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In this paper, we propose a novel prediction-based reversible steganographic scheme based on image inpainting. First, reference pixels are chosen adaptively according to the distribution characteristics of the image content. Then, the image inpainting technique based on partial differential equations is introduced to generate a prediction image that has similar structural and geometric information as the cover image. Finally, by using the two selected groups of peak points and zero points, the histogram of the prediction error is shifted to embed the secret bits reversibly. Since the same reference pixels can be exploited in the extraction procedure, the embedded secret bits can be extracted from the stego image correctly, and the cover image can be restored losslessly. Through the use of the adaptive strategy for choosing reference pixels and the inpainting predictor, the prediction accuracy is high, and more embeddable pixels are acquired. Thus, the proposed scheme provides a greater embedding rate and better visual quality compared with recently reported methods.