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arXiv · 1906.04578

Semiparametric estimation for incoherent optical imaging

Mankei Tsang
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Abstract

The theory of semiparametric estimation offers an elegant way of computing the Cram\'er-Rao bound for a parameter of interest in the midst of infinitely many nuisance parameters. Here I apply the theory to the problem of moment estimation for incoherent imaging under the effects of diffraction and photon shot noise. Using a Hilbert-space formalism designed for Poisson processes, I derive exact semiparametric Cram\'er-Rao bounds and efficient estimators for both direct imaging and a quantum-inspired measurement method called spatial-mode demultiplexing (SPADE). The results establish the superiority of SPADE even when little prior information about the object is available.

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Mankei Tsang. 2019-06-11. Semiparametric estimation for incoherent optical imaging. https://doi.org/10.1103/physrevresearch.1.033006

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