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Impulsive noise filtering is an important problem of image processing. The problem of noise elimination is closely connected with the problem of maximal preservation of image edges. The requirement of maximal preservation of edges is especially important for images corrupted by impulsive noise with a low corruption rate. To avoid smoothing of the image during filtering, all noisy pixels must be detected. Then only these detected pixels must be corrected. We present in this paper two solutions to the edge preservation problem. The first one is an impulse detector. This detector is based on a comparison of signal samples within a narrow rank window. It is quite efficient for precise detection of impulses in images corrupted by impulsive noise with a low corruption rate. The second solution is based on threshold Boolean filtering, when the binary slices of an image, obtained by the threshold decomposition, are processed by original Boolean functions.