We address the problem of localizing small targets with random gray levels that appear in random background clutter. We consider the recently proposed maximum-likelihood ratio test (MLRT) algorithm, which scans the observed scene with an estimation window in which the local statistics are estimated. In the presence of a spatially homogeneous background, we show that if the estimation window is a few times larger than the target itself, the MLRT is quasi-equivalent to the optimal maximum-likelihood (ML) algorithm, which uses the whole scene for estimating the background statistics. The MLRT thus constitutes an efficient alternative to the ML algorithm and is more robust in dealing with spatially nonhomogeneous clutter since it utilizes a small estimation window.
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