Super-resolution Optical Fluctuation Imaging -- fundamental estimation theory perspective

Abstract

We provide a quantitative analysis of super-resolution imaging techniques which exploit temporal fluctuations of luminosity of the sources in order to beat the Rayleigh limit. We define an operationally justified resolution gain figure of merit, that allows us to connect the estimation theory concepts with the ones typically used in the imaging community, and derive fundamental resolution limits that scale at most as the fourth-root of the mean luminosity of the sources. We fine-tune and benchmark the performance of state-of-the-art methods, focusing on the cumulant-based image processing techniques (known under the common acronym SOFI), taking into account the impact of limited photon number and sampling time.

17 pages + 14 appendix

References in corpus (3)

• Quantum Illumination with Gaussian States
• Beating Abbe diffraction limit in confocal microscopy via non-classical photon statistics
• On superresolution imaging as a multiparameter estimation problem

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• Weak convexity of Fisher information matrix and superresolved localization of blinking sources of light
• Quantum-enhanced passive remote sensing