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In this study, the authors introduce a highly efficient reversible data hiding system. It is based on dividing the image into tiles and shifting the histograms of each image tile between its minimum and maximum frequency. Data are then inserted at the pixel level with the largest frequency to maximise data hiding capacity. It exploits the special properties of medical images, where the histogram of their non-overlapping image tiles mostly peak around some grey values and the rest of the spectrum is mainly empty. The zeros (or minima) and peaks (maxima) of the histograms of the image tiles are then relocated to embed the data. The grey values of some pixels are therefore modified. High capacity, high fidelity, reversibility and multiple data insertions are the key requirements of data hiding in medical images. The authors show how histograms of image tiles of medical images can be exploited to achieve these requirements. Compared to the data hiding method applied to the whole image, the authors' scheme can result in 30-200% capacity improvement and still with better image quality, depending on the medical image content. Additional advantages of the proposed method include hiding data in the regions of non-interest and better exploitation of spatial masking.