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Preventing secret from being suspicious during transferring over Internet has become an emergent issue in the past decades. Several protecting data methods such as cryptographic techniques, watermarking or steganography techniques, etc. have been proposed to conceal secrets from being discovered. In this paper, we introduce the Minima-Maxima Preserving (MMP) data hiding algorithm for absolute moment block truncation coding (AMBTC) compressed images, which preserves the high and low values in each block to reversibly extract secret and recover host images during the extracting procedure. As a result, image quality is maintained that makes the secret messages hidden and avoids suspicion from attackers. Experimental results show that the scheme has better performance compared to state-of-theart schemes in terms of visual quality and embedding rate. Besides, with the high embedding rate, the scheme can be widely used in practice. Keywords Data hiding . Absolute moment block truncation coding (AMBTC) . Compressed image . Embedding rate . Visual quality Multimed Tools Appl

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