From Image to Audio Watermarking Using Self-Inverting Permutations
Maria Chroni, Angelos Fylakis and Stavros D. Nikolopoulos
Department of Computer Science and Engineering, University of Ioannina, GR-45110 Ioannina, Greece
Keywords:
Watermarking Techniques, Audio Watermarking Algorithms, Self-inverting Permutations, Representations of
Permutations, Frequency Domain, Embedding/Extracting Algorithms, Performance Evaluation.
Abstract:
The intellectual property infringement in music due to the proliferation of the internet and the ease of creating
and distributing identical digital objects has brought watermarking techniques to the forefront of digital rights
protection. Towards this direction, a significant number of watermarking techniques have been proposed in
recent years in order to create robust and imperceptible audio watermarks. In this work we propose an au-
dio watermarking technique which efficiently and secretly embeds information, or equivalently watermarks,
into an audio digital signal. Our technique is based on the main idea of a recently proposed image water-
marking technique expanding thus the digital objects that can be efficiently watermarked through the use of
self-inverting permutations. More precisely, our audio watermarking technique uses the 1D representation
of self-inverting permutations and utilizes marking at specific areas thanks to partial modifications of the au-
dio’s Discrete Fourier Transform (DFT); these modifications are made on the magnitude of specific frequency
bands. We have evaluated the embedding and extracting algorithms by testing them on various and different in
characteristics audio signals that were in WAV format and we have obtained positive results. The algorithms
have been developed and tested using the mathematical software package Matlab.
1 INTRODUCTION
Digital watermarking is a technique for protecting the
intellectual property of a digital object; the idea is
simple: a unique marker or identifier, which is called
watermark, is embedded into a digital object which
may be used to verify its authenticity or the identity of
its owners (Grover, 1997; Collberg and Nagra, 2010).
Audio Watermarking. In a copyright protection
framework, an audio watermarking technique aims to
embed a unique identifier, i.e., the watermark w, into
audio’s data through mainly the introduction of errors
not detectable by human perception. Within the same
framework, audio watermarking can be described as
the problem of embedding a watermark w in the host
signal S producing thus the watermarked audio sig-
nal S
w
such that w can be reliably located and ex-
tracted from S
w
even after S
w
has been subjected to
transformations such as compression, filtering, noise
addition, cropping, etc. It is worth noting that, if a
watermarked audio signal S
w
is copied or transferred
through the internet then the watermark w is also car-
ried with the copy into the audio’s new location en-
suring thus the maintenance of copyright protection.
Recently, a significant number of watermarking
techniques have been proposed in the literature in or-
der to create robust and imperceptible audio water-
marks. Initial research on audio watermarking dates
back to the mid-nineties where Bender et al. (Bender
et al., 1996) presented data hiding techniques for au-
dio signals; the first techniques were directly inspired
from previous research on image watermarking. A
broad range of audio watermarking techniques goes
from simple least significant bit (LSB) scheme to the
various spread spectrum methods and can be classi-
fied according to the domain where the watermarking
takes place in frequency, time, and compressed do-
main (Sharma et al., 2012; Cox et al., 2008; Alsalami
and Al-Akaidi, 2003; Hartung and Kutter, 1999).
Motivation. Nowadays, digital audio is a representa-
tive sample of internet data that has been subjected
to extensive intellectual property violation. Thus, we
consider important the development of methods that
deter malicious users from claiming others’ owner-
ship, motivating thus internet users to feel more safe
to publish their work online.
Audio watermarking, in contrast with other tech-
niques, allows audio signals to be available to third
internet users but simultaneously carry an “id” that is
actually the ownership’s proof. This way audio wa-
177
Chroni M., Fylakis A. and D. Nikolopoulos S..
From Image to Audio Watermarking Using Self-Inverting Permutations.
DOI: 10.5220/0004855901770184
In Proceedings of the 10th International Conference on Web Information Systems and Technologies (WEBIST-2014), pages 177-184
ISBN: 978-989-758-023-9
Copyright
c
 2014 SCITEPRESS (Science and Technology Publications, Lda.)

termarking achieves its target of deterring copy and
usage without owner’s permission.
Watermarking digital objects such as image, au-
dio, video, text and software enables the proof of
ownership on copyrighted objects preventing thus the
intellectual property infringement.
Contribution. In this work we present an efficient
and easily implemented technique for watermarking
audio signals. What is important of the proposed
technique is the fact that it suggests a way in which
an integer number w can be represented first as a
self-inverting permutation π
∗
and then as an one-
dimensional array (or, equivalently, 1D representa-
tion). The idea comes from our previous work on im-
age watermarking where the integer watermark num-
ber w is represented as a two dimensional array.
More precisely, our proposed algorithm embeds a
self-inverting permutation π
∗
over n elements into an
audio signal S by first mapping the elements of π
∗
into
an n ×n matrix A
∗
and then, based on the information
stored in A
∗
, marking specific areas of audio S in the
frequency domain resulting thus the watermarked au-
dio S
w
. An efficient algorithm extracts the embedded
self-inverting permutation π
∗
from the watermarked
audio S
w
by locating the positions of the marks in S
w
;
it enables us to reconstruct the 1D representation of
π
∗
and, then, obtain the watermark w.
At this point we would like to point out that the
primary purpose of the paper is not to fill a gap of the
existing audio watermarking methods by proposing
a new embedding technique, but to expand the idea
used on our previous work and show that it can be
efficiently applied for audio watermarking depicting
thus the high versatility of the whole concept.
Evaluation. We have evaluated the embedding and
extracting algorithms by testing them on various and
different in characteristics audio signals that were in
WAV format and we had positive results as the wa-
termark was successfully extracted. What is more,
the method is open to extensions as the same method
might be used with a different marking procedure.
Note that, all the algorithms have been developed and
tested in MATLAB (Ingle and Proakis, 2010).
2 OUR WATERMARKING TOOLS
In this section we present the structural and algorith-
mic tools we use towards the watermarking of an
audio signal. We first briefly discuss a codec sys-
tem which encodes an integer number w into a self-
inverting permutation π, and then we present a trans-
formation of a self-inverting permutation into 2D and
1D representations.
2.1 Self-inverting Permutations
In a formal (i.e., mathematical) way, a permutation of
a set of objects S is defined as a bijection from S to
itself, that is, a map S → S for which every element of
S occurs exactly once as image value.
Permutations may be represented in many ways,
where the most straightforward is simply a rearrange-
ment of the elements of the set N
n
= {1,2,... ,n}; for
example, the permutation π = (4, 7, 6,1, 5,3, 2) is a re-
arrangement of the elements of the set N
7
(Sedgewick
and Flajolet, 1996; Golumbic, 1980).
Definition 2.1.1. Let π = (π
1
,π
2
,. . ., π
n
) be a permu-
tation over the set N
n
, where n > 1. The inverse of the
permutation π is the permutation q = (q
1
,q
2
,. . ., q
n
)
with q
π
i
= π
q
i
= i. A self-inverting permutation (or,
for short, SiP) is a permutation that is its own inverse,
that is π
π
i
= i.
There are several systems that correspond integer
numbers into permutations (Sedgewick and Flajolet,
1996). Recently, we have proposed algorithms for
such a system which efficiently encode an integer w
into a self-inverting permutation π and efficiently de-
code it; our algorithms run in O(n) time, where n is
the length of the binary representation of w.
2.2 2D and 1D Representations
In the 2D representation, the elements of the permu-
tation π = (π
1
,π
2
,. . ., π
n
) are mapped in specific cells
of an n × n matrix A as follows:
number π
i
−→ entry A(π
−1
π
i
,π
i
)
or, equivalently, the cell at row i and column π
i
is la-
beled by the number π
i
, for each i = 1 , 2, .. ., n.
Figure 1(a) shows the 2D representation of the self-
inverting permutation π = (4, 7, 6,1, 5,3, 2).
Based on the previously defined 2D representa-
tion of a permutation π, we next propose a two-
dimensional marked representation (2DM representa-
tion) of π which is an efficient tool for watermarking
images. In our 2DM representation, a permutation π
over the set N
n
is represented by an n ×n matrix A
∗
as
follows:
◦ the cell at row i and column π
i
is marked by a
specific symbol, for each i = 1, 2, .. ., n;
where, in our implementation, the used symbol is
the asterisk, i.e., the character “*”. Figure 1(b)
shows the 2DM representation of the permutation
π = (4,7, 6,1, 5,3,2).
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2
6
5
4
3
2
1
1
2
3 4
5
6
3
4
1
6
5
6
5
4
3
2
1
1
2
3 4
5
6
*
*
*
*
*
*
(a)
(b)
7
7
7
7
7
*
1
2
3 4
5
6
8
9
10
11
12
13
7
14
15
. . .
*
*
36 37
38 39
40
41
43
44
45
46
47
48
42
49
35
. . .
*
*
(c)
22 23
24 25
26
27
29
28
21
. . .
*
. . .
Figure 1: The 2D, 2DM and 1DM representations of the
self-inverting permutation π = (4,7, 6, 1,5, 3, 2).
In our 1D representation, the elements of the per-
mutation π are mapped in specific cells of an array B
of size n
2
as follows:
number π
i
−→ entry B((π
−1
π
i
− 1)n + π
i
)
or, equivalently, the cell at the position (i −1)n +π
i
is
labeled by the number π
i
, for each i = 1,2, .. .,n.
We next describe the 1DM representation ac-
quired in a similar manner as the 2DM representation.
In our 1DM representation, a permutation π over the
set N
n
is represented by an n
2
array B
∗
as follows:
◦ the cell at the position (i − 1)n + π
i
is marked by
a specific symbol, for each i = 1, 2, .. ., n;
where, in our implementation, the used symbol is
again the asterisk character “*”. Figure 1(c) shows
the 1DM representation of the same permutation π =
(4,7, 6, 1,5, 3,2).
Hereafter, we shall denote by π
∗
a self-inverting
permutation and by n
∗
the number of elements of π
∗
.
3 PREVIOUS RESULTS ON
IMAGE WATERMARKING
In a recent work of ours, we have proposed an image
watermarking technique that embeds watermarks into
digital images by interfering in the frequency domain
of images. Since our audio watermarking technique,
that is going to be later described, is mainly based
on the idea of image watermarking, we next briefly
describe the main steps of our image watermarking
technique and state points regarding some of its main
characteristics.
The embedding image watermarking algorithm
first computes the 2DM representation of the permu-
tation π
∗
, that is, the n
∗
× n
∗
array A
∗
(see, Sub-
section 2.2). Next, it takes the input image I, cov-
ers it with an n
∗
× n
∗
imaginary grid C, resulting in
n
∗
× n
∗
grid-cells C
i j
, and takes the Discrete Fourier
Transform (DFT) F
i j
of each C
i j
. The algorithm goes
to each grid-cell C
i j
, takes the magnitude M
i j
, and
places on it two imaginary ellipsoidal annuli denoted
as “Red” and “Blue”. It then computes the average
of the magnitude values grouped by the “Red” and
the “Blue” annuli, say,
AvgR
i j
and
AvgB
i j
, respec-
tively, and after that, for each M
i j
computes the value
D
i j
= |AvgB
i j
−AvgR
i j
| if AvgB
i j
< AvgR
i j
, otherwise
D
i j
= 0. Subsequently, the algorithm computes for
each row i the maximum value MaxD
i
. Once again
the embedding algorithm goes to each grid cell C
i j
and if A
i j
= “∗” it increases the values of M
i j
grouped
by the “Red” annulus by AvgB
i j
− AvgR
i j
+ MaxD
i
+
c
opt
. Finally, it reconstructs each DFT cell F
i j
using
the modified M
i j
with the trigonometric formula and
with the inverse DFT it reconstructs the grid cells C
i j
.
The extracting algorithm works in a similar manner.
Regarding the main characteristics of this tech-
nique, we should first mention that it is efficient. As
the experimental results showed, watermarks are im-
perceptible leading also to high fidelity. Moreover,
watermarks are robust to distortions as we got pos-
itive results testing the watermarked images against
JPEG compression and other attacks.
4 THE AUDIO WATERMARKING
TECHNIQUE
In this section we present an algorithm for encoding a
self-inverting permutation π
∗
into an audio signal S by
marking specific time segments of S in the frequency
domain resulting thus the watermarked audio signal
S
w
. We also present a decoding algorithm which ex-
tracts the embedded permutation π
∗
from S
w
by locat-
ing the positions of the marks in S
w
.
4.1 Embed Watermark into Audio
The embedding algorithm of our proposed technique
encodes a self-inverting permutation (SiP) π
∗
into a
digital audio signal S. Recall that, the permutation π
∗
is obtained over the set N
n
∗
, where n
∗
= 2n + 1 and n
is the length of the binary representation of an integer
FromImagetoAudioWatermarkingUsingSelf-InvertingPermutations
179

Figure 2: Segmentation of the S’s signal into specific frames
according to 1DM representation of the permutation π
∗
.
Figure 3: The DFT representation of a marked frame.
w which actually is the audio’s watermark (author’s
technique).
The Main Idea of embedding. The watermark w, or
equivalently the corresponding self-inverting permu-
tation π
∗
, is imperceptibly inserted in the frequency
domain of specific frames on the audio track signals S;
see, Figure 2. More precisely, we mark certain frames
getting the DFT and do alterations at the magnitude
values of high frequencies for each audio frame to be
marked; see, Figure 3. This is achieved by choosing
two groups of magnitude values specified with two
segments of the magnitude vector namely “Red” and
“Blue” and the alterations are actually on their differ-
ence; see, Figure 4. In our implementation we use
fixed segments’ widths and distances from the cen-
ter of symmetry of the DFT’s magnitude vector. The
added value is specified by the maximum value in the
defined area.
The Embedding Algorithm. Our embedding algo-
rithm takes as input a SiP π
∗
and an audio signal S
and returns the watermarked audio signal S
w
; it per-
forms the following main processes:
i. construct the 1DM representation of the water-
mark number w;
ii. transform the input audio signal S and acquire the
frequency representation of it;
iii. modify signals’ frequency representation accord-
ing to the 1DM representation of the signal S;
iv. returns the watermarked audio signal S
w
;
We describe below in detail the embedding algorithm
in steps.
Algorithm: Embed SiP-to-Audio.
Input: the watermark π
∗
≡ w and the original audio
signal S;
Output: the watermarked audio signal S
w
;
Step 1: Compute first the 1DM representation of the
permutation π
∗
, i.e., construct the array B
∗
of size
n = n
∗
× n
∗
; recall that the entry B
∗
((i − 1)n
∗
+ π
∗
i
)
contains the symbol “*”, 1 ≤ i ≤ n
∗
.
Step 2: Segment the audio signal S into n non-
overlapping frames f
i
of size f
i
[a,b] = ⌊
N−1
n
⌋, 1 ≤
i ≤ n, where N is the length of the audio signal.
Step 3: For each frame f
i
, compute the Discrete
Fourier Transform (DFT) using the Fast Fourier
Transform (FFT) algorithm, resulting in n DFT
frames F
i
of size F
i
[a,b] = ⌊
N−1
n
⌋, 1 ≤ i ≤ n, that is,
F
i
= FFT( f
i
).
Step 4: For each DFT frame F
i
, compute its magni-
tude M
i
and phase P
i
vectors (or, arrays) which are
both of size M
i
[a,b] = P
i
[a,b] = ⌊
N−1
n
⌋, 1 ≤ i ≤ n.
Step 5: Then, the algorithm takes each of the n mag-
nitude vectors M
i
and determines two segments in M
i
,
1 ≤ i ≤ n, denoted as “Red” and “Blue” (see, Fig-
ure 4). In our implementation,
◦ each “Red” segment [x
r
,y
r
] has length ℓ
r
(even),
where x
r
= ⌊
N−1
2n
⌋ −
ℓ
r
2
and y
r
= ⌊
N−1
2n
⌋ +
ℓ
r
2
;
◦ each “Blue” segment [x
b
,y
b
] has length ℓ
b
(even),
where x
b
= x
r
−
ℓ
b
2
and y
b
= y
r
+
ℓ
b
2
The “Red” and the “Blue” segments determine two
groups of magnitude values on M
i
; the Red Values
and the Blue Values (see, Figure 4).
Figure 4: The “Red” and “Blue” segments on DFT.
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Step 6: For each magnitude vector M
i
, 1 ≤ i ≤ n,
compute the average value AvgR
i
of the Red Values
and the average value AvgB
i
of the Blue Values of M
i
.
Step 7: For each magnitude vector M
i
, 1 ≤ i ≤ n,
compute first the variable D
i
as follows:
◦ D
i
= |AvgB
i
− AvgR
i
|, if AvgB
i
≥ AvgR
i
◦ D
i
= 0, otherwise.
Step 8: Partition the n values D
1
, D
2
, . .., D
n
into
n
∗
sets E
1
,E
2
,. . ., E
n
∗
, each of size n
∗
(recall that n =
n
∗
×n
∗
); let {D
i1
,D
i2
,. . ., D
in
∗
} be the elements of the
i-th set E
i
, 1 ≤ i ≤ n
∗
. Then, compute the values
◦ MaxD
1
, MaxD
2
, . . ., MaxD
n
∗
where MaxD
i
is the maximum value of the i-th set
E
i
= {D
i1
,D
i2
,. . ., D
in
∗
}, 1 ≤ i ≤ n
∗
.
Step 9: For each marked cell B
∗
(i) of the 1DM repre-
sentation matrix B
∗
of the permutation π
∗
(i.e., the call
which contains the symbol “*”), mark the correspond-
ing frame F
i
, 1 ≤ i ≤ n; the marking is performed by
increasing all the Red Values in M
i
by the value
AvgB
i
− AvgR
i
+ MaxD
k
+ c, (1)
where k = ⌈
i
n
∗
⌉ and c = c
opt
. The additive value of
c
opt
is a predefined value which enables successful
extracting.
Step 10: Reconstruct the DFT of the correspond-
ing modified magnitude vector M
i
, using the trigono-
metric form formula (Gonzalez and Woods, 2007),
and then perform the Inverse Fast Fourier Transform
(IFFT) for each frame F
i
, 1 ≤ i ≤ n, in order to obtain
the audio signal S
w
.
Step 11: Return the watermarked audio signal S
w
.
Note that concerning the placement of the “Red” and
“Blue” segments, their position can vary according
to the frequency band in which we want to mark a
frame. At the above illustration we mark it in the
high frequencies but there can be a different approach.
Specifically, we can mark instead lower frequencies
and that is performed by moving the segments from
the center to the right and left edges of the magnitude
array of the Discrete Fourier Transform (DFT) repre-
sentation.
4.2 Extract Watermark from Audio
In this section we describe the decoding algorithm of
our proposed technique. The algorithm extracts the
SiP π
∗
from a watermarked digital audio signal S
w
,
which can be later represented as an integer w.
The Main Idea of Extracting. The main idea behind
the extracting algorithm is that the self-inverting per-
mutation π
∗
is obtained from the frequency domain
of specific frames of the watermarked audio signal
S
w
. More precisely, using the same two “Red” and
“Blue” segments, we detect certain areas of the wa-
termarked audio signal S
w
so that the difference be-
tween the average values of the “Red” segment have
the maximum positive difference over the average val-
ues of the “Blue” segments. In this way we can detect
marked frames that enable us to obtain the 1DM rep-
resentation of the permutation π
∗
.
The Extracting Algorithm. We next describe the
extracting algorithm which consists of the following
steps.
Algorithm: Extract SiP-from-Audio.
Input: the watermarked audio S
w
marked with π
∗
;
Output: the watermark π
∗
= w;
Step 1: Take the input watermarked audio S
w
and
compute its size N. Then, segment S
w
into n non-
overlapping frames f
i
of size f
i
[a,b] = ⌊
N−1
n
⌋, 1 ≤
i ≤ n.
Step 2: Then, using the Fast Fourier Transform
(FFT), get the Discrete Fourier Transform (DFT) for
each frame f
i
, resulting in n DFT frames F
i
, 1 ≤ i ≤ n.
Step 3: For each DFT frame F
i
, compute its magni-
tude M
i
and phase P
i
vectors, which are both of size
M
i
[a,b]=P
i
[a,b]=
⌊
N−1
n
⌋
, 1 ≤ i ≤ n.
Step 4: For each magnitude vector M
i
, compute the
average values AvgR
i
and AvgB
i
of the Red Values
and Blue Values of M
i
, respectively, as described in
the embedding algorithm.
Step 5: Partition the n vectors M
i
, 1 ≤ i ≤ n,
into n
∗
sets L
1
,L
2
,. . ., L
n
∗
, each of size n
∗
; let
{M
i1
,M
i2
,. . ., M
in
∗
} be the elements of the i-th set L
i
and let AvgR
i j
and AvgB
i j
be the average values of
the Red Values and Blue Values, respectively, of the
vector M
i j
, 1 ≤ i, j ≤ n
∗
.
Step 6: For each set L
i
= {M
i1
,M
i2
,. . ., M
in
∗
} find the
k
th
vector M
i j
such that AvgB
ik
− AvgR
ik
is minimum
and set π
∗
i
= k, 1 ≤ k ≤ n
∗
.
Step 7: Return the self-inverting permutation π
∗
.
Having presented the embedding and extracting algo-
rithms, we next briefly comment on the purpose of the
additive value c = c
opt
(see, Step 9 of the embedding
algorithm). Similar to image watermarking, we add at
the corresponding embedding marking step the addi-
tive value c
opt
which by getting greater increases the
FromImagetoAudioWatermarkingUsingSelf-InvertingPermutations
181

DFT
for each frame
F
B
*
Initial signal S
Watermarked signal Sw
i
Figure 5: The encoding process of audio signal watermarking.
robustness of the marks; in our audio watermarking
case, we just used a very small value for it.
5 EXPERIMENTAL RESULTS
This section summarizes the experimental results
of the proposed audio watermarking codec algo-
rithms; we implemented our algorithms and car-
ried out tests using the general-purpose mathematical
software package Matlab (Version 7.7.0) (Ingle and
Proakis, 2010).
Testing of our embedding and extracting algo-
rithms has been made by the use of various 16-bit
digital audio tracks in wav format with 44.1 KHz
sampling frequency. Concerning the audio samples
used, they where relatively short abstracts with dif-
ferent characteristics. For instance there were tracks
containing speech which have many silent segments
as well as music track samples and tracks with ex-
treme features such as low and high frequency sounds.
Many of the audio tracks that we used for testing were
acquired from a web audio repository called wav-
source and enriched by some other audio tracks from
various sources.
It is well known in the field of watermarking that
there are three main characteristics to take into ac-
count describing and evaluating a digital watermark-
ing system: Fidelity, Robustness, and Capacity (Cox
et al., 2008).
Concerning our watermarking system, it seems to
be of high fidelity as watermarked tracks were not dis-
tinguished over the original ones and the results using
the PSNR metric were interestingly positive.
Concerting the marking procedure of our imple-
mentation, we set both lengths ℓ
r
and ℓ
b
of the “Red”
and “Blue” segments respectively, equal to 20% of
half the length of magnitude vector as it is mirrored
(see, Section 4.1). Recall that, the value 20% is a
relatively small percentage which allows us to mod-
ify the audio track segments in a satisfactory level
in order to detect the watermark and successfully ex-
tract it without affecting audio tracks’ initial quality.
Moreover, we choose to alter higher frequencies and
thus the two segments are at the center of the magni-
tude vector. This is because high frequencies are less
perceptible according to the human auditory system.
What is more, at high frequencies audio tracks con-
tain less information which means that information is
less likely to be lost due to post alterations.
Fidelity. In order to evaluate the watermarked audio
track quality obtained from our proposed watermark-
ing method we used the Peak Signal to Noise Ratio
(PSNR) metric. Our aim was to prove that the wa-
termarked audio track is closely related to the origi-
nal track proving the high fidelity attribute of our sys-
tem. This is something vital as watermarking should
not introduce audible distortions in the original audio
track, as that would certainly reduce its commercial
value.
Giving a short introduction to the PSNR metric,
we should mention that it is defined as the ratio be-
tween the reference (or, original) signal and the dis-
torted (or, watermarked) signal of an audio track and
it is given in decibels (dB). It is well known that PSNR
is most commonly used as a measure of quality of
reconstruction of lossy compression codecs (e.g., for
image or audio compression methods). The higher
the PSNR value the closer the distorted signal is to
the original or the better the watermark conceals. We
mentions that PSNR is a popular metric due to its sim-
plicity.
For an initial audio signal S of size N and its wa-
termarked equivalent signal S
w
, PSNR is defined by
the formula:
PSNR(S, S
w
) = 10log
10
N
2
max
MSE
, (2)
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Table 1: The hamming distance of the watermark w and the extracted watermark w
∗
after common signal attacks.
Filename Gaussian Noise Cropping Resampling Requantization MP3 Compression
bach.wav 0 1 0 0 3.2
clarinet.wav 0 1 0 0 2.4
castanets.wav 0 1 0 0 5.2
elvis riverside.wav 0 1 0 0 2.8
family man.wav 0 1 0 0 0.2
high10sec.wav 0 1 0 0 3.0
low10sec.wav 0 1 0 0 2.0
where N
max
is the maximum signal value that exists in
the original audio track and MSE is the Mean Square
Error which is given by the following formula:
MSE(S, S
w
) =
1
N
N−1
∑
i=0
(S(i) − S
w
(i))
2
. (3)
Comparing the original audio tracks with the water-
marked ones, we immediately get to notice that they
depict excellent fidelity according to the PSNR values
that we have obtained. In every case PSNR is over
50 dB which proves that fact that there is a striking
similarity between the original and the watermarked
signal of an audio track.
Table 2: The PSNR values of the watermarked audio sig-
nals.
Filename PSNR
bach.wav 67.2
clarinet.wav 67.9
castanets.wav 68.2
elvis riverside.wav 75.3
family man.wav 73.8
high10sec.wav 58.8
low10sec.wav 64.5
In Table 2 you can see the performance of our method
as we demonstrate the PSNR values of some audio
tracks that we used in this work. Each of them was
sampled at 41.1 KHz and the duration was of about
10 sec. Additionally, each one has much different
characteristics. More specifically, the audio tracks
◦ bach.wav, clarinet.wav and castanets.wav
where a concert, a clarinet and castanets solo respec-
tively. The audio track
◦ elvis riverside.wav
combines human voice with music, while the
◦ family man.wav
contains only speech which means that it also has pe-
riods of silence. Lastly the audio tracks
◦ high10sec.wav and low10sec.wav
are some extreme cases of high and low frequency
sounds.
Robustness. The watermarked signals were subjected
to distortions or common signal attacks in order to
evaluate the robustness of our audio watermarking al-
gorithms. We tested the performance of each audio
track under white noise addition, cropping, resam-
pling, requantization and MP3 compression. Below
we describe in more details each one of the five dif-
ferent attacks that we applied in our experiments.
(a) Gaussian Noise. A white gaussian noise of SNR
20 dB was added to the original audio signal.
(b) Cropping. A 10% of the beginning of the wa-
termarked audio signal was cropped and subse-
quently replaced by zeros.
(c) Resampling. The watermarked signal, originally
sampled at 44.1 KHz, is resampled at 22.05 KHz,
and then restored back by sampling again at
44.1 KHz
(d) Requantization. The 24-bit watermarked audio
signal is re-quantized down to 16 bits/sample and
then back to 24 bits/sample.
(e) MP3 compression. The watermarked audio signal
is compressed using a bit rate of 128 Kb/s and
then decompressed back to the WAV format.
Since the watermark that we embed in our audio sig-
nal is a permutation, i.e. a vector over the set N
n
(n > 1), we test after each attack the similarity of the
extracted watermark with the original one using the
Hamming distance (Hamming, 1950).
The Hamming distance d(x,y) between two vec-
tors x and y is the number of coefficients in which
they differ (Hamming, 1950). The Hamming distance
equals to zero, i.e., d(x, y) = 0, if x and y agree in all
coordinates; it happens if and only if x = y. In our case
the Hamming distance is computed between the wa-
termark w = π
∗
that we embedded into the audio track
and the watermark π
∗
ext
that we extract from the audio.
If d(π
∗
,π
∗
ext
) = 0 the watermark w = π
∗
successfully
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extracts from the attacked audio signal. Additionally,
it is worth noting that if d(π
∗
,π
∗
ext
) is relatively small,
then the watermark π
∗
can be reconstructed with high
probability by exploiting the self-inverting properties
of the permutation π
∗
.
In Table 1 we demonstrate similarity results be-
tween the watermark that we embedded into the au-
dio track and the watermark that we extracted after
various signal processing attacks. As the experimen-
tal results show, our audio watermarking algorithm is
robust against additive gaussian noise of SNR 20 dB,
cropping, resampling and requantization. Evaluating
our method’s robustness over lossy compression we
tested it using the MP3 encoding format with a bit
rate of 128 Kb/s. In order to optimize the results as
high frequency information is mostly lost using MP3
we made the appropriate adjustments concerning the
width of the segments to be marked as well as the
additive value c = c
opt
(see, Algorithm Embed SiP-
to-Audio). For most cases the results were positive
as despite not being able in every case to successfully
extract all the elements of the watermark, using the
properties of self-inverting permutations recovery of
the initial watermark can be successfully operated.
Closing the robustness evaluation of our method,
we should point out that a drawback of our method is
actually when we want to watermark an audio track
with extreme high frequencies; it is something that
could be encountered on future work.
Capacity. The capacity of our audio watermark
method has been computed by measuring the percent-
age of the watermarked parts of an audio track over
the length of the entire audio track. Our method par-
titions the audio track into n
∗
× n
∗
frames, where n
∗
is the length of the permutation π
∗
, and marks only
one frame of a set of n
∗
frames; recall that our em-
bedding method groups the frames into n
∗
sets each
containing n
∗
frames (see, Algorithm Embed SiP-to-
Audio). That means, a total n
∗
over n
∗
× n
∗
frames
are marked, so the ratio of the watermarked part over
the entire length of the audio track is
n
∗
(n
∗
×n
∗
)
. Thus,
our audio watermarking method has
1
n
∗
capacity.
6 CONCLUDING REMARKS
In this paper we presented an audio watermarking
technique which efficiently and invisibly embeds in-
formation, i.e., watermarks, into an audio digital sig-
nal. Our technique is based on the same main idea of a
recently proposed image watermarking technique ex-
panding thus the digital objects that can be efficiently
watermarked through the use of self-inverting permu-
tations.
We experimentally tested our embedding and ex-
tracting algorithms on WAV audio signals. Our test-
ing procedure includes the phases of embedding a nu-
merical watermark w = π
∗
into several audio signals
S, storing the watermarked audio S
w
in WAV format,
and extracting the watermark w = π
∗
from the audio
S
w
. We obtained positive results as the watermarks
were invisible, they didn’t affect the audio’s quality
and they were extractable.
The performance evaluation of our audio water-
marking technique on several other attacks remains a
problem for further investigation.
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