Reversible data hiding for high quality images using modification of prediction errors

Abstract

In this paper, a reversible data hiding scheme based on modification of prediction errors (MPE) is proposed. For the existing histogram-shifting based reversible data hiding techniques, though the distortion caused by embedding is low, the embedding capacity is limited by the frequency of the most frequent pixel. To remedy this problem, the proposed method modifies the histogram of prediction errors to prepare vacant positions for data embedding. The PSNR of the stego image produced by MPE is guaranteed to be above 48 dB, while the embedding capacity is, on average, almost five times higher than that of the well-known Ni et al. techniques with the same PSNR. Besides, MPE not only has the capability to control the capacity-PSNR, where fewer data bits need less error modification, but also can be applied to images with flat histogram. Experimental results indicate that MPE, which innovatively exploits the modification of prediction errors, outperforms the prior works not only in terms of larger payload, but also in terms of stego image quality.

Introduction

During transmission, if the digital media itself shows artifact of hiding effect, the intentional opponent may doubt the digital media carries secret messages. Therefore, an embedded digital should maintain an imperceptible quality to keep the embedded media from drawing attention (Wang et al., 2008). In general, the major concerns of data hiding techniques are the embedding capacity and imperceptibility. These two concerns are different from the techniques of digital watermarking. The purpose of digital watermarking is to protect the ownership of a digital media. Since a digital media is easily tampered or modified, a watermarking technique must be designed to have the capability against some common signal processing operations such as noise or lossy compression. The retrieved watermarks may not be exactly the same as the original ones; however, the ownership can still be verified according to the retrieved watermarks. On the other hand, a data hiding technique must extract embedded data without losing any bit. Therefore, the requirements of the robustness against common signal processing operations, or the ability to prevent bit errors occurring during storage and transmission, are not as emphasized as in digital watermarking technique (Yu et al., 2007, Wang and Wang, 2004).

Any existing digital media such as audios, videos, and digital images can be used as carriers. The digital image is often used as carrier since it is delivered the most over the Internet. It is important that the image with embedded data should not arouse any suspicious. The image for carrying data is called a cover image, and the image carrying the embedded information is called a stego image. When the information is embedded into images, the pixel values in the image will be changed, and thus the image quality is degraded. Since the altered pixels cannot be recovered into their original state after the secret messages has been extracted, permanent distortion will occur. Distortion for some applications is unacceptable. For example, a distorted chest X-ray image could result in an incorrect medical diagnosis. In these applications, techniques for reversible data hiding are necessary.

Reversible data hiding is a technique that not only embeds data into cover images, but also restores the original images from the stego images after the embedded data have been extracted (Alattar, 2004). Since the original cover image must be recovered after extracting the secret message, this requirement imposed on reversible data hiding technique a penalty of lower payloads, larger distortion and higher computational cost-in comparison to those non-reversible techniques. Despite these drawbacks, the number of reversible data hiding techniques proposed in literature has increased recently; suggesting the increasing needs in this field. The reversible data hiding technique developed at the early stage mainly relies on lossless compression technique. In 2002, Fridrich et al. proposed an R–S scheme for which compressed message bits were reversibly embedded in the status of group of pixels (Fridrich et al., 2002). Gelik et al. devised a generalized least significant bit (G-LSB) technique to increase the payload of Fridrich et al. method (Celik et al., 2002). Awrangjeb and Kankanhalli proposed a reversible scheme that embedded compressed data into the original image with the consideration of the human visual system to minimize the perceptible artifacts (Awrangjeb et al., 2005). The methods mentioned above involved approaches that embedded losslessly compressed features extracted from the original cover image.

The other type of reversible data hiding methods can be categorized as expansion–embedding based techniques. A common feature of these techniques is using a decorrelation operator to create features with small magnitudes. Data can be embedded by expanding these features to create vacant space into which message bits are embedded. The first approach under this category was proposed by Tian (Tian, 2003), and extended by many recent researches (Alattar, 2004, Kamstra and Heijmans, 2005, Thodi and Rodriguez, 2007, Kim et al., 2008). Expansion embedding based approaches usually suffer from undesirable distortion when the values of features are large. Therefore, this method might not be suitable for applications where higher image quality is demanded. Another category of reversible data hiding can be classified as histogram-shifting based techniques. In these techniques, a histogram of feature elements is created, and data can be embedded by shifting histogram bins. The well-known technique proposed by Ni et al. in 2006 is of this category (Ni et al., 2006). Some other histogram-shifting based reversible data hiding techniques can be found in Hwang et al., 2006, Fallahpour and Sedaaghi, 2007. Unfortunately, the capacity of histogram-shifting based techniques is low and highly dependent on the histogram distribution of the cover image. In general, the higher the peak of image histogram, the more the embedding capacity is. In addition to the techniques mentioned above, Coltuc introduced a very different approach to reversibly embedded data based on simple transforms with low mathematical complexity (Coltuc, 2007). These emerging remarkable reversible techniques suggested the increasing attention of the reversible data hiding techniques have been receiving.

Many applications demand high quality images, such as medical or military images. The well-known reversible data hiding method proposed by Ni et al. can produce relatively high quality stego image (⩾48.13 dB); however, the embedding capacity is low and is limited by the distribution of image histogram. Several studies were based on Ni et al.’s method and were either trying to enhance the image quality further or to increase the embedding capacity (Hwang et al., 2006, Fallahpour and Sedaaghi, 2007, Xuan et al., 2007). For example, Xuan et al. proposed a novel optimum histogram pair based reversible data hiding technique using integer wavelet transform and adaptive histogram modification with excellent performance (Xuan et al., 2007). However, their method involved integer wavelet transform (IWT) and optimal parameters selection, the computational cost is higher than Ni et al. method.

In this paper, we proposed a new reversible data hiding technique based on modification of prediction errors (MPE). Since the histograms in the domain of prediction errors are sharply distributed, the embedding capacity is higher than that of traditional histogram-shifting method for the same image quality. Besides, MPE only modifies less error values for embedding fewer data bits; therefore, a high quality stego image can be obtained.

Detailed advantages of MPE over Ni et al. method will be discussed in Section 4. The rest of this paper is organized as follows. In Section 2, Ni et al.’s histogram-shifting technique for reversible data hiding will be described. The MED predictor and the proposed method are presented in Section 3, followed by the experimental results in Section 4. Conclusions from the experimental results are addressed in Section 5.