OPTIMUM FILTER FOR DETECTING A TARGET IN MULTIPLICATIVE NOISE AND ADDITIVE NOISE

We derive an optimum filter function to detect a target degraded by mu ltiplicative noise and additive overlapping noise and placed in backgr ound noise. The filter is designed do maximize the metric peak-to-outp ut energy, which is the ratio of the expected value squared of the out put peak at the target position to the expected value of the average o utput energy. The optimum filter provides improved discrimination as w ell as robustness to input noise. One advantage of the filter describe d here over the homomorphic filters is that the additional preprocess on the input image, that is, the input logarithmic operation, is not r equired for reducing the effects of multiplicative noise. The performa nce of the filter is examined in terms of discrimination against backg round noise and robustness to multiplicative and additive input noise. Both multiplicative amplitude noise and multiplicative complex noise are considered. (C) 1997 Optical Society of America.