# Hybrid Data Hiding Based on AMBTC Using Enhanced Hamming Code
## 1 Introduction
For this reason, it seems many researchers are interested in DH based on Absolute Moment Block Truncation Coding (AMBTC) [25; 26; 27], originated from BTC recently. [PERSON] and [PERSON] [28] proposed a DH method based on AMBTC replacing the bitmaps of smooth blocks with the secret bits after dividing the blocks of an image into smooth blocks and complex blocks directly. It is called the Direct Bitmap Substitution (DBS) method. The merit of this method is that it may control the quality of the stego image by adjusting the threshold \(T(=b-a)\) because the number of blocks using DH is decided according to the threshold value \(T\). Here, \(a\) and \(b\) are quantization levels for each block in AMBTC. With the increase of the threshold \(T\), the embedding capacity will be increased, while the image quality will be worse. In the case of decreasing the threshold \(T\), the quality of the image will be improved, but the embedding capacity may be reduced. capacity of DH without significantly improving the image quality. [PERSON] et al. [32] proposed a lossless DH method using the order of two quantization levels in _trio_. This method is named the Order of Two Quantization Level (OTQL) method, which can conceal one bit per a block. For example, to store the bit \"1\", the order of two quantization levels, \(a\) and \(b\), is reversed as \(\textit{trio}(b,a,BM)\). This method does not change the coefficients of both quantization levels, so it does not affect the quality of the image. [PERSON] [33] proposed a DH using Pixel Pair Matching (PPM) [34], where PPM is applied to the quantization levels; while the existing OTQL and DBS are used together for complex and smooth blocks, respectively. In 2017, [PERSON] et al. [35] proposed a scheme for hiding data using pixel differences (hidden bits \(=log_{2}T\): derived from the difference expansion method) at two quantization levels and introduced a method to adjust the differences in the quantization levels to maintain image quality. This method is also a hybrid method by using OTQL and DBS as well. [PERSON] and [PERSON] [36] sub-divided less complex blocks and highly complex blocks. In 2016, [PERSON] et al. [37] introduced a DH based on AMBTC using a two bit plane and four quantization levels. The merit of this method is the high payload, and the demerit is the decrease in the compression rates. The motivations to propose a DH method using the Hamming code based on the image compressed with AMBTC are as follows. First, AMBTC is suitable for DH because it has reasonable compression performance, very low computational complexity, and (although not many) redundant bits. In addition, DH is relatively less studied for grayscale images. Second, the Hamming code is very efficient for redundant bits, such as for grayscale images. This has been demonstrated in previous studies [7; 10]. However, since the image compressed with AMBTC has fewer redundant bits than the grayscale image, the embedding of enough secret bits at two quantization levels results in a negative effect on the image in the decoding of the bitmap. Third, [PERSON] and [PERSON] [30] attempted to conceal data at two quantization levels, but this did not achieve optimized performance. Therefore, it is essential to develop an optimized method in the DH process. The main contributions of this paper are summarized as follows:  
1. We introduce a general framework for DH based on AMBTC with the minimal squared error by the optimal Hamming code using a Lookup Table (LUT). 2. Our method calculates the codeword corresponding to the minimum distance from the standard array of the (7,4) Hamming code table and then extracts the corresponding code. The method has little effect on program performance and can be easily conducted. 3. We provide a comparative analysis and evaluate the efficiency based on the specified criteria. 4. Sufficient experimental results are used to show the effectiveness and advantages of the proposed method. The rest of this paper is organized as follows. Section 2 gives the introduction of the background research.