Statistical Experimental Design in Compressed Sensing Set-ups for Optical and Transmission Electron Microscopy
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The Cramér Rao lower bound on the variance of parameters estimated from measurements obtained through the compressed sensing (CS) schemes customary for optical microscopy and scanning transmission electron microscopy (STEM) is compared to that of serial acquisitions under the constraint of constant recording time and constant dose. Besides the inevitable Poisson noise associated with a finite dose also various levels of read-out noise in the detector are investigated to better reflect the physical constraints encountered in practice. The detective quantum efficiency of the recordings is shown to be a good and practical approximation to the lower bound and well suited for experimental design. It is shown that for recordings limited by Poisson noise, CS provides no advantage relative to a denoised Shannon scan. But in the presence of read-out noise, an advantage for CS emerges. The theoretical findings are corroborated with results from simulations and STEM experiments, reconstructed under the constraint that the measurements' log-likelihood must equal its expected value.
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