What are the advantages of ghost imaging? Multiplexing for x-ray and electron imaging

Ghost imaging, Fourier transform spectroscopy, and the newly developed Hadamard transform crystallography are all examples of multiplexing measurement strategies. Multiplexed experiments are performed by measuring multiple points in space, time, or energy simultaneously. This contrasts to the usual method of systematically scanning single points. How do multiplexed measurements work and when they are advantageous? Here we address these questions with a focus on applications involving x-rays or electrons. We present a quantitative framework for analyzing the expected error and radiation dose of different measurement scheme that enables comparison. We conclude that in very specific situations, multiplexing can offer improvements in resolution and signal-to-noise. If the signal has a sparse representation, these advantages become more general and dramatic, and further less radiation can be used to complete a measurement.