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In this letter, a no-reference perceptual sharpness metric based on a statistical analysis of local edge gradients is presented. The method takes properties of the human visual system into account. Based on perceptual properties, a relationship between the extracted statistical features and the metric score is established to form a Perceptual Sharpness Index (PSI). A comparison with state-of-the-art metrics shows that the proposed method correlates highly with human perception and exhibits low computational complexity. In contrast to existing metrics, the PSI performs well for a wide range of blurriness and shows a high degree of invariance for different image contents.