Advanced Computing: An International Journal ( ACIJ ), Vol.2, No.1, January 2011
ψ LH 2 ( x, y ) and ψ HH 2 ( x, y ) , where ( x, y ) indicates the coordinate of the coefficients in each subband. Recovering LL Sub-band Step 2: Create sub-band difference Dψ1(x, y) between the reference sub-band ψ LH 2 and the destination sub-band ψ HH 2 according to the following formulas: Dψ 1 ( x , y ) = ψ
LH 2
( x, y ) − ψ
HH 2
(x, y) .
(31)
Step 3: Denote the histogram of Dψ 1 ( x, y ) as hψ 1 ( j ) , where ( j ) indicates the value of each bin. Step 4: Check the distribution of the histogram hψ 1 ( j ) . If there is more than one occurrence at hψ 1 ( j ) = − 1 , the subsequent steps will be stopped immediately. Step 5: Check the embedding status. Once the value of f is equal to 1, it can be concluded that the sub-band is completely filled with hidden message bits. Subsequently, first restore the original difference histogram. The bins greater than or equal to zero will be shifted to the right by 4 and those less than zero to the left by 4. The restored hψ′ 1 ( j ) can be calculated as follows: hψ 1 ( j ) + 4, if hψ 1 ( j ) ≥ 0, hψ′ 1 ( j ) = hψ 1 ( j ) − 4, if hψ 1 ( j ) < 0.
(32)
These can also be obtained by the following formulas: Dψ′ 1 ( x , y ) = ψ LH 2 ( x , y ) − ψ HH ′ 2 ( x, y ) ,
(33)
where ψ HH ′ 2 ( x, y ) can be expressed as: ψ HH 2 ( x, y ) − 4, if hψ 1 ( j ) ≥ 0, (34) ψ HH 2 ( x, y ) + 4, if hψ 1 ( j ) < 0.
ψ HH ′ 2 ( x, y ) =
Extracting Data: Step 6: Extract the hidden message φ (n) , where n denotes the index of a message bit, by
shifting hψ′ 1 ( j ) with reference to the bitmap and inverting the embedding process. First, the iteration index l is set to 0. Once a hψ′ 1 ( j ) with a value of ±(l + 4) is encountered, a binary bit “1” is retrieved. On the other hand, a binary bit “0” is retrieved if hψ′ 1 ( j ) has a value of ±(l + 8) . This procedure is repeated until there are no hψ′ 1 ( j ) values of ±(l + 4) or ±(l + 8) .
Subsequently, l is increased by 1. The same procedures as described above are repeated until l reaches T+1. The retrieving rule is as follows: h′ ( j ) − 8, hψ′′1 = ψ 1 hψ′ 1 ( j ) − 4,
if hψ′ 1 ( j ) = 8, if hψ′ 1 ( j ) = 4,
(35)
for l = 0 . 9