• East Asian mathematical journal
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• v.39 no.5
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• pp.515-522
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• 2023

In the case that the set of sorts is countable, we will prove that any sorted profinite group has the unique SEP-cover using the notion of prime model in model theory.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.12
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• pp.5170-5188
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• 2015

This paper proposes a novel progressive secret image-hiding scheme based on the inpainting technique, the vector quantization technique (VQ) and the exploiting modification direction (EMD) technique. The proposed scheme first divides the secret image into non-overlapping blocks and categorizes the blocks into two groups: complex and smooth. The blocks in the complex group are compressed by VQ with PCA sorted codebook to obtain the VQ index table. Instead of embedding the original secret image, the proposed method progressively embeds the VQ index table into the cover images by using the EMD technique. After the receiver recovers the complex parts of the secret image by decoding the VQ index table from the shadow images, the smooth parts can be reconstructed by using the inpainting technique based on the content of the complex parts. The experimental results demonstrate that the proposed scheme not only has the advantage of progressive data hiding, which involves more shadow images joining to recover the secret image so as to produce a higher quality steganography image, but also can achieve high hiding capacity with acceptable recovered image quality.