Iterative filtering and smoothing of measurements possessing poisson noise

The minimum-variance filter and smoother are generalized to include Poisson-distributed measurement noise components. It is shown that the resulting filtered and smoothed estimates are unbiased. The use of the filter and smoother within expectation-maximization algorithms are described for joint estimation of the signal and Poisson noise intensity. Conditions for the monotonicity and asymptotic convergence of the Poisson intensity iterates are also established. An image restoration example is presented that demonstrates improved estimation performance at low signal-to-noise ratios.