Assume that a translation-invariant imaging system with an infinitely large detector C = R 2 is used to image a stationary object located at θ = (x 0 , y 0 ) ∈ R 2 , whose image is described by the 2D...

Assume that a translation-invariant imaging system with an infinitely large detector C = R
²
is used to image a stationary object located at θ = (x₀, y₀) ∈ R
²
, whose image is described by the 2D Gaussian image function. The photon distribution profile for this scenario is given by

Use the result of Exercise 17.3 to show that under the data model that guarantees the detection of exactly N₀
> 0 photons in each repeat image acquisition, the Cram´er-Rao lower bound pertaining to the estimation of this object’s positional coordinates is given by