# Efficient Reversible Data Hiding Scheme for AMBTC-Compressed Images
## 1 Introduction  
Data hiding is an important technique by which a secret message is protected by being embedded into a cover image. Data hiding can be classified into two types of schemes, i.e., irreversible and reversible. One essential property of irreversible data hiding schemes is high embedding capacity [1, 2]. However, they distort the cover image significantly. Moreover, this visual quality cannot be reconstructed after secret message extraction. Therefore, this type cannot be used in some special applications, i.e., military and medicine, in which a cover image is required to be restored to its original version. To solve this problem, reversible data hiding schemes [3, 4, 5, 6, 7] are a promising solution for these applications because the schemes can recover the original version of cover images without any distortion after the secret message was extracted. Recently, many data hiding schemes for compressed images have been proposed to save the bandwidth space of the embedding image. This is because the size of the compressed image is much smaller than that of the original image, regardless of whether the secret message has been embedded. Some compression techniques, i.e., JPEG [8, 9], vector quantization (VQ) [10, 11, 12], and block truncation coding (BTC) [13, 14, 15, 16, 17, 18, 19, 20], are applied for data hiding to achieve high embedding capacity while maintaining a low bit rate. In the literature, various data hiding schemes [13, 14, 15, 16, 17, 18, 19, 20] have been proposed for BTC-compressed images. In 2004, [PERSON] and [PERSON] [13] introduced a data hiding scheme based on LSB replacement for BTC-compressed images. This scheme obtained a small distortion of a stego image. To improve the visual quality of the stego image, in 2006, [PERSON] and [PERSON] [14] used smooth regions of the bitmap table in a BTC-compressed image to contain a secret message. However, this scheme is irreversible, meaning that the original BTC-compressed image cannot be recovered after the secret message was extracted. In 2008,Chang et al. [15] proposed a reversible data hiding scheme based on the order of mean values to embed a secret message into BTC-compressed images. Moreover, in 2008, [PERSON] et al. [16] proposed a new reversible data hiding scheme for BTC-compressed images that toggled or preserved the BTC bitmap table to hide the secret bits. In addition, in [PERSON] et al. 's scheme, the relationship between the high mean value and low mean value is used for embedding data. However, when two mean values are the same, the extracted bits will contain errors. To overcome the weakness in [PERSON] et al. 's scheme, [PERSON] et al. [17] proposed an improved reversible data hiding scheme for BTC-compressed images. In this scheme, the difference value of the high mean value and low mean value is calculated and used to determine whether only one secret bit is embedded into the block or more secret bits are embedded into the bitmap table of the block by toggling. In 2011, [PERSON] et al. [18] proposed a reversible data hiding scheme for BTC-compressed images by using bitmap flipping and histogram shifting for high mean values and low mean values. However, [PERSON] et al. 's scheme obtained low embedding capacity when, on average, only one secret bit is embedded into each image block. To further improve embedding capacity, in 2013, [PERSON] et al. [19] proposed a new reversible data hiding scheme based on the joint neighbor coding algorithm (JNC) to embed a secret message into BTC-compressed images. This scheme can obtain a high embedding capacity, which is four times larger than that of [PERSON] et al.' scheme [18]. However, the efficiency rate of this scheme is still low. Later, in 2017, [PERSON] et al. adopted a median edge detection (MED) predictor to predict the quantization values of blocks first. Next, they further designed a centralization error division (CED) technique to modify the classification rule and ensure all zero prediction errors can be categorized into a new division and no more bits are required.