## 1 Introduction  
People generally exchange information on the internet using a computer and smart phone, since it provides easy and rapid communication in recent years. Malicious people may monitor illegally, steal, and disrupt this information during the transmission, thus it is an important topic to preserve data security and integrity. We utilize common cryptography [1] and steganography [2] techniques to provide the data security and integrity. While the cryptography encrypts the secret data in such a way that it has puzzling data to third parties, the steganography hides secret data unobtrusively in various files such as text, audio, image and video. In data hiding studies, selecting image files to embed data is known as image steganography. Image Steganography consists of the cover image, secret data, data embedding algorithm and the stego image [3; 4; 5]. The cover image indicates the carrier media used to hide secret data, while the stego image represents the result media containing the secret data and cover image [4]. In the algorithm studies of image steganography, it is expected that the cover and stego images are highly similar and the high embedding capacity [6; 7]. Most studies in literature have focused only on retrieving secret data, not dealing with restoring the original image [8]. Steganography techniques involving such literature studies are called irreversible data hiding. In the techniques used in some literature studies, both the secret data and the original image must be recovered, which are called reversible data hiding (RDH) [9; 10]. RDH methods have been popular in recent years for many reasons, such as security, capacity, and reversibility [11; 12; 13]. The most widely used RDH techniques are the difference expansion [14; 15; 16], histogram shifting [17; 18; 19; 20], pixel value order [21], interpolation [22; 23; 24; 25; 26; 27; 28; 29], and dual image [30; 31; 32; 33; 34; 35; 36; 37; 38] based methods. The difference expansion method, known as the expansion of the difference between two non-overlapping pixels to hide a bit, was proposed by [PERSON] in 2003 [14]. The payload (0.5 bpp) and visual quality of the stego image are low in this method and have the fall of boundary problem. Due to its low computational complexity, it can be preferred reversible methods to hide a small amount of data. There are many studies in the literature to increase the visual quality and payload in the method. [PERSON] et al. (2011) offered an adaptive data concealing method that separates pixel complexities into rough and flat parts. In addition, this study decided on the embedded pixel estimation error and the amount of embedded secret data according to diverse classification results [15]. [PERSON] et al. (2014) developed the method of [PERSON] et al. (2011) by increasing the types of complexity to increase the embedding capacity of the prediction error [16]. The histogram shifting algorithm utilizes statistical techniques to create the histogram of pixel values or differences and embed the secret data at the highest value. [PERSON] et al. (2006) concealed the secret data into the most frequently repeated pixels using the histogram shifting technique [17]. [PERSON] et al. (2009) suggested a histogram-based approach. To improve data embedding capacity, secret data are hidden in the residual images after linear prediction and used the pairs of peaks and zero points for extra capacity [18]. In the method proposed by [PERSON] et al. (2011), firstly, they created positive and negative difference histograms by using pixel differences with a linear estimation method. Then, the blank columns are obtained because of the shifting process on these histograms. And finally, they have implemented data hiding by distributing a zero-center range to these blank columns [19]. [PERSON] et al.