IEEE Computational Intelligence Magazine - November 2021 - 74
shown in Fig. 4, when ()
r
05
pi ..
mi ,1= correct
extraction can be guaranteed
a s long as
mi ,1
r
mr () 2 The space
between pimr () and 0.5 is thus redundant
when () = and vice versa. As a
result, the proposed scheme is robust to
some extent. More discussion regarding
robustness is given in Subsection IV-C
B. Data Hiding Scheme
In the representative data hiding framework,
additional data are embedded
into the cover media by matrix coding
[31] based on matrix multiplication.
Given a cover sequence
pp w201Tw
P [( ),p 1=xx
(),, ()][ ,] , additional
bits M mm mt12= [( ), (),, ()]T
1} t
xx !
f
f
Px to make HP MS
=
!
#
! {0,
can be embedded by modifying
, where PS
i s the stego sequence. The matrix
H {, }01 tw
is a low-density paritycheck
matrix that is determined by
payload, embedding speed, and embedding
efficiency. The additional data M
can be directly extracted using the
matrix computation HP MS
= in the
phase of data extraction. Inspired by
this, this paper proposes using matrix
multiplication to achieve the embedding
function. This means
Z
[
\
]
]
HP P
HP P
1
2
]]f
x
x
=
=
x =
M
M
1
2
(10)
HP P ,nMn
where {, ,, }HH Hn12
f are embedding
matrixes that can be generated using
{, ,, }.KK Kn12
f {, ,, }MM Mn12
f can
be directly extracted by the matrix multiplication
in Equation (10) and rounding
operation.
Pτ
PMn
Sigmoid
FIGURE 5 Data decoding networks.
Since this paper aims to embed additional
data into CapsNets, the process
of embedding should be combined
with the training process of CapsNets.
In deep learning, matrix multiplication
can be achieved by the FC (fully
connected) layer. The embedding
matrix can be regarded as the parameters
of the FC layer. Therefore, the
data decoding networks are designed
as n FC layers connected with a part
of the elements (cover elements )Px
in DigitCaps, as shown in Fig. 5. The
activation function of each FC layer is
set as sigmoid to limit the value range
of {, ,, }
PP PMM Mn12
f
to [0, 1], and the
parameters in each FC layer are generated
using the corresponding embedding
key instead of by training. In the field of
data hiding, embedding keys can be
transmitted via a secure subliminal channel
[32]. Key security can thus be guaranteed
by the subliminal channel.
Additional data cannot be extracted
TABLE I Extraction error of different connections with capacity 500 bits.
CONNECTED ELEMENTS
EXTRACTION
ERROR e
IEEE Computational Intelligence Magazine - November 2021
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