Improved reversible data hiding in JPEG images based on new coefficient selection strategy
 Fisseha Teju Wedaj^{1},
 Suah Kim^{2},
 Hyoung Joong Kim^{2}Email author and
 Fangjun Huang^{3, 4}
https://doi.org/10.1186/s1364001702061
© The Author(s). 2017
Received: 16 February 2017
Accepted: 14 August 2017
Published: 6 September 2017
Abstract
Recently, reversible data hiding (RDH) techniques for JPEG images have become more extensively used to combine image and authentication information conveniently into one file. Although embedding data in JPEG image degrades visual quality and increases file size, it is proven to be useful for data communication and image authentication. In this paper, a data hiding method in JPEG image using a new coefficient selection technique is proposed. The proposed scheme embeds data using the histogram shifting (HS) method. According to the number of zero AC coefficients, block ordering is used to embed data first in the blocks causing less distortion. In order to further reduce the distortion, positions of AC coefficients are selected carefully. Finally, AC coefficients valued +1 and −1 are used for embedding, and the remaining nonzero AC coefficients are shifted to the left or right directions according to their sign. Compared to the current stateoftheart method, experimental results show that the proposed method has higher peak signal to noise ratio (PSNR) and smaller file size.
Keywords
Reversible data hiding JPEG AC coefficient selection1 Introduction
These days, the growth of multimedia technologies and the attractiveness of the Internet are dramatically increasing. Multimedia technologies are key players in this digital information age. Data communication and information exchange between people are done in digital form and mostly over the open Internet. This means information exchange allows a third party to access all types of multimedia information. Easy accessibility of multimedia information threatens privacy, and there is no guarantee for multimedia ownership and integrity. In general, the reliability, security, integrity, and confidentiality of multimedia information are under risk while in digital form, especially on the Internet. Other than these risks, there are cases where important metadata such as encrypted patient information or digital signature for a file is accidentally deleted or the image itself is maliciously doctored. Reversible data hiding (RDH) provides a mitigation methodology for those types of scenarios by allowing users to hide a payload into their cover media. It does it in a way that the original cover image can be recovered without any distortion. For some applications such as medical and military imaging, where even the slightest distortion is not desired, RDH can be useful.
JPEG standard is one of the oldest and most commonly used digital image formats in daily life. Most current media broadcasting corporations and digital devices use JPEG image compression to store information in graphic form. Data hiding in a JPEG compression domain in a reversible manner is also a useful and reasonable research area for image archive management, image authentication, and image privacy.
The first data hiding method was proposed by Barton’s patent [1] in 1997. Following that, numerous schemes of data hiding and lossless data hiding have been proposed. Tian [2] proposed a difference expansion technique to embed data in the spatial domain; the host image is divided into pixel pairs, and the difference value of the two pixels in a pair is expanded to carry one message bit. Subsequently, Tian’s work was improved upon in many aspects [3, 4]. In 2006, Ni et al. [5] proposed a histogram shifting technique to embed data more efficiently, preferring to embed a message into coefficients belonging to some selected frequencies. The minimum points of the histogram are used for data embedding. Qu et al. [6] proposed a novel embedding strategy for reversible watermarking based on compensation. Some of the modified pixel values return to their original values after data hiding, compensating image distortion. These days, many algorithms exploit prediction errors (PE) and pixel value ordering (PVO) [4, 7–9]. Some authors [8, 9] use blockbased pixel ordering, whereas one author [7] uses pixelbased ordering (neighboring pixel ordering). Sachnev et al. [4] proposed a popular efficient data hiding using a sorting and prediction technique. Among these research ideas, most use a histogram shifting (HS) strategy to embed data. In the HS method, while the embeddable bins have the payload embedded, the rest of the bins must be shifted either to the right or to the left depending on their sign. Embeddable and expandable bins are specified by the encoder threshold values. Compared to other methods, PE and PVO schemes have better embedding performance. However, the PVO method works well for lowcapacity embedding. On the other hand, reversible data hiding based on least squared prediction [10–12] gained popularity. These methods work quite well in highcapacity embedding. Most of the existing reversible data hiding techniques focus on the pixel domain.
However, these days, researchers have been giving attention to data hiding in JPEGcompressed image. JPEG image compression is based on discrete cosine transform (DCT), which is one of the basic building blocks for JPEG compression [13, 14]. The most important aspect of DCT for JPEG compression is the ability to quantize the DCT coefficients using visually weighted quantization table values. In [15, 16], Huffman code mapping is used for embedding the payload into a JPEG bitstream. They used the unused variablelength code (VLC) for AC coefficients by applying a map from the unused codes to used codes. Hu et al. [17] improved the VLCbased lossless data hiding scheme for JPEG images. In their work, a lossless data hiding scheme that directly embeds data into the bitstream of JPEG images based on unused variablelength codes in the Huffman table is presented. Their method [17] is an improvement on the first method [15] of this kind. Chang et al. [18] presented a blockbased lossless and reversible data hiding scheme for hiding payload in DCTbased compressed images. From each block of the mediumfrequency elements, two successive zero coefficients are used for embedding. Mobasseri et al. [16] embedded payload in the JPEG bitstream by code mapping.
The rest of this paper is organized as follows. In Section 2, an overview of the JPEG image standard is provided and related works of reversible data hiding in JPEG images are discussed. In Section 3, the proposed RDH scheme for JPEG images is introduced. Experimental results and analysis are given in Section 4. Finally, Section 5 concludes the work.
2 Related works
2.1 Overview of legacy JPEG image compression standard
2.2 Reversible data hiding in JPEG image
Unlike the pixelbased reversible data hiding technique, JPEG reversible data hiding embeds in the quantized DCT coefficients. Reversible data hiding in JPEG DCT coefficients is based on four general data hiding approaches [19]. The first one is a lossless compressionbased method proposed by Fridrich and Goljan [20], in which the embedding space is preserved by compressing the redundant component of the image. Since the message capacity is too small, this method has received less attention.
The second is a quantization table modification approach proposed by Fridrich et al. [21] and later improved by Wang et al. [22]. Their techniques work by preprocessing the quantized DCT coefficients and modifying the quantization table to create space for data hiding. Although the experimental results of [22] achieve high peak signal to noise ratio (PSNR), the file size increases greatly.
The third method [16] modifies the Huffman table. In this method, data embedding is performed by mapping a used variable length coding (VLC) to an unused VLC. Qian and Zhang [15] improved this method, but the payload size is very small for these methods.
The fourth method [18, 23] modifies the quantized DCT coefficients. Xuan et al. [23] shifted the quantized DCT coefficient histogram with an optimum searching strategy. This optimum strategy helped the technique to achieve good performance. In order to make data embedding unperceivable and the visual quality of marked image high, when a certain amount of data is embedded, only lower and middle frequency DCT coefficients are chosen to embed data in the embedding process. Sakai et al. [24] improved this scheme, producing better image quality with a new block selection strategy. Li et al. [25] proposed a reversible data hiding scheme on JPEG images based on the smaller DCT value selection method and three slight modifications of the quantization table. Using the HS analogy, Lin et al. [26] discussed highcapacity reversible data hiding for JPEG images. They used different block sizes and got high embedding capacity. Celik et al. [27] also proposed lossless data hiding in the least significant bit (LSB) of the JPEG DCT coefficients. Those DCT values, which have high distortion, are padded as side information in the payload. Huang et al. [19] proposed a histogram shifting technique on AC coefficients valued +1 or −1 and employ a block ordering based on the statistical properties of the number of zero AC coefficients in the blocks. The method is quite fresh and achieves huge improvements compared to the past work.
3 Proposed scheme
This section describes the proposed JPEG reversible data hiding method. In subsection 3.1, the embedding of the AC coefficients will be explained. Subsection 3.2 explains the block ordering method proposed by Huang et al. [19] in details. Subsection 3.3 explains the main contribution of this paper, which is the process of selecting the positions of AC coefficients for minimizing the distortion. Subsection 3.4 details which side information is needed and how they are embedded. Subsection 3.5 briefly explains the recovery of the original DCT coefficients and the extraction of the payload. A short explanation of the complexity of the algorithm is also found in subsection 3.6. Finally, the section concludes with a precise description of the proposed algorithm pseudo code.
3.1 Embedding

Embeddable coefficients: AC coefficients valued either +1 or −1.

Unchangeable coefficients: AC coefficients valued 0.

Shiftable coefficients: AC coefficients which are greater than +1 or less than −1.
3.2 Block ordering
Huang et al. [19] first proposed a block ordering based on the number of zero AC coefficients. The experimental results show that blocks with many zero AC coefficients will likely contain many −1 or +1 valued AC coefficients. Using this statistical feature, [19] proposed only embedding in +1 and −1 and set embedding order such that the blocks with more zero AC coefficients are embedded first. This strategy effectively reduced distortion. Additionally, the file size increase is also lessened. The modification of zero AC coefficient increases the file size. This is because whenever a zero AC coefficient is modified to nonzero, an extra symbol is needed to be coded. Therefore, their method leads to smaller distortion and smaller file size than the existing schemes, which embed in zero AC coefficients.
Before the AC coefficients selection step, in the proposed scheme, a similar block ordering scenario is used. A block with a higher number of zero coefficients will be at the top with the highest embedding priority and a block with less number of zero coefficients will be at the bottom with lowest embedding priority.
3.3 AC coefficient position selection
(2) Embedding capacity and distortion: The positions are chosen by considering the embedding capacity and the distortion. The embedding capacity is measured using the number of embeddable AC coefficients. The distortion is modeled using the number of shiftable AC coefficients, quantization table, and PSNR function.
(3) PSNR function: For PSNR function, although it is not the best model for evaluating perceptual distortion, it is the most agreed upon method for measuring the distortion. It penalizes modification as a square of deviation, i.e., f(x) = x ^{2}.
where, E _{(i, n)} ∈ {0, 1} represents whether the AC coefficient in position i in the n ^{ th } block is embeddable (1) or not (0). Similarly, S _{(i, n)} represents whether the AC coefficient in position i in the n ^{ th } block is shiftable (1) or not (0). Q _{ i } is the quantization table entry at position i. Note that the nominator of the equation represents the total embedding capacity when AC coefficients in position i are used for embedding, whereas the denominator represents the corresponding estimated distortion: sum of total shiftable AC coefficients and half of the embedding capacity (assuming the payload is pseudorandom, approximately half of the embeddable will cause distortion) with the squared quantization term of penalty. The reason to squaring the quantization table entry is, to consider its effect on dequantization phase. Although the number of embeddable coefficients are many and shiftable coefficients are small on a given position, if the quantization table entry is a large number, then image may be highly distorted after data embedding. To make clear the difference between positions with respect to the value of R, this method squared the quantization table values. So, from two positions which have similar distortion (denominator result from Eq. (4) without squaring Q _{ i }), the one which has the smaller Q _{ i } value will be preferred for embedding. Therefore, the best position to embed will have the largest embedding efficiency R _{ i } value, whereas the worst one will have the lowest value. For Eq. (4), the image with 512 × 512 size is considered and the number blocks becomes 4096.
(6) Sorting and position selection: Once the embedding efficiency is calculated for all 63 positions, the values can be sorted from the highest to the lowest. From here, we have to ensure that enough positions are chosen so that the payload can be embedded, this can be done by choosing the minimum number of positions from the top of the list such that the embedding capacity for each chosen positions is equal or higher than the payload. Once the positions are chosen, the embedding can take place for each block, in the order previously defined from block ordering. To make sure the encoder and the decoder uses the same order for the positions, authors suggest embedding from the lowest to the highest position, i.e., if positions (5, 1, 6, 9) are chosen from embedding, then for each block, embed in position 1 first, 5 next, then 6, and finally 9 and for extraction, extract in position 1 first, 5 next, then 6, and finally 9.
3.4 Side information
In order to make the proposed scheme truly reversible, side information such as payload length and the positions of the embedded AC coefficients need to be embedded in the DC coefficients. The maximum payload length which must be transmitted is log_{2}(W × H), where W is the width and H is the height of the image. This is 18 bits for 512 × 512sized images. The positions of AC coefficients which are used for embedding can be represented in the binary vector of size 63 bits, one bit for each position, i.e., if positions (5, 1, 6, 9) are chosen from embedding, then from the total 63, bits at vector index 1, 5, 6, and 9 will be valued 1 and the other will be valued 0. Therefore, the total side information needed for a 512 × 512 image is 81 bits and this can be embedded in the first 81 LSBs of the DC values. In order to facilitate perfect recovery of the LSB of the original DC values, they are appended as part of the payload before embedding.
3.5 Extraction and image recovery
3.6 Complexity
The computational complexity of the proposed method is quiet minimal. To select the positions of the AC coefficients for embedding, embeddable, shiftable and unchangeable AC coefficients must be counted. This can be done quite efficiently by adding a counter loop during the Huffman codeword decoding of the quantized coefficients. For determining the efficiency ratios, multiplication (squaring the 63 entries of the quantization table) and division (63 times) are required. Finally, the sorting of 63 ratios should be not much of a task. Overall, the computational complexity is very low.
3.7 Encoder and decoder
In this section, a brief overview of the proposed encoder and decoder is presented to aid with understanding.
3.7.1 Encoder

Sort the blocks by the number of zero AC coefficients

Count the total number of embeddable, shiftable, and unchangeable AC coefficients for each of the 63 possible positions

Calculate the embedding efficiencies of each position and determine the positions which will lead to the lowest distortion to embed the payload (including the original LSBs of the 81 DC coefficients).

Sort the positions using embedding efficiency R _{ i }

Embed the payload

Replace the LSBs of the first DC coefficients with the side information.
3.7.2 Decoder

Read the LSBs of the first 81 DC coefficients to extract the payload size and the positions of the AC coefficients used for embedding

Sort the blocks by the number of zero AC coefficients

Extract the payload and recover the original AC coefficients

Replace the LSBs of the DC coefficients with the original values (which were extracted along with the payload)
4 Experimental results
4.1 Visual quality
Comparison in terms of PSNR (dB) with payload size of 8000 bits
Comparison in terms of PSNR (dB) on USCSIPI 23 images with payload size of 10,000 bits
Image  Methods  

[24]  [23]  [19]  Proposed  
4.2.01  42.65  42.33  43.90  44.88 
4.2.02  40.85  40.64  43.35  44.13 
4.2.03  37.05  36.97  40.69  41.41 
4.2.04  40.51  40.22  43.69  43.94 
4.2.05  39.68  39.36  42.71  43.15 
4.2.06  39.23  39.08  42.82  43.23 
4.2.07  41.25  41.07  43.89  44.39 
5.2.08  39.38  39.21  41.47  42.72 
5.2.09  37.96  37.99  40.68  41.25 
5.2.10  38.64  38.52  39.90  41.01 
7.1.01  41.02  40.82  42.62  43.39 
7.1.02  42.15  41.31  45.96  45.99 
7.1.03  41.71  41.45  42.97  43.58 
7.1.04  41.89  41.58  41.97  43.23 
7.1.05  40.65  40.57  40.34  41.66 
7.1.06  40.69  40.68  40.30  41.66 
7.1.07  41.31  41.33  40.56  41.96 
7.1.08  42.64  41.96  44.54  45.01 
7.1.09  40.98  40.94  41.61  42.50 
7.1.10  41.85  41.67  41.92  43.07 
boat.512  39.01  38.78  41.92  42.97 
elaine.512  42.01  41.71  42.85  44.75 
house  38.23  38.23  40.70  41.84 
Average  40.49  40.28  42.23  43.12 
4.2 File Size
Comparison in terms of increasing file size (bytes) on USCSIPI 23 images with payload size of 10,000 bits
Image  Methods  

[24]  [23]  [19]  Proposed  
4.2.01  1674  1714  1656  1636 
4.2.02  1595  1613  1556  1474 
4.2.03  1501  1521  1563  1495 
4.2.04  1633  1695  1587  1432 
4.2.05  1574  1666  1444  1376 
4.2.06  1595  1571  1449  1363 
4.2.07  1672  1712  1667  1493 
5.2.08  1506  1524  1495  1397 
5.2.09  1233  1259  1704  1529 
5.2.10  1453  1451  1712  1508 
7.1.01  1290  1475  1491  1247 
7.1.02  1677  1774  1515  1559 
7.1.03  1392  1385  1693  1427 
7.1.04  1433  1468  1755  1185 
7.1.05  1171  1191  1696  1426 
7.1.06  1244  1237  1720  1373 
7.1.07  1179  1182  1864  1418 
7.1.08  1480  1582  1495  1300 
7.1.09  1264  1237  1599  1384 
7.1.10  1442  1316  1737  1126 
boat.512  1564  1592  1588  1364 
elaine.512  1847  1844  1921  1639 
house  1629  1602  1580  1459 
Average  1480  1505  1630  1418 
File size increase (bytes) with payload size of 8000 bits
5 Conclusions
The popularity and easy accessibility of the JPEG image format is becoming a great area of research for data hiding. Modification to the JPEG image introduces distortion and increase in the file size. In the proposed method, reversible data hiding for JPEG images is discussed. The technique uses the HS strategy to embed data. From nonzero AC coefficients, only +1 and −1 are used for embedding, and the others are expanded/shifted in either direction according to their sign. Before embedding, block ordering is done and then, appropriate embeddable sections with the best coefficients for RDH are selected based on the distortion sum of AC coefficients in a section. In general, the proposed scheme has better embedding efficiency as measured by visual quality and less file size compared with previous related research. The major contribution of this paper is in exploiting Eqs. (3) and (4). Using these equations, we can choose the appropriate AC coefficients that can reduce distortion and file size.
Declarations
Acknowledgements
Not applicable.
Funding
This work was in part supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (NRF2015R1A2A2A0104587) and in part by the National Natural Science Foundation of China under Grant 61772572.
Availability of data and materials
Not applicable.
Authors’ contributions
FW created the proposed idea, did the experiments, and drafted the manuscript. SK participated in the experiment and manuscript editing. HK and FH helped in coordinating the paper work and finishing the manuscript of the paper. All authors read and approved the final manuscript.
Authors’ information
Fisseha Teju Wedaj
He received a B.Sc. degree in Information Communication Technology from Wollo University in 2010, Ethiopia, and M.Sc. degree in Information Security from Korea University, South Korea, in 2015. Currently, he is a lecturer and researcher at Adama Science and Technology University, Adama, Ethiopia. His research interests include multimedia security and machine learning.
Suah Kim
He received his B.S. degree in Mathematics from the University of Waterloo, Canada. He is a PhD student of the Graduate School of Information Security, Korea University, Korea.
Hyoung Joong Kim
He is currently with the Graduate School of Information Security, Korea University, Korea. He received his B.S., M.S., and Ph.D. from Seoul National University, Korea, in 1978, 1986, and 1989, respectively. He was a professor at Kangwon National University, Korea, from 1989 to 2006. He was a visiting scholar at University of Southern California, LA, USA, from 1992 to 1993. His research interests include data hiding such as reversible watermarking and steganography.
Fangjun Huang
He is currently with the School of Data and Computer Science, Sun Yatsen University, China. He received his B.S. degree from Nanjing University of Science and Technology, China, in 1995, and the M.S. and Ph.D. degrees from Huazhong University of Science and Technology, China, in 2002 and 2005, respectively. From June of 2009 to June of 2010, he was a Postdoctoral Researcher at New Jersey Institute of Technology, NJ, USA. From August of 2013 to August of 2014, he was a Korea Foundation for Advanced Studies (KFAS) scholar at Korea University, Seoul, Korea. His research interests include reversible data hiding, steganography, steganalysis, and digital forensics.
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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