Digital watermarking is a key ingredient to copyright protection. It provides a solution to illegal copying of digital material and has many other useful applications such as broadcast monitoring and the recording of electronic transactions. Now, for the first time, there is a book that focuses exclusively on this exciting technology. Digital Watermarking covers the crucial research findings in the field: it explains the principles underlying digital watermarking technologies, describes the requirements that have given rise to them, and discusses the diverse ends to which these technologies are being applied. As a result, additional groundwork is laid for future developments in this field, helping the reader understand and anticipate new approaches and applications.

Digital Watermarking

Reversible data embedding has drawn lots of interest recently Being reversible, the original digital content can be completely restored We present a novel reversible data-embedding method for digital images We explore the redundancy in digital images to achieve very high embedding capacity, and keep the distortion low

Reversible data embedding using a difference expansion

This article is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is well-known to algebraists (and expressed by the formulaSL(n;R[z, z−1])=E(n;R[z, z−1])); it is also used in linear systems theory in the electrical engineering community. We present here a self-contained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering. This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the biorthogonal, i.e., non-unitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a wavelet-like transform that maps integers to integers.

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Factoring wavelet transforms into lifting steps

1 Introduction to Wavelets 2 A Multiresolution Formulation of Wavelet Systems 3 Filter Banks and the Discrete Wavelet Transform 4 Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases 5 The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients 6 Regularity, Moments, and Wavelet System Design 7 Generalizations of the Basic Multiresolution Wavelet System 8 Filter Banks and Transmultiplexers 9 Calculation of the Discrete Wavelet Transform 10 Wavelet-Based Signal Processing and Applications 11 Summary Overview 12 References Bibliography Appendix A Derivations for Chapter 5 on Scaling Functions Appendix B Derivations for Section on Properties Appendix C Matlab Programs Index

Introduction to Wavelets and Wavelet Transforms: A Primer

A novel reversible data hiding algorithm, which can recover the original image without any distortion from the marked image after the hidden data have been extracted, is presented in this paper. This algorithm utilizes the zero or the minimum points of the histogram of an image and slightly modifies the pixel grayscale values to embed data into the image. It can embed more data than many of the existing reversible data hiding algorithms. It is proved analytically and shown experimentally that the peak signal-to-noise ratio (PSNR) of the marked image generated by this method versus the original image is guaranteed to be above 48 dB. This lower bound of PSNR is much higher than that of all reversible data hiding techniques reported in the literature. The computational complexity of our proposed technique is low and the execution time is short. The algorithm has been successfully applied to a wide range of images, including commonly used images, medical images, texture images, aerial images and all of the 1096 images in CorelDraw database. Experimental results and performance comparison with other reversible data hiding schemes are presented to demonstrate the validity of the proposed algorithm.

Reversible data hiding

In the digital information age, digital content (audio, image, and video) can be easily copied, manipulated, and distributed. Copyright protection and content authentication of digital content has become an urgent problem to content owners and distributors. Digital watermarking has provided a valuable solution to this problem. Based on its application scenario, most digital watermarking methods can be divided into two categories: robust watermarking and fragile watermarking. As a special subset of fragile watermark, reversible watermark (which is also called lossless watermark, invertible watermark, erasable watermark) enables the recovery of the original, unwatermarked content after the watermarked content has been detected to be authentic. Such reversibility to get back unwatermarked content is highly desired in sensitive imagery, such as military data and medical data. In this paper we present a reversible watermarking method based on an integer wavelet transform. We look into the binary representation of each wavelet coefficient and embed an extra bit to expandable wavelet coefficient. The location map of all expanded coefficients will be coded by JBIG2 compression and these coefficient values will be losslessly compressed by arithmetic coding. Besides these two compressed bit streams, an SHA-256 hash of the original image will also be embedded for authentication purpose.

https://www.digimarc.com/docs/default-source/technology-resources/published-technical-papers/reversible-techniques/dmrc_wavelet_reversible.pdf

Wavelet-based reversible watermarking for authentication

A watermark embedder transforms a media signal from its perceptual domain to frequency domain regions and embeds a hash of data from one frequency domain region into a watermark in another frequency domain region. Alternatively, it encodes instances of the same message into the frequency domain regions. To detect alteration of the media signal, a watermark decoder transforms a suspect signal into the frequency domain regions, extracts the watermark message from a first frequency domain region and compares it with a reference derived from another frequency domain region. The reference signal is either a hash computed from the other frequency domain region of the watermarked signal, or another instance of the same message embedded into the other frequency domain region. The decoder can be used to detect alteration of the signal, such as alteration that occurs with reproduction (printing, scanning, copying, D/A-A/D conversion, etc.), compression, cropping or swapping of media signal content, etc.

Watermarking recursive hashes into frequency domain regions

We present an embedded image coding method, which basically consists of three steps, Discrete Wavelet Transform, Differential Coding, and Binary Reduction. Both J. Shapiro’s embedded zerotree wavelet algorithm, and A. Said and W. A. Pearlman’s codetree algorithm use spatial orientation tree structures to implicitly locate the significant wavelet transform coefficients. Here a direct approach to find the positions of these significant coefficients is presented. The encoding can be stopped at any point, which allows a target rate or distortion metric to be met exactly. The bits in the bit stream are generated in the order of importance, yielding a fully embedded code to successively approximate the original image source; thus it’s well suited for progressive image transmission. The decoder can also terminate the decoding at any point, and produce a lower (bit) rate reconstruction image. Our algorithm is very simple in its form (which will make the encoding and decoding very fast), requires no training of any kind or prior knowledge of image sources, and has a clear geometric structure. The image coding results of it are quite competitive with almost all previous reported image compression algorithms on standard test images.

Embedded Image Coding Using Wavelet Difference Reduction

Summary form only. We propose a new lossy image codec based on index coding. Both Shapiro's embedded zerotree wavelet algorithm, and Said and Pearlman's codetree algorithm use spatial orientation tree structures to implicitly locate the significant wavelet transform coefficients. A direct approach to find the positions of these significant coefficients is presented. The new algorithm combines the discrete wavelet transform, differential coding, variable-length coding of integers, ordered bit plane transmission, and adaptive arithmetic coding. The encoding can be stopped at any point, which allows a target rate or distortion metric to be met exactly. The bits in the bit stream are generated in the order of importance, yielding a fully embedded code to successively approximate the original image source; thus it is well suited for progressive image transmission. The decoder can also terminate the decoding at any point, and produce a lower bit rate reconstruction image. Our algorithm is very simple in its form (which will make the encoding and decoding very fast), requires no training of any bind or prior knowledge of image sources, and has a clear geometric structure. The image coding results of it are quite competitive with almost all previous reported image compression algorithms on standard test images.

Jun Tian

Papers

Reversible data embedding using a difference expansion

Wavelet-based reversible watermarking for authentication

Watermarking recursive hashes into frequency domain regions

Embedded Image Coding Using Wavelet Difference Reduction

A lossy image codec based on index coding