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Edge detection in the presence of noise is a well-known problem. This paper examines an applications-motivated approach for solving the problem using novel techniques and presents a method developed by the authors that performs well on a large class of targets. ROC curves are used to compare this method with other well-known edge detection operators, with favorable results. A theoretical argument is presented that favors LMMSE filtering over median filtering in extremely noisy scenes. Simulated results of the research are presented.