This thesis is principally concerned with investigating two alternative uses for pseudonoise sequences -- digital watermarking and time delay estimation.
After a review of the properties of pseudonoise sequences and what constitutes a pseudonoise sequence, a number of different sequences with pseudonoise and pseudonoise-like properties are described. A number of methods of constructing multidimensional arrays using these sequences are also shown. The constructed arrays are then used to create a number of different types of digital watermark.
Digital watermarking involves embedding a secret message or image within a `cover' image, such that the secret message cannot be seen. This requires the secret message to be embedded subtly and with low power. Pseudonoise sequences can be used to encode message data such that the resultant information can be `spread very thinly' over the cover image. It is this `holographic' spreading of the message over the image that give pseudonoise sequences such power in this application. A number of specific watermarks are described. One such linear watermark has the property that multiple watermarks of the same type can be embedded in an image. A second type of nonlinear angle based watermark will interfere destructively when an attempt is made to embed another watermark of the same type into the host data. A third watermark is designed such that its presence can be detected with this detection process revealing very little about the nature of the watermark.
Time-delay estimation, in the context of this thesis, involves sending a `probe' signal into unknown linear and some non-linear time-invariant `black-box' systems and observing the delay of the signal and any harmonics created by this system. The `system' can be an electronic, communications or some other physical system. The method of probing such a system may involve electromagnetic or acoustic sources. Pseudonoise sequences are useful for this purpose because a carrier signal with an embedded sequence can be designed to interact minimally with harmonics of the carrier. Such sequences are not restricted to being binary when used to phase-modulate a sinusoidal carrier, so the effect on the phase modulation of each of the harmonics is used to extract each harmonic response individually. Moreover, by phase modulating a non-sinusoidal carrier with a pseudonoise sequence, it is shown how requiring a separate correlation for each order of response can be reduced to requiring 1 or 2 correlations to obtain the delay for all orders of response. These techniques thus provide a useful analysis tool for probing unknown systems.
The central aim of this thesis is thus to show a number of ways that the properties of pseudonoise sequences in both applications can be best employed for optimal signal embedding and extraction. These properties are similar in both cases as are the measurement requirements imposed.
Front matter (ps.gz) (150kB - 20 pages)
Contents
Abstract
Declaration
Acknowledgements
List of Figures
List of Tables
Glossary
1 Introduction (ps.gz) (179kB - 14 pages)
1.1 Using PN sequences for Digital Watermarking
1.2 Using PN Sequences for Time Delay Estimation
1.2.1 System Identification
1.2.2 Time Delay Estimation
1.2.3 Our Approach to Time Delay Estimation
1.3 Thesis Overview and Contributions
2 Pseudonoise Sequences and Arrays (ps.gz) (288kB - 32 pages)
2.1 Introduction
2.2 Preliminaries
2.2.1 What is Random?
2.2.2 Complex Sequences
2.2.3 Common Properties of All Pseudonoise Sequences
2.3 1D Seed Sequences
2.3.1 The Generalised M Sequence
2.3.2 The Generalised Legendre Sequence
2.3.3 The Generalised Chirp-like Polyphase Sequence
2.3.4 The Cyclic All-Pass Sequence
2.4 2D Array Constructions
2.4.1 Why Use Higher Dimensional Arrays
2.4.2 Review of some 2D Constructions
2.4.3 Perfect Arrays
2.4.4 Product Arrays
2.4.5 Folding Arrays
2.4.6 Distinct Sums Arrays
2.5 Information Embedding in Sequences and Arrays
2.5.1 1D Sequence Capacity
2.5.2 2D Array Capacity
2.5.3 Sequence Recovery
2.6 Summary of Sequence and Array Constructions
3 Using PN Sequences for Linear Watermarking (ps.gz) (457kB - 20 pages)
3.1 Introduction
3.2 Watermarking Digital Data
3.2.1 Digital Watermarking using PN sequences
3.2.2 Measures of Distortion
3.3 Multiple Watermarks with Minimal Mutual Interaction
3.3.1 Results using Multiple DSA Watermarks
3.4 Public or Asymmetric Digital Watermarking
3.4.1 Legendre Sequences and Fourier Invariance
3.4.2 Results for the Legendre Public Watermark
3.4.3 Generalisation of the Technique
3.5 Summary
4 Data Hiding in the Angle Domain (ps.gz) (1.2MB - 46 pages)
4.1 Introduction
4.2 Deriving Complex Values from Images
4.2.1 The Vector Models
4.2.2 Comparing the Vector Models
4.3 Watermark Embedding in the Angle Domain
4.4 Optimising the Angle Watermark
4.4.1 Estimating θo Without the Original Image
4.4.2 Using a Spatially Varying Scale Factor
4.5 Watermark Embedding using Angle Quantisation
4.6 Implementation of Angle Watermarking
4.6.1 Colour Images
4.6.2 Images in a Transform Domain
4.7 Experiments
4.7.1 Angle Quantisation Effects
4.7.2 Pixel Quantisation Effects
4.7.3 Angle Decoding Using Soft and Hard Decision Boundaries
4.7.4 Number of Quantisation Levels
4.7.5 Choice of Sequence / Array
4.7.6 Effect of Mismatched Scale Factor
4.7.7 Angle-Preserving Quantisation
4.7.8 Effects of Lossy Compression on Angle Recovery
4.8 Attacks on the Angle Quantisation Mechanism
4.9 Summary and Further Work
5 Time Delay Estimation for Non-linear Systems (ps.gz) (970kB - 24 pages)
5.1 Introduction
5.2 The Measurement Model
5.2.1 Phase Encoding the Probe Signal
5.2.2 Control of Bandwidth
5.3 Higher-Order Signal Characterisation
5.4 Using Non-Sinusoidal Carriers
5.5 The Test System Implementation
5.6 Summary and Discussion
6 Conclusions (ps.gz) (140kB - 6 pages)
6.1 Summary and Discussion
6.2 Conclusion and Future Directions
A PDF Calculation for the Image Vector Models (ps.gz) (218kB - 7 pages)
A.1 Uniformly Distributed Pixels
A.2 Gaussian Distributed p1 and p2
B Publications Arising from this Thesis (ps.gz) (1.3MB - 26 pages)
B.1 Secure Arrays for Digital Watermarking
B.2 Delay Recovery from a Non-Linear Polynomial-Response System
B.3 Key Independent Watermark Detection
B.4 Discrete Angle Watermark Encoding and Recovery
B.5 Using Phase-Modulated Probe Signals to Recover Delays from Higher Order Non-linear Systems
C Angle Quantisation Watermarked Images (ps.gz) (404kB - 4 pages)
R References (ps.gz) (155kB - 15 pages)
I Index