On the achievability of the Cramer-Rao bound for Poisson distribution

This correspondence examines the Cramer-Rao (CR) bound for data obtained in emission tomography. The likelihood function involved is the combined prob ability of independent Poisson random variables, the expectation of each be ing a linear function c(i)(T)lambda of the parameter vector X. We investiga ted the achievability of the CR bound in the interior and on the boundary o f the domain of the problem. For the former, we found that the CR bound is achievable if and only if the vectors ci's are obtained from a basis for R- N, by repeating some vectors, multiplied by constant factors. A similar res ult holds for the boundary case. The practical implication of the achievabi lity condition is that the CR bound is not attainable for typical emission tomographic systems.