately bright spatial coherent light. However, the arrayed source will introduce artefacts to the phase-contrast image due to the point source spatial distribution. To eliminate these artefacts, an optimization-based algorithm is used to reconstruct the image as an optimization problem. An iterative method was developed to numerically solve the optimization problem by using the first-order primal-dual algorithm. The simulations demonstrate its convergence and reconstruction accuracy.

X-Ray Phase-Contrast Image Reconstruction Based on the Chambolle-Pock Algorithm