On Random-Matrix Bases, Ghost Imaging and X-ray Phase Contrast Computational Ghost Imaging

Abstract

A theory of random-matrix bases is presented, including expressions for orthogonality, completeness and the random-matrix synthesis of arbitrary matrices. This is applied to ghost imaging as the realization of a random-basis reconstruction, including an expression for the resulting signal-to-noise ratio. Analysis of conventional direct imaging and ghost imaging leads to a criterion which, when satisfied, implies reduced dose for computational ghost imaging. We also propose an experiment for x-ray phase contrast computational ghost imaging, which enables differential phase contrast to be achieved in an x-ray ghost imaging context. We give a numerically robust solution to the associated inverse problem of decoding differential phase contrast x-ray ghost images, to yield a quantitative map of the projected thickness of the sample.

15 pages, 3 figures. V2 contains several points of added clarification and figure updates in response to helpful feedback

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Cited by in corpus (11)

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• Neutron Ghost Imaging
• X-ray phase-contrast imaging: a broad overview of some fundamentals
• On the Inherent Dose-Reduction Potential of Classical Ghost Imaging
• Optimizing illumination patterns for classical ghost imaging
• One mask to rule them all: Writing arbitrary distributions of radiant exposure by scanning a single illuminated spatially-random screen
• Ghost projection. II. Beam shaping using realistic spatially-random masks
• Two-photon X-ray Ghost Microscope
• Universal mask for hard X rays
• X-ray ghost tomography: denoising, dose fractionation and mask considerations
• High-speed x-ray imaging with single-pixel detector