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Recently, among various data hiding techniques, a new subset, lossless data hiding, has received increasing interest. Most of the existing lossless data hiding algorithms are, however, fragile in the sense that the hidden data cannot be extracted out correctly after compression or other incidental alteration has been applied to the stego-image. The only existing semi-fragile (referred to as robust in this paper) lossless data hiding technique, which is robust against high-quality JPEG compression, is based on modulo-256 addition to achieve losslessness. In this paper, we first point out that this technique has suffered from the annoying salt-and-pepper noise caused by using modulo-256 addition to prevent overflow/underflow. We then propose a novel robust lossless data hiding technique, which does not generate salt-and-pepper noise. By identifying a robust statistical quantity based on the patchwork theory and employing it to embed data, differentiating the bit-embedding process based on the pixel group's distribution characteristics, and using error correction codes and permutation scheme, this technique has achieved both losslessness and robustness. It has been successfully applied to many images, thus demonstrating its generality. The experimental results show that the high visual quality of stego-images, the data embedding capacity, and the robustness of the proposed lossless data hiding scheme against compression are acceptable for many applications, including semi-fragile image authentication. Specifically, it has been successfully applied to authenticate losslessly compressed JPEG2000 images, followed by possible transcoding. It is expected that this new robust lossless data hiding algorithm can be readily applied in the medical field, law enforcement, remote sensing and other areas, where the recovery of original images is desired.