Maximum Likelihood based Phase-Retrieval using Fresnel Propagation Forward Models with Optional Constraints

X-ray phase-contrast tomography (XPCT) is widely used for high contrast 3D imaging using either synchrotron or laboratory microfocus X-ray sources. XPCT enables an order of magnitude improvement in image contrast of the reconstructed material interfaces with low X-ray absorption contrast. The dominant approaches to 3D reconstruction using XPCT relies on the use of phase-retrieval algorithms that make one or more limiting approximations for the experimental configuration and material properties. Since many experimental scenarios violate such approximations, the resulting reconstructions contain blur, artifacts, or other quantitative inaccuracies. Our solution to this problem is to formulate new iterative non-linear phase-retrieval (NLPR) algorithms that avoid such limiting approximations. Compared to the widely used state-of-the-art approaches, we show that our proposed algorithms result in sharp and quantitatively accurate reconstruction with reduced artifacts. Unlike existing NLPR algorithms, our approaches avoid the laborious manual tuning of regularization hyper-parameters while still achieving the stated goals. As an alternative to regularization, we propose explicit constraints on the material properties to constrain the solution space and solve the phase-retrieval problem. These constraints are easily user-configurable since they follow directly from the imaged object's dimensions and material properties.