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proposed. This format was intended for thrifty representation of a digital image des-
tined for hiding in a cover one. Use of SVD transform for data hiding was originally
proposed in [10].
Let cover image be represented in a 24 bit ( RGB ) format. Assume that it is seg-
mented into small blocks of size l
k pixels, and A is the matrix of an arbitrary block
corresponding to one of Red , Green or Blue color layer. Let bit b be embedded into
block A . The algorithm of the embedding procedure is as follows:
×
V
λ
1. Compute SVD of matrix A . Let
] be the vector composed of
singular values of matrix A ordered in decreasing mode,
=[
λ
,
λ
,...,
λ
1
2
r
Y are singular
X and
vectors of matrix A , i=1,2,…,r , and r is the rank of matrix A .
2. Compute Euclidean norm of vector
V
=
λ
r
i
, Norm (
V
λ
)=
(
v λ
)
2
, where
i v ,
1
i=1,2,…,r , are the components of the vector V .
3. Select the value of the step of quantization of the Euclidean norm of the vector
V , Delta [10].
4. Compute the integer N=[Norm( V )/Delta]*, where * symbolizes the integer part
of the quotient of the above division.
5. Embed bit b according to the following algorithm:
If b=1 then
{if N is odd then ~ =N+1 else ~ =N}
else (if b=0)
{if N is even then ~ =N else ~ =N+1}}
6. Compute the modified norm of the vector of the singular values:
) = ~
V
λ
Norm (
× Delta+(Delta/2).
7. Compute the modified vector of the singular values:
V ~
V ~
V
V
λ
λ
λ
λ
=
× (Norm (
)/ Norm (
)).
8 . Compute the modified matrix of the block in which bit b is embedded:
~ =
=1 ~
r
i
λ
X
Y
T
.
i
i
i
9. End of the single bit embedding procedure.
The described algorithm must be applied to each block of the cover image in which
a bit of data is to be embedded.
The extraction procedure is blind . Let ~
be the matrix of a block containing hid-
den bit b of data, which must be extracted.
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