Estimation in signal-dependent noise

A measurement model incorporating signal dependent noise is investigated. The penalty for employing estimators that ignore the signal dependence is found in terms of bounds on the mean square estimation error (MSEE). The minimum achievable MSEE for any unbiased estimator based on the signal dependent noise model is derived. Estimators based on various optimality criteria are explored. The structure of these estimators is investigated for the specific case of signal dependent photographic film grain noise. Various suboptimal estimators are next explored. Computer simulations are then employed to compare the performance, in terms of MSEE, of all the estimators, as well as their sensitivity to variations in certain parameters. The model is generalized to the vector case. Joint maximum likelihood and joint maximum a posterion probability estimates are derived. The state space approach is formulated, and the inapplicability of the traditional Kalman-Buoy filter is discussed.