Semiparametric estimation for incoherent optical imaging. (arXiv:1906.04578v1 [eess.IV])

The theory of semiparametric estimation offers an elegant way to compute 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, 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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