Step-change localization in additive and multiplicative noise via multiscale products

We address the problem of estimating the parameters of a step change in the presence of both additive and multiplicative Gaussian or non-Gaussian noise (AMNGN). Relevant applications include edge localization in the presence of speckle noise in SAR. A detector/estimator based on multiscale products has been proposed and analyzed in the case of AWGN, for a discrete wavelet transform that approximates smoothed gradient estimation. Here, we propose a multiscale product based estimator for the AMNGN case. Statistics of the resulting estimator are derived. We also derive Cramer-Rao bounds for the parameters of a step-change observed in additive and multiplicative noise. In order to satisfy regularity conditions, we model the step-change by a smooth function, parameterized by a rise-time parameter, /spl alpha/. Closed-form expressions for the large sample bound are obtained for several special cases. These bounds can be used to assess the performance of proposed and existing estimators.