# A Robust Image Watermarking Scheme Based on SVD in the Spatial Domain
## 1 Introduction  
With the widespread use of digital products, it becomes more and more convenient for us to obtain and modify digital multimedia. However, a negative effect arises at the same time that the copyright of digital multimedia is suffering from a serious threat. To solve this thorny problem, the robust watermarking technique has been proposed. The basic idea of a robust watermarking scheme is to embed a watermark, which is usually a logo or image, into the host image in advance. On the receiving end, the embedded watermark is extracted to prove the ownership of the received image [1]. For the purpose of copyright protection, the watermark should meet two basic conditions: invisibility and robustness. Invisibility refers to that the embedded watermark cannot be discovered by naked eyes. The image after watermark embedding is basically the same as the original host image. Robustness means that the embedded watermark could be well extracted from the image distorted by various attacks. According to different embedding domains, the digital watermarking schemes can be broadly classified into two categories [2]: spatial domain watermarking and transform domain watermarking. In spatial domain watermarking, the watermark is embedded into the host image by directly modifying the pixel values. This method has low computational cost, and it is easy to implement. However, since the watermark embedding process is performed in the spatial domain, spatial domain watermarking is less secure and it has limited ability in resisting some image processingattacks. In transform domain watermarking, the watermark is embedded by modulating the transform coefficients of the host image. Compared with the former, it achieves stronger robustness and better visual quality. The most commonly used transforms include the discrete cosine transform (DCT) [3] and the discrete wavelet transform (DWT) [4]. In recent years, singular value decomposition (SVD) has been extensively applied in transform domain watermarking due to its good stability in signal processing. In [5], a classical robust watermarking method based on SVD was proposed by [PERSON] and [PERSON]. In their scheme, the watermark embedding process is completed by adding the watermark to the singular values of the host image directly. The left and right singular vectors generated in the watermark embedding process are stored and used as side information to extract the watermark on the receiving end. However, later research found that this method is subjected to a severe false positive problem [6,7]. A different watermark can be extracted from the watermarked image by using different singular vectors. To resolve this issue, [PERSON] et al. [8] suggested a reliable SVD-based watermarking. Unlike [5], the principal component of the watermark is utilized to adjust the singular values of the host image, and one of the singular vectors is served as side information to extract the watermark. Since the singular vectors still contain a wealth of image information, no one can obtain the watermark without correct side information. Therefore, this method provides an effective solution for the false positive problem. The main drawback of this scheme is that it has much influence on the visual quality of the host image, which cannot be applied in our real lives. To further improve the performance of the SVD-based watermarking scheme, many hybrid watermarking schemes have been put forward, which combine SVD with DCT, DWT, and other transforms. In [9], [PERSON] and [PERSON] proposed a DWT-SVD-based watermarking method. In their method, the original image is first decomposed by DWT decomposition, and the singular values of high frequency sub-bands in the horizontal and vertical directions (HL and LH) are modified by the watermark. [PERSON] and [PERSON] [10] presented a robust watermarking scheme that is based on DWT and singular values replacement. The principal component of the watermark is embedded into the singular values of the diagonal high frequency sub-band (HH).