Robust reversible watermarking (RRW) is one of the most popular areas in information hiding. Existing schemes have two drawbacks: 1) schemes that can resist conventional attacks often fail to resist geometric attacks, and 2) schemes that can resist geometric attacks often are not robust against conventional attacks and have poor stability. Inspired by the high robustness of fractional-order orthogonal moments (FoOM) and the good feature of resistance to geometric attacks of Zernike moments and pseudo-Zernike moments (ZM/PZM), in this research, FoOM is used to optimize ZM/PZM to obtain FoZM/FoPZM (namely, fractional-order Zernike moments and fractional-order pseudo-Zernike moments). Furthermore, a denoiser is proposed to preprocess the watermarks to improve the robustness against geometric and conventional attacks, the amount of extracted auxiliary information is decreases and the extraction process of auxiliary information is designed to be more stable. Specifically, first, the source of the difference between the watermarked image and the carrier image is identified, that difference is represented with less information, and then that information is embedded into the cover image as auxiliary information. Second, the watermark is embedded in the low-order FoZM/FoPZM component. Finally, the watermarked image is denoised using a denoiser before extracting the watermark. The experimental results show that the scheme has good stability and strong robustness. Compared with existing methods, the proposed scheme has a small and stable auxiliary information size, strong robustness to noise attacks such as Gaussian noise and salt-and-pepper noise attacks, and better resistance to geometric attacks such as rotation and scaling attacks.