## 1 Introduction  
The modification of digital multimedia content has become easier, especially in terms of images, and thus the issue of image copyright protection has attracted more attention. Accordingly, image watermarking technology aims at providing a reliable way to alleviate this problem related to the intellectual management. The robust watermarking method can protect copyright of the image, and have two basic characteristics, namely, robustness and fidelity. Since these two characteristics are contradictory, a good robust watermarking method can balance the relationship between robustness and fidelity. The robust watermarking technology is divided into the spatial and the frequency domain. Compared with the spatial domain, the frequency domain watermarking-based watermarking method can obtain much more watermarking robustness without a great amount of image distortion. Therefore, the present study focuses on the image watermarking schemes in the frequency domain. Many frequency techniques have been presented for the robust watermarking, such as discrete wavelet transform [1, 2], discrete Fourier transform [3], discrete cosine transform [4, 5], quaternion discrete Fourier transform [6, 7, 8], and quaternion Hadamard transform [9]. [PERSON] et al. [10] proposed a watermarking method that embedded a watermark into the two-level DCT coefficients using a specified technology. [PERSON] et al. [11] developed a robust watermarking scheme based on the wavelet domain. Due to the fact that the above two methods are single transform that have deficiencies without using inherent correlations in the frequency domain, hybrid transform watermarking schemes achieve better robustness and fidelity--many image-watermarking techniques combining several transform methods have been proposed [12; 13; 14]. In [12], a new method was presented, to hybrid SVD and integer wavelet transform to embed a watermark. [PERSON] et al. [13] proposed a mixed watermarking method based on SVD and FRAT. [PERSON] and [PERSON] [14] suggested a new image-watermarking method that blended a discrete wavelet transform and singular value decomposition. The method embedded a watermark on singular value of the host image's DWT sub-bands. From the above discussion, most image watermarking methods have been proposed to embed a watermark in a gray image or a channel. With the wide application of color images, the watermarking schemes for color images can be proposed [2; 6; 8; 15; 16; 17; 18; 19; 20; 21]. [PERSON] and [PERSON] [2] proposed a new color-image watermarking algorithm based on wavelet transform and significant difference, and embedded the maximum watermark information under imperceptible distortion. [PERSON] et al. [6] modulated at least one component of QDFT coefficients, and propagated the watermark to two or three RGB color channels. They used the characteristics of QDFT to avoid watermark energy loss. A color image-watermarking algorithm mingling with QDFT, LS-SVM and pseudo-Zernike moments has been proposed by [PERSON] et al. [8]. In [8], quaternion Fourier transform allows watermark information energy to be propagated to all channels simultaneously to improve the robustness. [PERSON] et al. [15] developed a local quaternion Fourier transform for the color image-watermarking method. The method used deeds of quaternion Fourier transform to improve watermark invisibility, and considered an invariant feature transform to resist the geometric attacks of the image. [PERSON] et al. [16] proposed a method for image tampering detection, that has an underlying hashing process based on estimation of image gradient, and the performance of the method was compared to the use of QDFT method. [PERSON] et al. [17] introduced a robust digital watermarking algorithm for geometric correction using quaternion Exponential moments. [PERSON] et al. [18] developed a color image-watermarking method based on QDFT and quaternion QR.