An optimal distortion-invariant filter for detecting a distorted target in input noise is designed. The input noise consists of two kinds of noise, overlapping additive noise and nonoverlapping background noise. We obtain the filter function by statistically maximizing the peak-to-output-energy ratio criterion, which is defined as the ratio of the square of the expected value of the output signal at the target location to the expected value of the average output energy. This results in a filter output with a well-defined output peak at the target location and a low output-noise floor. This filter is designed to take into account the effects of both overlapping additive noise and nonoverlapping background noise, the finite size of the input data, and the target distortion. The special cases of detecting a distorted target in nonoverlapping background noise and detecting a distorted target in overlapping additive noise are discussed. Computer simulation results are provided to show the performance of the filter.
© 1995 Optical Society of America
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