Wavelet-Domain Image Watermarking Using Optimization-Based Mean Quantization

Wavelet‐domain audio watermarking using optimal modification on low‐frequency amplitude

“…To avoid the situation that the value of some entries becomes arbitrarily large, without loss of generality we may set the summation of all the scaling factors equal to a constant N. For example, A = 0.91 .21 .20 .7 is a suitable selection when N = 4. With the suitable scaling vector A, we consider the optimisation problem for watermarking is to select the vectorĈ N such that the SNR is maximised under the constraint (12) or (13). The solution of the vectorĈ N will be derived optimally in next section.…”

“…Assuming we are embedding the watermark with the binary bit of value 1, by connecting (17) with (12) we have the following corresponding optimisation problem whose optimal solution can be computed via the KKT theorem with m = 1. Thus, there are two possible solutions by using (4) or (7).…”

“…For the copyright protection of music, many audio watermarking methods have been proposed recently. These methods can be grouped into two categories: time-domain [1][2][3][4][5][6][7][8][9] and frequency-domain [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. In the time-domain, different embedding techniques [1][2][3]a r efirst applied to digital watermarking.…”

“…However, it is very vulnerable to re‐sampling, amplitude and time scaling. Some authors improved this method by using multi‐coefficient quantisation [12–14, 24, 25]. The methods of multi‐coefficient quantisation are still vulnerable to amplitude and time scaling.…”