The relationship between and can be expressed as where is permuted to the pixel position in a secret order using the secret key Since the audio signal is one-dimensional, we should transform the permuted watermark image into the one-dimensional sequence in order to embed it in the audio signal.
During detection, the same pairs of pixels are identified and then, by checking (23) if the result is or not-transformed and transformed (bringing the watermark) couples are respectively individuated.
Based on the above-mentioned robustness property of the transform domain watermarking, the moment transform according to which an image is described by a set of moment coefficients with respect to an orthogonal polynomial basis is considered herein.
Take the inverse Arnold transform to restore the watermark image, termed W ˜ i, j. .
Also, embedding in some transform domains makes the watermark more compatible with common compression algorithms and consequently, more robust.
The host is almost decorrelated in this transform domain like the watermark signal, while the watermark signal amplitude is shaped as the one of the host.
The resultant DWT matrix is processed by the SVD transform to embed the watermark bits, as will be explained in the next subsection.
The watermark embedding procedure transforms the audio signal using DWT and SVD, embeds the bits of a binary image watermark in appropriate locations in the transformed signal, and finally produces a watermarked audio signal by performing inverse SVD and DWT operations.
The insertion step consists in combining the two diagonals matrices of the SVD transforms of the watermark and the best tree.
In order to improve the robustness and imperceptibility, a binary image encrypted by Arnold transform as watermark is embedded in the vector norm of the segmented approximation components, the count of which depends on the size of the watermark image, after DWT of the original audio signal through quantization index modulation (QIM) with an adaptive quantization step selection scheme.
