News & Events

Set Theoretic Framework for Multimedia Security and Data Hiding: Applications to Watermarking, Steganography, Fingerprinting and Beyond

Huseyin Oktay Altun

Prof. Mark Bocko

Goergen 109

Abstract

The digital revolution is affecting our daily activities, changing our habits and indeed reshaping cultures around the world. The intellectual products of today are now primarily created and distributed in digital format. Furthermore, the Internet has become a pervasive communication and sharing network. All of these factors naturally have led to concerns over the security of digital information. Among the many proposed solutions to such concerns, digital watermarking has proven to be unique by its not requiring a safe auxiliary communication channel. However, proposed watermarking techniques and attacks against such methods make the watermarking problem dynamic, complicated, and challenging. We show that several of the requirements in watermarking applications can be mapped onto convex constraints or can be closely approximated as convex constraints. These include watermark detectability, robustness to added noise, multiple watermark detectability, imperceptibility, robustness against lossy compression, robustness against low-pass filtering attacks, robustness against non-linear soft/hard wavelet shrinkage denoising attacks, and fragility under aggressive compression. This approach allows determination of feasible solutions by using the powerful method of projections onto convex sets (POCS). The POCS algorithm is employed to find an image that satisfies all requirements simultaneously. We further extend the POCS formulation of watermark design into constrained optimization formulations where a single performance criterion may need to be optimized. We propose an algorithmic framework for solving these optimal embedding problems via a multi-step feasibility approach that combines projections onto convex sets (POCS) based feasibility watermarking with a bisection parameter search for determining the optimum value of the objective function and the optimum watermarked image. The framework is general and can handle optimum watermark embedding problems with convex and quasi-convex formulations of constraints and furthermore the algorithm has assured convergence to the global optimum. The proposed scheme is a natural extension of set-theoretic watermark design and provides a link between convex feasibility and optimization formulations for watermark embedding. We demonstrate a number of optimal watermark embeddings in the proposed framework corresponding to maximal robustness to additive noise, maximal robustness to compression, minimal frequency weighted perceptual distortion, and minimal texture watermark visibility. Experimental results demonstrate that the framework is effective in optimizing the desired characteristic while meeting the constraints. The results also highlight both anticipated and unanticipated competition between the common requirements for watermark embedding. Utilizing the same framework, we pose the problem of determining a steganographic image as a feasibility problem subject to constraints of data communication, imperceptibility, and statistical indistinguishability with respect to the steganalyzer's features. A stego image is then determined using set theoretic feasible point estimation methods. The proposed framework is applied to a state of the art steganalysis method based on higher order statistics (HOS) steganalysis. We show that the steganographer can significantly reduce the classification performance of the steganalyzer by employing a statistical constraint during embedding, although the image is highly distorted. Then we show that the steganalyzer can develop a counter-strategy against the steganographer's actions to gain back some classification performance. This interchange represents an empirical iteration in the game between the steganographer and steganalyzer. Finally, we consider mixture strategies to find the Nash equilibrium of the interplay. The framework is general and suits many other important multimedia design problems such as fingerprinting, multiple watermark embedding, fractional Fourier transform domain watermark embedding, and improved embedding efficiency for pre-coding. We describe a set theoretic formulation of some of these problems as well. The set theoretic approach in watermarking design is systematic, flexible, and it has desirable properties that are hard to replicate in other methods. Specifically, it enables many requirements defined in various transform domains to be handled simultaneously, and it offers great flexibility of the design formulation.