Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems

Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear image formation from a given object to the observations is often available, explicit inversion formulas are typically not known. Moreover, the measured data might be insufficient for stable image reconstruction, in which case it has to be complemented by suitable a priori information. In this work, regularized Newton methods are presented as a general framework for the solution of such ill-posed nonlinear imaging problems. For a proof of principle, the approach is applied to x-ray phase contrast imaging in the near-field propagation regime. Simultaneous recovery of the phase- and amplitude from a single near-field diffraction pattern without homogeneity constraints is demonstrated for the first time. The presented methods further permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval and tomographic inversion. We demonstrate the potential of this approach by three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.Comment: (C)2016 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibite

A joint-reconstruction approach for single-shot edge illumination x-ray phase-contrast tomography

Edge illumination X-ray phase-contrast tomography (EIXPCT) is an imaging technique that estimates the spatially variant X-ray refractive index and absorption distribution within an object while seeking to circumvent the limitations of previous benchtop implementations of X-ray phase-contrast tomography. As with gratingor analyzer-based methods, conventional image reconstruction methods for EIXPCT require that two or more images be acquired at each tomographic view angle. This requirement leads to increased data acquisition times, hindering in vivo applications. To circumvent these limitations, a joint reconstruction (JR) approach is proposed that concurrently produces estimates of the refractive index and absorption distributions from a tomographic data set containing only a single image per tomographic view angle. The JR reconstruction method solves a nonlinear optimization problem by use of a novel iterative gradient-based algorithm. The JR method is demonstrated in both computer-simulated and experimental EIXPCT studies