High dynamic range (HDR) imaging technique has received much attentions in the recent years for its abundant details and wide dynamic range of luminance. In order to display HDR images on low dynamic range display devices, tone mapping (TM) process is required. However, the TM can be deemed as an inevitable attack in the field of HDR image copyright protection. In this paper, a highly robust HDR image watermarking algorithm based on Tucker decomposition is proposed. Firstly, Tucker decomposition is carried out on HDR color image to obtain the first feature map of the core tensor, which contains most of the energies in the HDR host image. Then, a Auto-Regressive prediction method is used to establish a local correlation model of the first feature map, so that watermark can be embedded in the first feature map according to the prediction result and its true value. Furthermore, a low-complexity luminance masking approach is designed based on modified specular free map to exclude the areas not suitable for watermark embedding, and an embedding intensity selection strategy is used to balance the imperceptibility and robustness of the watermark. The experimental results show that the proposed algorithm is robust against existing TM attacks while keeping better image imperceptibility and embedding capacity.INDEX TERMS High dynamic range image, digital watermarking, tone mapping, tucker decomposition, luminance mask.