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Speckle noise is one of the most critical disturbances that alter the quality of Synthetic Aperture Radar (SAR) coherent images. Before using SAR images in automatic target detection and recognition, the first step is to reduce the effect of speckle noise. Several adaptive and non-adaptive filters are widely used for despeckling in SAR images. In this paper, an adaptive mathematical morphological filter is proposed to reduce the speckle noise in SAR images. The new filter performance is compared with a number of despeckling filters with different parameters. For performance measurements, several parameters were evaluated to test the filter ability to attenuate the speckle noise and keep target information. From experimental results, the new proposed morphological filter gives promising results for significantly suppressing speckle noise and preserving the potential targets.