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

Abstract

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.

(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 prohibited

References in corpus (2)

• A unified evaluation of iterative projection algorithms for phase retrieval
• Three-dimensional coherent X-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms

Cited by in corpus (9)

• Adorym: A multi-platform generic x-ray image reconstruction framework based on automatic differentiation
• Stability estimates for linearized near-field phase retrieval in X-ray phase contrast imaging
• Direct 3D Tomographic Reconstruction and Phase-Retrieval of Far-Field Coherent Diffraction Patterns
• Locality estimates for Fresnel-wave-propagation and stability of X-ray phase contrast imaging with finite detectors
• On phase retrieval via matrix completion and the estimation of low rank PSD matrices
• Fast three-dimensional phase retrieval in propagation-based x-ray tomography
• Generalized SART Methods for Tomographic Imaging
• A method of reconstruction for X-ray phase contrast imaging with arbitrary Fresnel number
• Fast algorithms for nonlinear and constrained phase retrieval in near-field X-ray holography based on Tikhonov regularization