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In this paper, a new reversible data hiding based on logarithm transformation function named improved reduced difference expansion (IRDE) was proposed. Reduced difference expansion (RDE) proposed by Lou et al uses logarithm transformation function to reduce the distortion cased by difference expansion (DE) effectively. Inspired by RDE, we modify the data embedding procedure and the data extraction correspondingly. The embedded data can be extracted correctly, and the original image can be restored completely from marked images without distortion. Performance comparisons with Lou's scheme demonstrate the superiority of the proposed scheme.