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We propose a new approach to the detection of masked targets and the estimation of target parameters with significant computational savings over standard approaches to this problem based on the CLEAN algorithm. In particular, our approach implements the CLEAN process efficiently because only a few select samples are used instead of using all samples from the matched filter output. For situations in which the signal amplitude and phase need to be estimated, we propose a modified data model for the algorithm so that these parameters and the image residues can be estimated simultaneously. We also provide a detection algorithm having a quantitative way for selecting detection samples and residue samples such that the detection performance is optimized.