Optimal estimation in signal-dependent noise

Abstract

Optimal estimators are derived for a class of signal-dependent noise processes. Such processes are of interest in optics because phenomena, such as film grain noise, are often modeled in this manner. This paper demonstrates that when one ignores the presence of signal-dependent noise and instead assumes only signal-independent noise models, the resulting estimators may pay a severe penalty in performance. This “mismatch” problem is explored, with the results of Monte Carlo simulations of the performances of both optimum and mismatched estimators being presented. The Cramér-Rao lower bounds on the mean-square estimation errors for unbiased estimators are evaluated and compared with the lower bounds derived for the signal-independent noise case. Overall, the results indicate that improved performance will, in most cases, offset the increased complexity inherent in estimators designed for the signal-dependent noise model.