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In this paper we introduce a highly efficient reversible data hiding technique. 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 maximize data hiding capacity. It exploits the special properties of medical images, where the histogram of their non-overlapping image tiles mostly peak around some gray 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. We show how histograms of image tiles of medical images can be exploited to achieve these requirements. Compared with data hiding method in the whole image, our scheme can result in 30%-200% capacity improvement with still better image quality, depending on the medical image content.