2.1 High-Order Statistics and Steganalysis
A number of prior studies have shown that high-order statistics are very effective
in differentiating stego-images from cover-images. In [15], Farid proposed a gen-
eral steganalysis algorithm based on image high-order statistics. In this method,
a statistical model based on the first (mean) and higher-order (variance, skew-
ness, and kurtosis) magnitude statistics, extracted from wavelet decomposition,
is used for image steganography detection. In [16], a steganalysis method based
on the moments of the histogram characteristic function was proposed. It has
been proved that, after a message is embedded into an image, the mass center
(the first moment) of histogram characteristic function will decrease. In [10],
Holotyak et al. used higher-order moments of the probability density function
(PDF) of the estimated stego-object in the finest wavelet level to construct the
feature vectors. Due to the limited number of features used in the steganalysis
technique proposed in [16], Shi et al. proposed the use of statistical moments of
the characteristic functions of the wavelet sub-bands [17]. Because the n
th
statis-
tical moment of a wavelet characteristic function is related to the n
th
derivative
of the corresponding wavelet histogram, the constructed 39-dimensional feature
vector has proved to be sensitive to embedded data.
Usually, the steganalysis algorithms based on the high-order statistics can
achieve satisfactory performance on image files, regardless of the underlying
embedding algorithm. However, these statistical models may not be appropriate
for audio files because these mo dels capture statistical regularities inherent to
the spatial composition of images which is not present in audio [5].
2.2 Distortion Measures and Steganalysis
The concept of using distortion measures to classify cover-objects and stego-
objects was introduced by Avcibas et al. in 2003 [18]. Since the presence of
steganography communication in a signal can be modeled as additive noise in
the time or frequency domains [16], the de-noised versions of the image signals
can be used to represent close approximations of the cover-images. It has been
shown that the distortion (measured by the distance in the feature space) of
the cover-image to its de-noised version is different than the distortion between
a stego-image and its de-noised version. Specifically, some image quality met-
rics, e.g., Minkowsky [18], correlation, and human visual system (HVS) based
measures [19][20], are selected as the feature set to distinguish between cover-
images and stego-images. This concept was extended to audio steganalysis in
[6]. Similar to [18], the potential of distortion audio metrics is used to build a
steganalyzer to discriminate between cover-audio objects and stego-audio ob-
jects. Particularly, the traditional audio quality metrics, such as SNR, PAQM,
and other such metrics are tested for their sensitivity to the presence of stegano-
graphic content. In [7], Avcibas proposed an audio steganalysis algorithm using
content-independent distortion measures. By removing content dependency dur-
ing the distortion measurement, the paper shows that the discriminatory power
is enhanced.