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Reversible digital watermarking techniques enable the recovery of the original 'cover image' from a watermarked image in a distortion-free way. Reversible watermarking techniques find application in military and medical imagery, where integrity of the cover image is of utmost importance. In this study, we propose a reversible digital image watermarking algorithm that predicts a pixel greyscale value exploiting its correlation with its neighbouring pixels, and embeds watermark bits into the prediction errors. Our algorithm succeeds in providing high embedding capacity with very low distortion, without 'multilayer embedding', hence reducing the computational burden compared with existing state-of-the-art algorithms. In addition, our results indicate that the resulting data overhead requirement is extremely low.