It is of great importance in telemedicine to protect authenticity and integrity of medical images. They are mainly addressed by two technologies, which are region of interest (ROI) lossless watermarking and reversible watermarking. However, the former causes biases on diagnosis by distorting region of none interest (RONI) and introduces security risks by segmenting image spatially for watermark embedding. The latter fails to provide reliable recovery function for the tampered areas when protecting image integrity. To address these issues, a novel robust reversible watermarking scheme is proposed in this paper. In our scheme, a reversible watermarking method is designed based on recursive dither modulation (RDM) to avoid biases on diagnosis. In addition, RDM is combined with Slantlet transform and singular value decomposition to provide a reliable solution for protecting image authenticity. Moreover, ROI and RONI are divided for watermark generation to design an effective recovery function under limited embedding capacity. Finally, watermarks are embedded into whole medical images to avoid the risks caused by segmenting image spatially. Experimental results demonstrate that our proposed lossless scheme not only has remarkable imperceptibility and sufficient robustness but also provides reliable authentication, tamper detection, localization, and recovery functions, which outperforms existing schemes for protecting medical images. INDEX TERMS Robust reversible watermarking, authenticity, integrity, medical image.