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Abstract—This paper presents a novel high-capacity audio watermarking
system to embed data and extract them in a bit-exact
manner by changing some of the magnitudes of the FFT spectrum.
The key idea is to divide the FFT spectrum into short frames and
change the magnitude of the selected FFT samples using Fibonacci
numbers. Taking advantage of Fibonacci numbers, it is possible
to change the frequency samples adaptively. In fact, the suggested
technique guarantees and proves, mathematically, that the maximum
change is less than 61% of the related FFT sample and the
average error for each sample is 25%. Using the closest Fibonacci
number to FFT magnitudes results in a robust and transparent
technique. On top of very remarkable capacity, transparency and
robustness, this scheme provides two parameters which facilitate
the regulation of these properties. The experimental results show
that the method has a high capacity (700 bps to 3 kbps), without
significant perceptual distortion (ODG is about 1) and provides
robustness against common audio signal processing such as echo,
added noise, filtering, and MPEG compression (MP3). In addition
to the experimental results, the fidelity of suggested system is
proved mathematically.
I. INTRODUCTION
I N THE current information age, with the rapid development
of various communication techniques, transferring digital
multimedia content becomes more and more usual. However,
the illegal copy and distribution of digital multimedia content
has also become easier, and a large number of authors’ and publishers’
intellectual property copyrights have suffered from violation,
which have led to huge damage of their benefits in many
applications. Thus, people pay more attention to copyright management
and protection nowadays. Embedding secret information,
known as watermarks, into multimedia content is considered
as a potential solution to copyright infringement [1].
Digital watermarking is a process by which a watermark is
hidden or embedded into a media (cover data), for example
digital content such as electronic documents, images, audio
and video. These embedded data can later be detected or extracted from the marked signal for various applications.
There are several applications of audio watermarking including
copyright protection, copy protection, content authentication,
fingerprinting and broadcast monitoring.
An audio watermarking system may have different properties
but must satisfy the following basic requirements:
1. Imperceptibility: The quality of the audio should be retained
after adding the watermark. Imperceptibility can be
evaluated using both objective and subjective measures.
2. Security: Watermarked signals should not reveal any clues
about the watermarks in them. Also, the security of the
watermarking procedure must depend on secret keys, but
not on the secrecy of the watermarking algorithm.
3. Robustness: The ability to extract a watermark from a watermarked
audio signal after various signal processing or
malicious attacks.
4. Payload: The amount of data that can be embedded into the
host audio signal without losing imperceptibility. For audio
signals, data payload refers to the number of watermark
data bits that may be reliably embedded within a host signal
per unit of time, usually measured in bits per second (bps).
Considering the embedding domain, audio watermarking
techniques can be classified into time-domain and frequency-domain
methods. In frequency-domain watermarking
[2]–[15], after applying one of the usual transforms such as
the Discrete/Fast Fourier Transform (DFT/FFT) [5]–[7], [11],
[12], the Modified Discrete Cosine Transform (MDCT) or the
Wavelet Transform (WT) from the signal [8], [10], [13], [14],
[15], the hidden bits are embedded into the resulting transform
coefficients.
In frequency-domain methods, the Fourier transform (FT)
is very popular. Among different Fourier transform, the Fast
Fourier transform (FFT) is often used due to its reduced
computational burden and it has been the chosen transform
for the proposed scheme. This transform is also used by different
authors, such as in [16], which proposes a multi-bit
spread-spectrum audio watermarking scheme based on a geometric
invariant log coordinate mapping (LCM) feature. The
watermark is embedded in the LCM feature, but it is actually
embedded in the Fourier coefficients which are mapped to the
feature via LCM. Consequently, the embedding is actually
performed in the FT domain. In Ref. [5], [7], [11], [12], which
were proposed by the authors of this paper, the FFT domain
is also selected to embed watermarks to take advantage of the
translation-invariant property of the FFT coefficients to resist
small distortions in the time domain. In fact, using methods
based on transforms provides better perceptual quality and
robustness against common attacks at the price of increasing
the computational complexity with respect to time-domain
approaches. Ref. [27] presents a time-spread echo-based audio watermarking scheme with optimized imperceptibility
and robustness. Specifically, convex optimization-based fi-
nite-impulse-response (FIR) filter design is used to obtain the
optimal echo filter coefficients. The desired power spectrum
of the echo filter is designed by the maximum power spectral
margin (MPSM) and the absolute threshold of hearing (ATH)
of the human auditory system (HAS) to ensure the optimal
imperceptibility.
In the algorithm suggested in this paper, we select a part of
the frequency of FFT spectrum for embedding the secret bits.
The selected frequency band is divided into short frames and a
single secret bit is embedded into each frame. The largest Fibonacci
number that is lower than each single FFT magnitude
in each frame must be computed and, depending on the corresponding
secret bit to be embedded, all samples in each frame
are changed. If the secret bit is “0”, all FFT samples in a frame
should be changed to the closest Fibonacci number with even
index. If the secret bit is “1”, all FFT samples in a frame should
be changed to closest Fibonacci number with odd index.
As mentioned above, the FFT is used to design a scheme in
many watermarking systems. To the best of our knowledge, this
is the first audio watermarking method based on Fibonacci numbers.
Using Fibonacci numbers for embedding the secret bits
increases transparency and robustness against attacks, whereas
embedding a secret bit into a single FFT sample is usually very
fragile. Almost all watermarking methods rely on experimental
results to prove the fidelity of watermarking system. However,
in this article, in addition to the experimental results, the fidelity
of suggested system is proved mathematically.
The experimental results show that this method achieves
a high capacity (about 0.7 to 3 kbps), provides robustness
against common signal processing attacks (even for strong
disturbances) and entails very low perceptual distortion.
The rest of the paper is organized as follows. In Section II,
Fibonacci numbers are presented. Section III presents the
proposed scheme. Section IV provides discussion about the
fidelity. In Section V, the experimental results are shown.
Finally, Section VI summarizes the most relevant conclusions
of this research.
II. FIBONACCI NUMBERS AND GOLDEN RATIO
The numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …, known as
the Fibonacci numbers, have been named by the nineteenth-century
French mathematician Edouard Lucas after Leonard Fibonacci
of Pisa, one of the best mathematicians of the Middle
Ages, who referred to them in his book Liber Abaci (1202) in
connection with his rabbit problem. The Fibonacci sequence has
fascinated both amateurs and professional mathematicians for
centuries due to their abundant applications and their ubiquitous
habit of occurring in totally surprising and unrelated places [17].
In this paper we apply Fibonacci numbers for the first time for
audio watermarking.