Abstract
In this paper, we propose to embed the watermark
information in the log-2-spatio domain by means of
spread spectrum technique. In log-2-spatio domain,
the variance of the information is reduced
significantly. This improves the efficiency and
robustness of spread spectrum technique. Low
intensity and mid-band regions are selected to embed
the information in order to guarantee an invisible
watermark as well as the robustness to JPEG
compression. Simulation results show that the
embedded information still survive up to the JPEG
compression ratio of 14.7.
1. SPREAD SPECTRUM TECHNIQUE
Spread spectrum technique has been used for
watermarking in [1]. For convenience, we use the
same symbol defined in [1]. According to [1], to
embed a bit sequence of m bits, the image is evenly
segmented to m mutually exclusive regions. Each
region responses to store one bit information. For
example, if the length of the bit sequence is 4, the
image will be segmented as shown in Figure 1. The jth
bit of the bit sequence, represented by the symbol
aj, is defined in eqn. 1:
The symbol aj, is then spread by a large factor cr,
called the clip rate, to obtain the spread sequence bi:
The spread sequence is modulated with a binary
pseudo-random sequence pi and amplified by a factor
, yielding the watermark sequence wi:
The watermark sequence is then added to the image
vi, to create the watermarked image :
The watermark embedding process can be visualized
in Figure 1.
Figure 1: Visualization of the embedding process
The embedded bit can be decoded by simply compute
the sign of the correlation sum between the
watermark sequence and the corresponding pseudonoise
sequence. The decoded jth bit, denoted by
, is compute by the following eqn.
To decode the right information, the amplification
factor a
j need to be large enough so that the second
term is larger than the first term in Eqn. 7 so as to
ensure the decoded bit is the same as the embedded
bit. However, a large a
j implies low Signal-to-Noise
ratio (SNR). As the amplitude of the embedded
watermark is independent of the intensity of the
pixels, the SNR can be very low for those pixels with
low intensity. Moreover, if the watermark sequence
is embedded in the regions with high frequency, the
watermark may be removed after the compression
process. As a result, the embedded bit sequence may
not survive if the watermarked image is compressed
at low bit rate. To solve this problem, we proposed to
embedded the bit sequence in the log-2-spatio domain
in the regions consisting mainly of mid-band
frequency.

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