Analysis of blind data hiding using discrete cosine transform phase modulation

https://doi.org/10.1016/j.image.2006.11.005Get rights and content

Abstract

This paper presents an analysis for data embedding in two-dimensional signals based on DCT phase modulation. A communication system model for this data embedding scheme is developed. Closed form expressions for estimating the number of bits that can be embedded given a specific distortion measure and the probability of bit error are developed. The data embedding process is viewed as transmitting data through a binary symmetric channel with crossover error probabilities, which depends only on the power in the selected coefficients and the noise created by the signal processing operations undergone by the image.

Introduction

Data hiding is the process of secretly embedding information into multimedia sources such as image, video, or audio signals without changing the perceptual quality of the host signal [9], [6]. In the last decade, there has been rapid development in the field of data hiding and its applications in multimedia communications. The major thrust of this research has been concentrated in the field of digital watermarking, which is a promising technique used for copyright protection against piracy and authentication of digital data sources.

In recent years, there has been an emphasis toward establishing a mathematical foundation for data hiding theory. Despite the variation in the requirements of data hiding systems which are application dependent, researchers have made a major advancement in establishing a general framework for analyzing data hiding systems. The theory reached a fair level of maturity toward establishing a strong mathematical foundation which most techniques build upon [12], [7], [2], [3], [4], [24], [8], [17], [16]. The vast majority of theoretical results developed for data hiding in images are based on techniques which use amplitude modulation or signal quantization to insert the data. Very little work has been done based on embedding the data in the phase of image transforms [21], [1], and no theoretical analysis has been proposed for data hiding based on image phase modulation.

The goal of this paper is to present a mathematical analysis for blind data hiding technique based on phase modulation of discrete cosine transforms (DCT). Due to the limited size of the paper, we only present a first order communication model for this data embedding system. Based on this model, we develop expressions for estimating the number of bits that can be embedded in an image, also known in the data hiding literature as the data embedding capacity. We also present expressions for evaluating the bit error rate (BER) based on certain constraints. Tradeoffs between the number of bits that can be embedded and robustness, given some level of perceptual distortion and fidelity such as the BER, are analyzed.

This paper is organized as follows. In Section 2, we describe the data embedding process for the proposed system. Section 3 presents an analysis of the system; a mathematical model for its data embedding capacity is also presented. In Section 4, an expression for estimating the BER for the proposed system is developed. Section 5 gives the conclusion and some suggestions for future work.

Section snippets

Embedding system

In this paper, the concept of embedding information in image transform domain using phase modulation of real transforms is introduced. In image processing, it is known that preserving image phase is particularly important for preserving its perceptual quality [10]. For example, Fig. 2a shows the Lenna image when retaining only phase information, while Fig. 2b shows the same image when retaining magnitude information and removing phase information. The two images indicate clearly the importance

System analysis and modeling

In this section we develop a simplified mathematical analysis for the proposed data hiding system. Given some data embedding subspace E1RL, we model the selected coefficients for data embedding as a sequence of L independent identically distributed (i.i.d.) random variables drawn from some random source X. Each selected coefficient Xi has a magnitude and a sign associated with it. The magnitude of each transform coefficient represents the square root of the energy in the selected coefficient,

Analysis of probability of bit error

This section presents an analysis of the merits of phase modulation data embedding system based on evaluating the BER. From previous analysis, the DCT coefficients were closely modeled with Laplacian pdf. The noise is modeled with Gaussian pdf. When a key K selects a group of coefficients their magnitude is known. Hence, the ith received coefficient Yi=X˜i+Ni consists of two parts: one deterministic which is the magnitude of X˜i, and the other is random Ni. Suppose that we want to embed the

Conclusion

This paper presents a non-additive blind data embedding technique, based on phase modulation of randomly selected coefficients, chosen from a subset taken from global DCT. A first order analysis to estimate the number of bits that can be embedded (capacity) in an image under JPEG compression is presented. Two approaches were used to estimate the capacity. The first is based on operational definition of channel capacity and the second is based on the theoretical definition of channel capacity.

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