# High Imperceptible Data Hiding Method Based on Combination Theory for AMBTC Compressed Images
## 1 Introduction  
A massive storm of large-scale data has come from the accelerated development of digital multimedia. Various applications produce images, audio, and videos daily. The security of critical data and the gigantic volume of data are the two major issues this trend has brought forth. To enhance the confidentiality of data transmission, the sender encrypts the data using conventional cryptographic techniques or imperceptibly transfers data using data-hiding techniques [1, 2, 3]. At the same time, the best way to minimize the data size and lower transmission costs is to use a data compression technique [4]. Inevitably, data-hiding research in the compression domain presents a immense challenge to academics because it is essential to balance the hiding capacity with compressed image quality. Data hiding is defined as an imperceptible method of hiding confidential data inside other media i.e., digital images, videos, and audio. An image-data-hiding scheme can be categorized into three domains [5] namely the spatial domain, the frequency domain, and the compressed domain. In order to embed confidential data, the spatial domain method directly modifies the image pixel [6, 7, 8]. It causes low imperceptibility. On the other side, the frequency domain method hides the confidential data into transformed coefficients. Lastly, the compressed domain method manages the confidential messages in the compressed codes of digital images. Both the frequency domain and the compressed domain perform better imperceptibility than the spatial domain. In general, two metrics are used to assess the performance of a data-hiding technique. The first is hiding capacity. Hiding capacity is identified as the quantity of confidential data concealed in a cover media. The second metric is imperceptibility. Imperceptibility is defined as the level of image quality after modification. The primary issue in data-hiding research is that the higher the hiding capacity, the lower the imperceptibility. Along with the big data age, where the volume and variety of data are abundant, compression technology is experiencing advancements. Data compression technology is efficient in data transmission. This is due to the fact that computing is simple and inexpensive. There are several widely used compression methods, including vector quantization (VQ) [9; 10; 11; 12], block truncation coding (BTC) [13; 14; 15; 16], AMBTC [17; 18], and JPEG compression [19; 20; 21], beginning with [PERSON] and [PERSON] [13] in 1979, who proposed block truncation coding (BTC) for image compression, and then further developed in 1984 by [PERSON] and [PERSON] [17], whose method is known as absolute moment block truncation coding (AMBTC). AMBTC offers simpler computation than BTC and acquires better image quality. Due to the benefits of the compression technique, data-hiding research is evolving into compression domain data hiding. Researchers have used the AMBTC compressed image-data-hiding method [22; 23; 24; 25; 26; 27; 28; 29; 30; 31]. In 2020, [PERSON] et al. published a data-hiding scheme for AMBTC compressed images utilizing quotient value differencing (QVD) and least significant bit (LSB) replacement [23]. In the same year, [PERSON] et al. [22] presented a reversible data-hiding method based on Turtle Shell for AMBTC-compressed images. The following year, in 2021, [PERSON] et al. [23] proposed a data-hiding scheme that employs the difference value of higher and lower quantizers. The three methods are block classification based on data hiding. After performing AMBTC encoding, this method divides the sub-blocks into smooth or complex ones based on a pre-defined threshold. Complex blocks are non-embedding blocks that cannot embed the secret bits. Otherwise, smooth blocks are defined as embeddable blocks in which a certain number of secret bits can be embedded. These methods provide lower computation complexity and achieved accepted image quality. Moreover, these methods benefit smooth images because they achieve higher embedding capacity.