Abstract
Ownership identification makes the digital watermarking technology important today. In this thesis, a communication model is proposed to deal with the digital watermarking problem in the frequency domain, which is also suitable for other watermarking methods. A new frequency-hopping spread spectrum (FH-SS) watermarking method is proposed in this thesis. The watermarks generated by this approach are unobservable and robust. To analyze the method, we model the noise sources and the associated detectors. Information capacity based on the noise model can then be estimated. Experiments for embedding watermarks on a standard 512x512 intensity image have been conducted. The simulation results of this method indicate a lower mark error rate (at least 10 %lower) than those of other methods. The other contribution of this study is the systematic analysis to the estimation of performance measurements and the information capacity. The digital watermarking technology plays an important role to protect the copyright. For example, the watermark detector can distinguish who is the illegal owners. Some software will not allow the illegal users to process the digital media without canceling the watermarks. To achieve the ownership protection, there are some requisitions in this technology. First, the watermarks should be alive after image processing, like compression, masking, edge sharpening, and smoothing. To avoid some conscious attacks, the watermarks should be unobservable. The watermarks have to confront some geometric distortions, like copying, cropping, etc., or intentional attacks. A question of reliability \cite{Crav}\cite{Low} exists between the legal and illegal users if both of them need original media files to get the watermarks. Next, the technology should be universal. It means that the technology is suitable to all kinds of the digital media. Finally, a challenging research is to build the systematic framework based on information theory. The watermark adder can embed digital watermarks in two domains. One is the spatial domain, and the other is the frequency domain. The benefits of spatial domain methods is easy implementation without any transformation, simple modeling, and the information acquisition without the original media files, although some necessary information is required to get the watermarks. However, the watermarks in the spatial domain are usually easily demolished by image processing, geometric distortions, and unconscious destruction. Some filtering methods are used to avoid the weakness property, but it is still difficult to achieve the goal. Furthermore, the watermarking methods in the spatial domain offer fewer information capacity than those in the frequency domain. The algorithms in the frequency domain use fast Fourier transformation (FFT), discrete cosine transformation (DCT) or other transformations to the original image, and embed watermarks in the frequency domain. Methods in the frequency domain usually provide robust watermarks. It is difficult to model the watermarking processes in the frequency domain. Therefore, it is hard to predict the performance exactly after compressing, noise adding, and image processing. The watermark designers can only compare the result of each approach case by case. Moreover, the legal users usually need the original media files to obtain the watermarks in the frequency domain. We first give a survey of previous work of some image processing and watermarking studies. These will be described in Chapter 2. In \cite{Hern}, the watermarking problem was modeled as a data-hiding system, and yet problems like modeling the source encoder, the channel, and the decoder can not be solved in this system. Thus, a new model is presented in the chapter. In Chapter 3, we modify a method mentioned in Chapter 2, in which a binary sequence is encoded as watermarks. An easier decoding algorithm is also achieved by this approach. In Chapter 4, a new FH-SS watermarking system is proposed. This method provides watermarks that can be decoded with the original media file or without it. In Chapter 5, noise models are discussed. We can predict the performance as the noise models and the optimal threshold detectors are built. In Chapter 6, the channel capacity of the system will be estimated. An information theoretic analysis will be presented. Besides, it will give a new aspect to the capacity question, and the estimated capacity can be realized under some assumptions. In Chapter 7, experiments will be conducted in a the standard 512x512 image with 8-bit gray scale. Simulation results and theoretic calculations will then be discussed.