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Therefore, it is unsuitable to represent those with Gaussian distribution, and we exploit GGD and Cauchy to account for the distribution.
We recapitulate the GGD parametrization of Nadarajah [27], where the p.d.f.
The Laplace distribution and the Gaussian distribution act as the special case of the GGD with c = 1 and c = 2, respectively.
We make use of Do's approach to estimate the parameters of GGD.
The estimated GGD and Cauchy distribution parameters with ML approach are listed in Table 2 (averaged with 1000 experiments).
As illustrated by the visual GoF in Figure 5, we conclude that the Cauchy distribution can be the better choice for modeling the NSCT subband coefficients compared to the GGD.
Nikolaidis and Pitas derived a watermark detector for additive spread spectrum watermarks exploiting RAO test in the DWT domain, which considered DWT coefficients as GGD variants [8].
The detection statistic of RAO test assuming GGD host signal is given by
The results show that the Cauchy distribution provides a more accurate fitting to the NSCT subband coefficients through a visual comparison to GGD.