An efficient singular value decomposition algorithm for digital audio watermarking

The singular value decomposition (SVD) mathematical technique is utilized, in this paper, for audio watermarking in time and transform domains. Firstly, the audio signal in time or an appropriate transform domain is transformed to a 2-D format. The SVD algorithm is applied on this 2-D matrix, and an image watermark is added to the matrix of singular values (SVs) with a small weight, to guarantee the possible extraction of the watermark without introducing harmful distortions to the audio signal. The transformation of the audio signal between the 1-D and 2-D formats is performed in the well-known lexicographic ordering method used in image processing. A comparison study is presented in the paper between the time and transform domains as possible hosting media for watermark embedding. Experimental results are in favor of watermark embedding in the time domain if the distortion level in the audio signal is to be kept as low as possible with a high detection probability. The proposed algorithm is utilized also for embedding chaotic encrypted watermarks to increase the level of security. Experimental results show that watermarks embedded with the proposed algorithm can survive several attacks. A segment-by-segment implementation of the proposed SVD audio watermarking algorithm is also presented to enhance the detectability of the watermark in the presence of severe attacks.