Non-Linear Phase-Retrieval Algorithms for X-ray Propagation-Based Phase-Contrast Tomography

X-ray phase-contrast tomography (XPCT) is widely used for high-contrast 3D micron-scale imaging using nearly monochromatic X-rays at synchrotron beamlines. 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.

X-ray Spectral Estimation using Dictionary Learning

As computational tools for X-ray computed tomography (CT) become more quantitatively accurate, knowledge of the source-detector spectral response is critical for quantitative system-independent reconstruction and material characterization capabilities. Directly measuring the spectral response of a CT system is hard, which motivates spectral estimation using transmission data obtained from a collection of known homogeneous objects. However, the associated inverse problem is ill-conditioned, making accurate estimation of the spectrum challenging, particularly in the absence of a close initial guess. In this paper, we describe a dictionary-based spectral estimation method that yields accurate results without the need for any initial estimate of the spectral response. Our method utilizes a MAP estimation framework that combines a physics-based forward model along with an $L_0$ sparsity constraint and a simplex constraint on the dictionary coefficients. Our method uses a greedy support selection method and a new pair-wise iterated coordinate descent method to compute the above estimate. We demonstrate that our dictionary-based method outperforms a state-of-the-art method as shown in a cross-validation experiment on four real datasets collected at beamline 8.3.2 of the Advanced Light Source (ALS).