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Restoring of the watermarking image in Arnold scrambling

It is common to use Arnold transformation to scramble the watermark image in the stage of pre-processing in watermarking to improve the capability of the algorithm. But the image restoration is computational expensive using the original methods. The anti-Arnold transformation arithmetic is presented with mathematical proof. Experimental results showed that Arnold transformation helped digital watermarking a lot. The proposed anti-Arnold transformation could be used to resume the original image accurately and faster with less computation.