Improved Lossless Data Hiding for JPEG Images Based on Histogram Modification

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1 Copyrght 2018 Tech Scence Press CMC, vol.55, no.3, pp , 2018 Improved Lossless Data Hdng for JPEG Images Based on Hstogram Modfcaton Yang Du 1, Zhaoxa Yn 1, 2, * and Xnpeng Zhang 3 Abstract: Ths paper proposes a lossless and hgh payload data hdng scheme for JPEG mages by hstogram modfcaton. The most n JPEG btstream conssts of a sequence of VLCs (varable length codes) and the appended bts. Each VLC has a correspondng RLV (run/length value) to record the AC/DC coeffcents. To acheve lossless data hdng wth hgh payload, we shft the hstogram of VLCs and modfy the DHT segment to embed data. Snce we sort the hstogram of VLCs n descendng order, the flesze expanson s lmted. The paper s key contrbuton ncludes: Lossless data hdng, less flesze expanson n dentcal pay-load and hgher embeddng effcency. Keywords: Lossless, data hdng, hstogram, VLC, JPEG. 1 Introducton Data hdng s a technque for hdng secret message nto dgtal cover, whch can serve as authentcaton watermarkng, annotaton, and secret data for covert transmsson. Wth the rapd development of computer technology, data hdng s wdely used n mltary, commercal, medcal, fnancal, etc. As a branch of data hdng, there are many new steganography algorthms proposed n recent years [Zhang, Qn, Zhang et al. (2018); Ma, Luo, L et al. (2018); Wang, L, Sh et al. (2017)]. In some applcatons, lke medcal mage system, mltary documents and multmeda archve management, any dstorton s ntolerable after data embeddng. Therefore, the reversble data hdng (RDH) methods are proposed. Recently some reversble data hdng algorthms have been proposed, such as the dfference expanson scheme [Tan (2003)] and the hstogram shftng (HS) algorthm [N, Sh, Ansar et al. (2006)]. As a sgnfcant branch n RDH, recently more and more HS-based data hdng methods are proposed [L, Yang and Zeng (2011); Wang, L, Sh et al. (2017); L, Zhang, Gu et al. (2017)]. For example, L et al. [L, Yang and Zeng (2011)] can exactly classfy the smooth and rough pxels by usng the local complexty parameter, and then adaptvely embed the data bts nto them. Snce the smooth pxels can be embedded wth more data on average, a better performance can be obtaned at the very hgh capacty. Wang et al. [Wang, N, Zhang et al. (2017)] further 1 Key Laboratory of Intellgent Computng & Sgnal Processng, Mnstry of Educaton, Anhu Unversty, Hefe, , P.R. Chna. 2 Department of Computer Scence, Purdue Unversty, West lafayette, 47906, USA. 3 School of Communcaton and Informaton Engneerng, Shangha Unversty, Shangha , P.R. Chna. * Correspondng Author: Zhaoxa Yn. Emal: ynzhaoxa@ahu.edu.cn. CMC. do: /cmc

2 496 Copyrght 2018 Tech Scence Press CMC, vol.55, no.3, pp , 2018 mproved the optmal bn-selecton mechansm by usng a developed rate and dstorton model and can gve a good embeddng performance wth low complexty by narrowng down the soluton space. L et al. [L, Zhang, Gu et al. (2017)] proposed the multple hstograms modfcaton (MHM) technque and took the expanson bns of hstograms as parameters. Snce the modfcaton manner on each hstogram can be dfferent, the overall modfcatons could be optmzed by adaptng the parameters to the statstcal propertes of hstograms. However, all of these HS-based methods [N, Sh, Ansar et al. (2006); L, Yang and Zeng (2011); Wang, L, Sh et al. (2017); L, Zhang, Gu et al. (2017)] ntroduced above are desgned for spatal doman and cannot be appled to compressed mages drectly. JPEG s the most popular fle format n relaton to dgtal mages, whch compress the mage data effectvely. Therefore, we focus on lossless data hdng based on hstogram shftng for JPEG mages. However, above HS-based methods cannot be appled to JPEG mages drectly. Consder the less redundancy, modfcaton-senstve and ncreased flesze, RDH for JPEG mages s more dffcult than uncompressed mages. Xuan et al. [Xuan, Sh, N et al. (2007)] proposed a HS-based method for JPEG mages by embeddng data nto the JPEG quantzed 8 8 block DCT coeffcents. Xuan et al. s method can obtan hgh-payload and unnotceable flesze extenson but the stego mage s dstorted. Huang et al. proposed a new HS-based method [Huang, Qu, Km et al. (2016)] that zero coeffcents reman unchanged and only coeffcents wth values 1 and - 1 are expanded to carry message bts n. Recently, Qan and Zhang proposed a lossless and flesze preserved scheme [Qan and Zhang (2012)] n JPEG btstream by VLC-mappng. They acheved the goal of lossless embeddng by replacng the orgnal VLC by a new VLC and mappng the new VLC to the same RLV. Snce the orgnal VLC and the new VLC correspondng to the same RLV, the decoded mage qualty s no dstorton entrely. To embed hgh capacty secret data, nspred by Qan and Zhang s method [Qan and Zhang (2012)], Lu et al. [Lu, Chang, Ln et al. (2016)] proposed a HS-based method for JPEG mages, whch modfy the VLCs n JPEG btstream drectly. They count all the VLCs usage and generate the hstogram of the RLVs whch correspondng to the VLCs. Then modfy the orgnal VLC accordng to the secret data drectly. Although the embeddng capacty s expanded, there are two problems exst n Lu et al. s method [Lu, Chang, Ln et al. (2016)]. The frst problem s that only modfyng the VLC drectly n the entropy-coded data wll cause the decoded results occur error. Another problem s the X-axs of hstogram generated accordng to Lu et al. s method [Lu, Chang, Ln et al. (2016)] s not logcal. In other words, the adjacent X-values of hstogram are no correlaton. To solve the two problems, we propose a novel HS-based method and modfy the JPEG fle header to preserve the mage qualty wth no dstorton as Qan et al. s method [Qan and Zhang (2012)]. In addton, snce we sort the RLVs n terms of the correspondng VLCs frequency n the entropy-coded data, the stego mage flesze s closer to cover mage than Lu et al. s method [Lu, Chang, Ln et al. (2016)]. The rest of ths paper s organzed as follows. Secton 2 brefly ntroduces the structure of JPEG mages and Lu et al. s method [Lu, Chang, Ln et al. (2016)]. Secton 3 presents the proposed scheme n

3 Improved Lossless Data Hdng for JPEG Images 497 detal. Detal expermental results wth analyss and comparsons are gven n Secton 4. Secton 5 concludes the paper. 2 Related works Snce the proposed method works on JPEG btstream, the knowledge of JPEG mage structure s requred. Furthermore, nspred by Lu et al. s method [Lu, Chang, Ln et al. (2016)], we proposed a lossless and reversble data hdng method. Thus, we ntroduce the structure of JPEG mage at frst and Lu et al. s method [Lu, Chang, Ln et al. (2016)]. 2.1 The structure of JPEG btstream A JPEG mage conssts of a sequence of segments, each begnnng wth a marker. Each marker begns wth a 0xFF byte followed by a byte ndcatng what knd of marker t s. For example, the DHT (Defne Huffman Table) segment begns wth 0xFFD8 and the SOS (Start of Scan) segment begns wth 0xFFDA. The structure of JPEG mage s shown n Fg. 1. Fgure 1: The structure of the JPEG btstream Accordng to the JPEG gudelne, after some preprocessng works, the pxels n the mage are transformed nto AC/DC coeffcents. To compress the mage flesze, the AC coeffcents are encoded n Run-Length encodng format as ntermedate symbols, (Run, Length) and (Ampltude). Further, to mprove the compresson rate, (Run, Length) s encoded n the format of VLC, and (Ampltude) s encoded n VLI (Varable Length Integer) format. The DHT segment contans the Canoncal Huffman table nformaton, whch s used for obtanng the VLCs. Each VLC s corresponded to a specfc RLV that represents an AC coeffcent n entropy-coded data. The VLCs are encoded by Canoncal Huffman code, for nstance, f the run/length value s 0/4, the correspondng VLC s For AC coeffcents of lumnance component, 162 dfferent VLCs are corresponded to the run/length value from 0/1 to F/A accompaned wth 0/0 (End of Block) and F/0 (Zero Run Length). The length of VLC s between 2 to 16 bts.

4 498 Copyrght 2018 Tech Scence Press CMC, vol.55, no.3, pp , 2018 Accordng to JPEG gudelne, f only change the VLC, the decoded results would be dfferent compared wth the cover mage s decoded results. Ths s due to the VLC s correspondng RLV has changed, whch affects the decoded results. To preserve the run/sze not changed after the replacement of the correspondng VLC, we modfy the DHT segment. 2.2 Lu et al. s method To obtan hgh embeddng capacty for JPEG mages, Lu et al. [Lu, Chang, Ln et al. (2016)] proposed a data embeddng method based on hstogram modfcaton n entropycoded data, whch dfferent from VLC mappng-based proposed by Qan et al. [Qan and Zhang (2012)]. The detal embeddng steps can be summarzed as follows: Input: An orgn JPEG btstream and a secret btstream. Output: A stego JPEG btstream, p and z. Step 1: Parse the JPEG mage and extract all the used-vlcs and unused-vlcs. Generate the hstogram of run/sze whch begns wth 0/0 and ends wth F/A. The Y-axs n the hstogram represents the occurrence number of each run/sze s correspondng VLC n the entropy-coded data. Step 2: Fnd a peak pont p and a zero pont z and save the values of p and z as overhead nformaton. The zero pont z s the nearest zero pont to p. Step 3: Scan all of the VLCs n the entropy-coded data sequentally. Shft all the run/length values to rght by one unt between p and z (not ncludng p and z). For nstance, the run/length 0/2, 0/3, 0/4 and 0/5 are shfted to 0/3, 0/4, 0/5 and 0/6. The correspondng VLC wll be changed accordng to the shfted run/length. For nstance, the VLC= 1011 (correspondng run/length value s 0/4 ), wll be changed to (correspondng run/length value s 0/5 ). Once the VLC that corresponds to run/length value equal to p s attaned, replace the VLC or not depend to the secret bt that wll be embedded. If the secret bt s 0, the VLC wll be mantaned and f the secret bt s 1, the VLC wll be replaced by another VLC that corresponds to the run/length value equals to p+1. Step 4: Generate a stego JPEG btstream. After the above steps, a stego JPEG btstream s generated. However, the stego JPEG btstream wll cause the results occur error durng JPEG decodng. Ths s because only VLCs n the entropy-coded data are modfed. The sze value of the modfed VLC s correspondng RLV s not equal to the length of orgnal appended bts. In addton, the RLV sortng manner s also not optmal for the hstogram of RLV. Because the VLC uses Huffman codng so sortng by VLC code length order can make the fle expanson generated after embeddng data effectvely reduce. Based on the above analyss, we propose an mproved lossless data hdng scheme for JPEG mages. 3 Proposed method Inspred by Qan et al. s scheme [Qan and Zhang (2012)], our method modfed the DHT segment of JPEG header based on Lu et al. s scheme [Lu, Chang, Ln et al. (2016)], resultng n a normal JPEG mage decodng and no dstorton of mage qualty. Thus, t s

5 Improved Lossless Data Hdng for JPEG Images 499 a lossless data hdng scheme. At the same tme, the fle expanson of the secret JPEG btstream s sgnfcantly reduced from that of Huang et al. [Huang, Qu, Km et al. (2016)] and Lu et al. [Lu, Chang, Ln et al. (2016)] and the performance s better than the above. The overall framework of the proposed method s depcted n Fg. 2, ncludng the data embeddng process and extracton process. The detals of the proposed method and the procedures of data embeddng and extracton are presented n the followng subsectons severally. Fgure 2: The overall framework of the proposed method 3.1 Lossless data embeddng based on hstogram modfcaton The hstogram establshment process of our method s dfferent from that of Lu et al. [Lu, Chang, Ln et al. (2016)]. Before generatng the hstogram, all VLCs n the entropy-coded data are frst extracted and ther frequency of occurrence s counted. Accordng to the order of the RLVs n the DHT segment, a hstogram of frequency dstrbutons of VLCs s generated. We use the Baboon mage wth a qualty factor of 80 as an example and compare t wth Lu et al. s hstogram establshment scheme [Lu, Chang, Ln et al. (2016)]. Fg. 3 s a hstogram of frequency dstrbuton of VLC. Fgure 3: The orgnal hstogram of VLCs ( Baboon mage, QF=80)

6 500 Copyrght 2018 Tech Scence Press CMC, vol.55, no.3, pp , Optmzaton of RLV orderng Consderng that, the encoder default Huffman code table s used n the JPEG fle header, whch s not the optmal Huffman code table for the current mage. Therefore, there are stll encodng redundances that cannot be gnored n JPEG mages. To reduce unnecessary encodng redundances as much as possble, we adjusted the order of the RLVs accordng to the feature of the Huffman codng before the hstogram was modfed. The strategy we adopted s as follows: 1. Fnd the peak pont p, and then look for the nearest zero pont z from the peak pont p accordng to the frequency dstrbuton nformaton of the VLC n the hstogram. A large number of statstcal results show that p s generally 0/1, whch s the ranked frst RLV n the default Huffman code table. In Fg. 3, p s 0/1 and z s 0/8. 2. Adjust the order of the RLVs correspondng to the VLC between the peak pont p and the zero pont z. After both p and z are determned, theoretcally we can already perform hstogram modfcaton operatons. However, consderng that the rankng of the VLC frequency dstrbuton between the peak pont and the zero pont s not strctly n accordance wth the order of the RLVs n the default Huffman code table, the RLV sequence needs to be optmzed. In other words, we need to readjust the RLV order n the DHT segment accordng to the descendng order of the current VLC frequency dstrbuton. The theoretcal bass for ths s that Huffman codng defnes a shorter code length for frequently occurrng codes, so adjustng the codng sequence based on the current VLC frequency of occurrence s equvalent to optmzng the Huffman codng, whch means that we further reduce encodng redundances. Fg. 4 shows a sorted hstogram wth the Baboon mage wth a qualty factor of 80 as an example. Fgure 4: The sorted hstogram of VLCs ( Baboon mage, QF=80) Before optmzaton, 162 VLCs are dvded nto n categores accordng to code length. The length of the -th category s L, that s: C = { VLC, VLC,..., VLC } (1) 1 2 L

7 Improved Lossless Data Hdng for JPEG Images 501 Reorder the VLC and the correspondng RLV between the peak pont p and the zero pont z accordng to the descendng order, then the VLC between p and z can be recorded as: ( ) ' ( ) ' ( ) ' 1 2 L C ' = { VLC, VLC,..., VLC } (2) ( ) ( ) ( ) 1 2 L ' ' ' Where VLC, VLC,..., VLC s the VLC sequence of the -th category adjusted by descendng orderng. Assume that reduced encodng redundancy s R, and then R can be represented as: nz L = np j= 1 ( ) ' ( ) ( ) j R = num VLC l (3) Where np s equal to the category number of the category where the peak pont s located; nz s equal to the prevous category number of the category where the zero pont s located; l s the code length of VLC correspondng to RLV before modfcaton; ( ) ( ' ) j num VLC denotes the frequency of occurrence of segment. j j ( )' VLC j n the entropy-encoded data Modfcaton of hstogram of VLCs After reorderng the RLVs, we can embed data by hstogram modfcaton. Frst, the RLV between the peak pont and the zero pont s shfted rghtward, e.g. 0/2 s modfed to 0/3. After the rght-shft operaton s completed, the frequency of the nearest VLC to the rght of the peak pont p s 0, that s, the zero pont at ths tme becomes p+1. The followng fgure shows the rght-shfted hstogram of a Baboon mage wth a qualty factor of 80. Fgure 5: The shfted hstogram of VLCs ( Baboon mage, QF=80) Modfcaton of DHT segment In order to ensure that the modfed JPEG mage generated after data embeddng has no dstorton compared to the orgnal mage, we also modfed the RLV sequence n the DHT segment whle rght-shftng the VLC hstogram. Because the RLVs at dfferent postons n the DHT segment correspond to dfferent VLCs, we also shft the RLV n the

8 502 Copyrght 2018 Tech Scence Press CMC, vol.55, no.3, pp , 2018 correspondng poston by one unt at the same tme accordng to the order n whch the VLC s shfted rght. In ths way, the RLV correspondng to each VLC before and after the hstogram modfcaton s unchanged, whch ensures that the result obtaned by the decodng process s consstent wth the orgnal mage and ensures that the mage s free of any dstorton. In addton, we modfy the RLV wth a value of p+1 to p so that when embeddng data, regardless of embeddng 0 or 1, the RLV correspondng to VLC s p, ensurng that the decodng result s unchanged Calculaton of the total flesze expanson Durng the modfcaton of the hstogram, the flesze expanson s unavodable. Because the length of the VLC may not be equal before and after the rght shft of the RLV, f the modfed VLC s longer than the orgnal VLC, JPEG fle sze wll ncrease. However, because we optmzed the RLV orderng, the VLCs are sorted n descendng order. Only the VLC wth the lowest frequency n each category wll ncrease the code length after modfcaton, so t can effectvely reduce the fle expanson. Formula (4) denotes the fle expanson caused by the modfcaton of the hstogram: nz = np ( ) ' ( L ) ( ) E = num VLC j (4) Where j represents the category number of the next category of C. As mentoned n 3.1.1, the RLV sortng optmzaton s performed before the hstogram s modfed so the encodng redundancy s reduced. Ths part of the reducton s R, then the total fle expanson (FE) can be represented as: nz nz L ( ) ' ( L ) ( ) = np = np j= 1 ( ) ' ( j ) ( ) (5) FE = num VLC j num VLC l 3.2 Data embeddng & extracton Fgure 6: Data embeddng process The process of data embeddng s shown n Fg. 6. The man process of the embeddng phase s as follows: Input: Secret btstream and orgnal JPEG btstream. Output: Modfed JPEG btstream. Step 1: Parse the JPEG entropy-coded segment and the DHT segment and count the frequency of occurrence of each VLC.

9 Improved Lossless Data Hdng for JPEG Images 503 Step 2: The frequency dstrbuton hstogram of the VLC s generated accordng to the order of the RLV values n the DHT segment. The locaton of the peak pont and zero pont are determned based on the length of the secret btstream. Step 3: Reorder the order of the RLVs n the DHT segment accordng to the optmzed Huffman encodng operaton mentoned n 3.1. Then perform hstogram modfcaton operaton and DHT segment modfcaton operaton. Step 4: Scan all the VLCs n the entropy-coded data and modfy the VLC n the entropycoded data accordng to the nformaton that needs to be embedded. When the VLC correspondng to the RLV wth the value of p s scanned, the data embeddng operaton can be performed. If 0 s embedded, the current VLC remans unchanged; f 1 s embedded, the current VLC s modfed to the orgnal VLC that correspond RLV s p+1. The entropy-coded data segment s scanned sequentally untl all the data n the secret btstream are embedded, then generate the modfed JPEG btstream. Fgure 7: Data extracton process The process of data extracton s shown n Fg. 7. The man flow of the secret data extracton and recovery phase s as follows: Input: Modfed JPEG btstream. Output: Secret btstream and orgnal JPEG btstream. Step 1: Parse the DHT segment of the JPEG fle header and calculate the correspondng VLC value accordng to the RLV rankng order. Fnd the frst two VLCs that correspond to the same RLV, namely the peak pont and the nearest zero pont. Step 2: Scan all the VLCs n the entropy-coded data segment and extract all secret data accordng to the peak pont and the length of the secret btstream. Step 3: After the secret data extracton s completed, the modfed RLV sequence s restored to the orgnal state accordng to the default Huffman code table and the correspondng VLC s modfed to generate a recovered JPEG btstream. 4 Expermental results and analyss In order to test the performance of the proposed method and compare wth other two methods, we have tested all the mages from UCID mage database. These mages are converted to grayscale and further compressed to JPEG fles wth dfferent qualty factors. Fg. 8 shows the comparson of the payload and flesze expanson rate (FER) of the three schemes under dfferent qualty factors. Denote the orgnal JPEG stream length as L, the FER can be represented as:

10 504 Copyrght 2018 Tech Scence Press CMC, vol.55, no.3, pp , 2018 FE FER = 100% L (6) (a) (b) (c) Fgure 8: Comparsons of payload n UCID Image Lbrary wth dfferent qualty factors. (a) QF=70. (b) QF=80. (c) QF=90. (d) QF=100 (d) (a) (b)

11 Improved Lossless Data Hdng for JPEG Images 505 (c) Fgure 9: Comparsons of FER n UCID Image Lbrary wth dfferent qualty factors. (a) QF=70. (b) QF=80. (c) QF=90. (d) QF=100 Accordng to the results n Fg. 8, Huang et al. s method [Huang, Qu, Km et al. (2016)] has the hghest embeddng capacty n full embeddng among the three methods. For the FER, t can be seen from Fg. 9 that the FER of Huang et al. s method [Huang, Qu, Km et al. (2016)] s hgher than other methods. Table 1: Comparson of the three methods (QF=80) Methods Payload(bts) FER (%) PSNR Huang et al. [Huang, Qu, Km et al. (2016)] Lu et al. [Lu, Chang, Ln et al. (2016)] Proposed Table 2: Comparson of the three methods (QF=90) Methods Payload(bts) FER (%) PSNR Huang et al. [Huang, Qu, Km et al. (2016)] Lu et al. [Lu, Chang, Ln et al. (2016)] (d) Proposed Tab. 1 and Tab. 2 respectvely lst the average values of all the ndexes of all three methods when QF=80 and QF=90. The peak sgnal-to-nose rato (PSNR) s an objectve crteron for evaluatng the vsual qualty of the mage between the modfed JPEG mage and the orgnal JPEG mage. The hgher the PSNR value, the hgher the vsual qualty of the modfed JPEG mage. Snce our proposed method has no effect on the mage qualty,.e. lossless, the PSNR value can be regarded as. However, snce Lu et al. s method [Lu, Chang, Ln et al. (2016)] only modfes the value of VLC n the entropy-coded data segment durng hstogram modfcaton, whle the correspondng RLV has not been

12 506 Copyrght 2018 Tech Scence Press CMC, vol.55, no.3, pp , 2018 modfed, whch means that the addtonal bt nformaton length after VLC does not correspond to the sze value of RLV. The decoder may generate exceptons when decodng. Therefore, PSNR s set to 0. The key pont of our proposed method s lossless, but our method also can obtan hgh payload, whch s not nferor to Huang et al. s RDH method [Huang, Qu, Km et al. (2016)]. In addton, the flesze expanson of our method s acceptable and less than Lu et al. s method. 5 Conclusons In ths paper, a lossless and hgh-payload data hdng scheme for JPEG mages s proposed. After ntroducng the HS-based method n JPEG btstream, we propose a novel method that optmze hstogram modfcaton and modfy the DHT segment to preserve the mage qualty wth no dstorton. After sortng the hstogram and replace the correspondng VLCs, we obtan less flesze expanson. Key contrbuton s lossless, less flesze expanson n dentcal payload. Acknowledgement: Ths research work s partly supported by Natonal Natural Scence Foundaton of Chna ( , , , U , ), CSC Postdoctoral Project ( ), Anhu Provncal Natural Scence Foundaton ( SQF216), Key Program for Excellent Young Talents n Colleges and Unverstes of Anhu Provnce (gxyqzd ), and Anhu unversty research and nnovaton tranng project for undergraduate students. References Huang, F.; Qu, X.; Km, H. J. (2016): Reversble data hdng n JPEG mages. IEEE Transactons on Crcuts and Systems for Vdeo Technology, vol. 26, no. 9, pp L, X.; Yang, B.; Zeng, T. (2011): Effcent reversble watermarkng based on adaptve predcton-error expanson and pxel selecton. IEEE Transactons on Image Processng A Publcaton of the IEEE Sgnal Processng Socety, vol. 20, no. 12, pp L, X.; Zhang, W.; Gu, X.; Yang, B. (2017): Effcent reversble data hdng based on multple hstograms modfcaton. IEEE Transactons on Informaton Forenscs & Securty, vol. 10, no. 9, pp Lu, X. L.; Chang, C. C.; Ln, C. C.; Yuan, S. M. (2016): A hgh-payload, reversble data hdng scheme based on hstogram modfcaton n JPEG btstream. Imagng Scence Journal, vol. 64, no. 7, pp Ma, Y.; Luo, X.; L, X.; Bao, Z.; Zhang, Y. (2018): Selecton of rch model steganalyss features based on decson rough set α-postve regon reducton. IEEE Transactons on Crcuts and Systems for Vdeo Technology. N, Z.; Sh, Y. Q.; Ansar, N.; Su, W. (2006): Reversble data hdng. IEEE Transactons on Crcuts and Systems for Vdeo Technology, vol. 16, no. 3, pp Qan, Z.; Zhang, X. (2012): Lossless data hdng n JPEG btstream. Journal of Systems & Software, vol. 85, no. 2, pp Tan, J. (2003): Reversble data embeddng usng a dfference expanson. IEEE Transactons on Crcuts & Systems for Vdeo Technology, vol. 13, no. 8, pp

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