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Top1. Introduction
Most of the common types of multimedia data in either image/audio/video/etc. formats need to be protected. Digital watermarking of these data types is one of the popular copyright protection schemes for authentication of content integrity and for avoidance of piracy (Macq and Pitas, 1998; Siwek, 2002). Achievement of robustness and imperceptibility are the main targets for any digital watermarking scheme (Swanson et al., 1998). This is because the quality of the original multimedia data should be visually unaffected as well as the watermark needs to survive intentional and unintentional attacks from noisy environment or agents (Langelaar et al., 2000; Acken, 1998).
Singular value decomposition (SVD) is one of the popular mathematical tools employed in the field of signal processing be it for compression or watermarking. It has been widely used individually or with popular transforms like discrete cosine transform (DCT)/ discrete wavelet transform (DWT) or any other. SVD is a generalized Eigen-value decomposition technique, but not restricted to only square matrices but rectangular metros as well. The idea of reducing a rectangular matrix into two orthogonal matrices and one diagonal matrix was initiated in 1870 by Beltrami and Jordan. But theirs was for squared matrices which Eckart and Young in 1930s extended to rectangular matrices (Liu and Tan, 2002; Kahaner et al., 1989).
For signal analysis, Kakarala and Ogunbona were the first to propose MR-SVD, which is a multiresolution form of the SVD with linear computational complexity. This makes it faster in computation for large size images compared to the original SVD operation (Kakarala and Ogunbona, 2001; Shnayderman et al., 2004). R Ashino and group of Japan under their NSF grant studied its properties in image compression and single dimension signal analysis submitted a detailed report in York University in 2003 and Riga Technical Universityin 2005 respectively (Ashino et al., 2003; Yoshikawa et al., 2005). B. Akhbari and S. Ghaemmaghami later applied this idea in watermarking for the first time in 2005 (Akhbari and Ghaemmaghami, 2005).
In this paper, a robust and imperceptible technique of watermarking has been presented. The robustness of the watermarking scheme is enhanced by employing MR-SVD based techniques. Whereas the human visual system (HVS) based noise visibility function (NVF) looks into enhancing the imperceptibility of the embedded watermark. This algorithm employs similar pattern of mathematical techniques like our previous work using DWT and SVD together along with NVF and contrast sensitivity function CSF (Majumder et al., 2011). The basics of the implementation is any way based on previous SVD based watermarking works of Ganic et al. (2004; 2003) and Liu et al. (2002). Ganic et. al. showed that the DWT and SVD based hybrid scheme produces good results, and have been proved to be optimal in a sense. Here only the hybrid form of DWT and SVD has been replaced by MR-SVD. While the robustness of the SVD scheme has been shown by Liu (2002). Moreover, the Kakarala proposed MRSVD has been implemented block based similar in some respect to that implemented with hadamard transform by Abdullah et.al. (2006). Together they make the overall algorithm faster and easier to implement in hardware while in place of both NVF and CSF only NVF is providing similar results.