Informed Audio Watermarking using Digital Chaotic Signals

1
Informed Audio Watermarking using Digital Chaotic
Signals

• G.C. Silvestre, N.J. Hurley, G.S. Hanau
• and W.J. Dowling
• University College Dublin, Ireland
• University of Dublin, Trinity College, Ireland

2
Overview

• Introduction
• Digital Chaotic Maps
• Psychoacoustic Model
• Model Formulation
• Simulation Results
• Discussion

3
Introduction

• We present a data embedding scheme for digital
  audio which shows strong robustness to MPEG-1
  encoding.
• Two important aspects of the model are
• The use of a psychoacoustic model to determine
  the perceptually significant components in which
  to embed the data AND moreover to adaptively
  determine the maximum strength at which the
  watermark can be embedded in different parts of
  the signal, while remaining imperceptible. The
  watermark strength is derived from an informed
  parameter which must be reliably extracted from
  the signal by the detector.
• The use of chaotic maps to spread each watermark
  symbol over a large number of samples. This
  ensures robustness of detection (at a cost of
  reduced embedding bit rate). Data symbols are
  represented so that blind detection is enabled at
  the decoder and self-synchronisation is possible
  by exploiting the correlation properties of the
  chaotic maps.

4
Digital Chaotic Maps

• Digital chaotic maps are a class of deterministic
  dynamical system admitting non-periodic signals
  characterised by a continuous noise-like broad
  spectrum.
• Chaotic maps have some advantages over
  conventional spread spectrum
• Spread spectrum techniques are limited by the
  periodic nature of the pseudo-random sequences
  exploited. Chaotic maps, on the other hand, are
  truly aperiodic
• Using differential chaos shift keying (DCSK) and
  the autocorrelation properties of chaotic maps, a
  self-synchronising blind watermarking scheme can
  be developed.
• In this work, we represent the embedded symbols
  using chaotic basis functions

5
Digital Chaotic Maps (contd)

• Given a chaotic map, , each watermark
  symbol bit, , is represented by a map of
  length T using a binary DCSK technique given by
• for a bit value 0, and by
• for a bit value 1.
• For example, c(n) might be a bernoulli map, given
  by

6
Detection

• Since they are aperiodic, there is no symbol
  duration T over which the chaotic map will have
  constant energy. Instead, the energy may be
  considered as a stochastic variable, centred at
  some mean value.
• It can be shown that the standard deviation of
  the energy scales approximately as 1/(BWT),
  where BW is the statistical bandwidth of the
  signal. Hence, by choosing T large enough, we
  can assure that the energy is almost constant
  over the symbol period.
• Once the chaotic map is extracted from the
  watermarked signal, the data symbols can be
  retrieved by performing the autocorrelation
• If a data symbol has been embedded, then this
  correlation peaks at
• Hence content are considered watermarked if, for
  some threshold Thgt0,
• If R is negative, then a 0 symbol is retrieved,
  if it is positive then a 1 is retrieved.

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Correlation Property of Digital Map

• Correlation of Digital Map Retrieved at the
  Decoder, with T600. The correlation in the case
  of no noise and in the case of WNR-6dB

T samples are chosen from offset k and the first
half is correlated with the second half. The
correlation peaks at values of kmT where m is an
integer. A positive correlation implies that a
symbol 1 is embedded while a negative correlation
implies that a 0 is embedded.
8
Psychoacoustic Principles

• Inaudible embedding is achieved through the use
  of a psychoacoustic model which characterises the
  perceptual properties of the Human Auditory
  System (HAS).
• The HAS is modelled by a set of 25 band-pass
  filters, whose associated critical bands,
  represent a non-linear mapping of the frequency
  range, such that perception is largely similar
  within each band.
• For each critical band, the psychoacoustic model
  seeks to determine all frequency maskers and
  hence, a global masking threshold corresponding
  to the sound pressure level below which a
  frequency component becomes inaudible. From this
  a Signal-to-Mask Ratio (SMR) is determined and
  the amount of noise which can be imperceptibly
  introduced to the critical band is derived.
• In our watermarking scheme, this calculation is
  performed for each critical band of the frames in
  which data is embedded and is used to determine
  the maximum strength of the watermark in that
  band.

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Psychoacoustic Principles
Critical Band 1
Critical Band2
masker2
Masking threshold
masker1
SPL(dB)
maskee
Frequency(Hz)
Spread of Masking of Masker1
10
Model Formulation

• To embed a data symbol, a T dimensional vector
  is extracted from a discrete time audio signal
  so that
• In practise, the extraction process, , is
  applied to a number N of audio frames in the
  fourier domain and 25 components are extracted
  from each frame, one corresponding to each
  critical band of the frame. So T25xN
• A modulation function, , is applied to to
  embed T samples of a chaotic signal ,
  resulting in a watermarked vector
• The watermarked signal is finally given by
  embedding back into i.e.
• where is the embedding process

11
Model Formulation (contd)

• The function is chosen such that the noise
  introduced in is perceptually
  insignificant.
• A parameter derived from the psycho-acoustic
  model is used to adaptively determine the
  strength at which the watermark can be inserted
  in each critical band without becoming
  perceptual.
• For example, may be a uniform quantiser
  designed so that the quantisation noise is
  bounded by a maximum noise determined from the
  parameter.
• The watermark data is modulated by dithering the
  quantisation process.

12
Simulation Results

• Computer Simulations are carried out using a 30s
  mono audio signal sampled at 44.1kHz
• Simulations compare
• A non-adaptive scheme in which the watermark
  strength is constant throughout all critical
  bands and
• An adaptive scheme which varies the watermark
  strength according to an informed parameter
  derived from the psychoacoustic model.
• Results are shown for frame sizes of 512 and 1024
  samples.
• The WSR for the simulations was set to 23dB, a
  level at which the watermark could not be
  perceived in subjective listening tests.

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Simulation Results

• Robustness of Adaptive Data Embedding Scheme as a
  function of perceptual coding attacks using an
  MPEG-1 algorithm for different values of the
  watermark bit-rate
• Frame Size 1024 Samples, WSR-23dB

14
Simulation Results

• Robustness of Non-Adaptive Data Embedding Scheme
  as a function of perceptual coding attacks using
  an MPEG-1 algorithm for different values of the
  watermark bit-rate
• Frame Size 1024 Samples, WSR-23dB

15
Simulation Results

• Robustness of Adaptive Data Embedding Scheme as a
  function of perceptual coding attacks using an
  MPEG-1 algorithm for different values of the
  watermark bit-rate
• Frame Size 512 Samples, WSR-23dB

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Simulation Results

• Robustness of Non-Adaptive Data Embedding Scheme
  as a function of perceptual coding attacks using
  an MPEG-1 algorithm for different values of the
  watermark bit-rate
• Frame Size 512 Samples, WSR-23dB

17
Simulation Results

• Robustness of Data Embedding Scheme to Additive
  White Gaussian Noise
• Frame Size 1024 Samples, WSR-23dB

18
Simulation Results

• Robustness of Informed Parameter derived from
  Psychoacoustic Model

19
Discussion

• Good robustness to MPEG-1 encoding and AGWN
  attacks is observed for the scheme. It is found
  possible to embed a watermark signal of 3.6
  bits/s which survived without detection error,
  perceptual filtering down to 96kbits/s.
• The advantage of the adaptive embedder is that
  the watermark energy is spread non-uniformly
  over the perceptually significant values. Hence
  it should be possible to sustain a larger WSR
  without perception than a non-adaptive scheme.
  On the other hand, for good performance, the
  decoder must be able to reliably extract the
  informed parameter from the watermarked signal.
• The results indicate that the adaptive scheme
  outperforms the non-adaptive scheme on a frame
  size of 1024 samples, but on a frame size of 512
  samples, the non-adaptive scheme is better. This
  can be attributed to a loss of accuracy in the
  psychoacoustic model at this frame size.
• In future work it should be possible to increase
  the embedding bit rate by embedding more than one
  bit in each critical band.

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Dither Quantisation

• The chaotic map is digitised to m levels and
  centred at mean0. Hence, it takes integer
  values
• It can be embedded in using an m-ary dither
  quantisation.

Dither Source Scaled Chaotic Map
Quantiser
Quantiser Step Size D
D/m
D