Data hiding for vector quantization images using mixed-base notation and dissimilar patterns without loss of fidelity

Abstract

Data hiding without loss of fidelity (also called reversible data hiding) allows an original image to be restored completely after extraction of hidden data embedded in a cover image. In this paper, we propose a reversible scheme based on mixed base notation and dissimilar pattern strategies for vector quantization (VQ) compressed images. The dissimilar patterns resulting from the declustering process make the proposed hiding method more efficient. Our experimental results show that the time required for the embedding process in the proposed method is much less than that in the side-matched VQ (SMVQ)-based reversible method. In addition, the use of declustering can reduce many more prediction errors than traditional clustering methods. The results also show that the number of declustered groups and the spatial characteristics of the cover image will affect the embedding capacity and the size of the stego VQ index table.

Introduction

Data hiding is the technique of embedding information into a cover digital object such as an image, audio, or video file. It is very useful for information security and authentication since more and more data are transmitted over the Internet. So far, some data hiding methods have been developed, but lose in fidelity [4], [9], [15], [18], [24]; that is, the original digital content cannot be restored completely after data extraction. In some applications, the distortion may be a troublesome problem when the original digital content needs to be used again. Intuitively, data hiding methods without loss of fidelity, also called reversible data hiding methods, are more suitable for these applications.

In the early development of reversible embedding methods, they were proposed for spatially uncompressed images. Some methods are made feasible by adopting the compression concept regarding the original data in order to accommodate the secret data. For example, Fridrich et al. [6] compressed one of the least-significant-bit (LSB) planes of a cover image in order to append the secret data. Later, Celik et al. [3] proposed another reversible hiding scheme that quantizes pixel values and then compresses the residuals by means of arithmetic coding. In addition, some reversible embedding schemes are based on histogram-shifting. For example, De Vleeschouwer et al. [23] applied a patchwork algorithm and the rotation of circular histogram to achieve reversible watermarking. After that, Ni et al. [17] proposed a reversible data hiding scheme by first finding the peak and zero points of the cover image histogram and then shifting all pixels between peak and zero points to vacate the spaces for hiding secret data. Recently, some schemes apply the difference-expansion for reversible embedding. The first difference-expansion scheme was developed by Tian [19], whose method was to partition the cover image into nonoverlapping pairs of pixels and to categorize these pairs into three groups: changeable, expandable, and exceptional. Then, a location map is created in order to record the categorized information. Finally, both the location map and the secret data are embedded into the cover image. Nowadays, both histogram-shifting and difference-expansion are well-known methods for reversible embedding; therefore, many variants have been developed in the past few years [1], [16], [20], [21].

Recently, some researches focused on embedding secret data in the compression domain because the digital images in compressed format can not only conceal secret data but also shorten transmission time on the Internet and take up less storage space. However, unlike spatially uncompressed images, compressed images, such as those obtained using the VQ or JPEG algorithms, are more difficult for data hiding. VQ (vector quantization) [7] is a block-based compression method in the spatial domain. VQ has many advantages, including simple framework, easy implementation, and high efficiency of encoding and decoding processes. Owing to these advantages, many hiding methods are developed for VQ compressed images. Several recent studies based on using VQ compressed images have investigated the possibility of irreversible watermarking [2], [8], [11], [12], [13], [15], [22]. For example, Lin and Wang proposed an LSB-like watermarking method for VQ compressed images [13]. They relied on a pairwise nearest clustering embedding (PNCE) method to divide a codebook into two sub-codebooks with equal size, G₀ and G₁, so that each pair of codewords between G₀ and G₁ is as similar as possible. During embedding, if the image block is originally encoded by the ith codeword of G₀ and the secret bit is “1”, the image block is replaced with the ith codeword of G₁; similarly, if the image block is originally encoded by the ith codeword of G₁ and the secret bit is “0”, the image block is replaced with the ith codeword of G₀. The strategy of such replacement causes little distortion since each pair of codewords is similar to each other. Later, Lu and Sun [15] and Jo and Kim [8] improved Lin and Wang’s method for increasing the embedding capacity and enhancing the image quality. Unfortunately, these aforementioned methods still have a drawback that they encourage more serious distortion in the decompressed image due to irreversible data hiding action.

As for reversible embedding methods for VQ compressed images, in 2006, Chang et al. [5] proposed a reversible scheme for SMVQ (side-match VQ) [10] compressed images. This method restores the image with the SMVQ quality rather than with the VQ quality to make reversibility feasible. In this paper, we propose an alternative reversible embedding scheme for VQ compressed images based on the concepts of mixed base notation and dissimilar patterns. The dissimilar patterns result from the proposed hierarchical declustering approach that puts dissimilar codewords together, which is the opposite of traditional clustering. This strategy makes reversible embedding feasible and requires no location map. The output of the declustering phase also can be used to increase the efficiency of the embedding and extraction processes. In addition, the proposed scheme cannot only completely recover the original VQ image but also provide high-payload additional information to the above real-time applications or low-computational devices.

The remainder of this paper is organized as follows. In Section 2, we briefly review previous research in this field. In Section 3, we present our new reversible embedding scheme for VQ images. Empirical results are discussed in Section 4, and some conclusions are presented in Section 5.