Optimum Reversible Information Hiding Based on Adaptive Joint Processing

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1 Internatonal Forum on Energy, Envronment and Sustanable Development (IFEESD 2016 Optmum Reversble Informaton Hdng Based on Adaptve Jont Processng Zhe Mao1,a, Ynfa Zhang1, Ln Zhou1, and Tnglong Du2 1 Department of Informaton Transmsson, X an Communcatons Insttute, Shaanx,710106, Chna 2 Department of Informaton Securty, X an Communcatons Insttute, Shaanx,710106, Chna a @qq.com Keywords: Informaton Hdng, Stego-nformaton, Integer Wavelet Transform (IWT, Assgnment Algorthm, Peak Sgnal to Nose Rato (PSNR. Abstract. Ths paper presents a novel reversble nformaton hdng method for dgtal mages by a ont wth nteger wavelet transform and assgnment algorthm. Ths scheme takes advantage of Gaussan-lke dstrbuton hstogram for utlzng nteger wavelet coeffcents n frequency and assgnment algorthm for best matchng between the secret mage and the orgnal one. Expermental results show that orgnal mage and extracted marked mage could have hgh vsual qualty and they are perceptually smlar to ther orgnal versons. In addton, results show that ths scheme outperforms peak sgnal to nose rato (PSNR than other methods. Introducton The securty of data problem, also known as the maxmum weghted bpartte reversble processng problem, s a wdely-studed problem applcable to many domans. Secure nformaton means to hde the secret data nto another data. The man targets of nformaton securty are to hde the secret data and avod unauthorzed attackers usng the secret. The secure communcaton s man purpose of the securty of data, n such a way that the stego-nformaton (modfed data whch contans secret data should not devate much from orgnal data (data not contanng any secret nformaton and the observer could not be able to dstngush any sense between them wth respectng to reman the real message nvsble for the observer. Several effcent data embeddng methods have been proposed. They nclude set parttonng n herarchcal trees n [1], embedded block based codng wth optmzed truncaton and set parttonng embedded block n [2,3]. These algorthms are effcent based on the dscrete wavelet transform (DWT. However, the mage coeffcents decomposed by the DWT are floatng-pont numbers, whch ncreases the computatonal complexty and s not well suted for effcent lossless codng applcaton. To solve the above problems, Daubeches and Sweldens presented the lftng scheme (LS [4]. Based on the LS, a knd of new transforms called nteger wavelet transforms (IWT are proposed, whch s a low complexty and effcent mplementaton of the DWT and can support the lossless data codng [5-8]. It s a basc modfcaton of lnear transforms, where each flter output s rounded to the nearest nteger. IWT can be used to have a unfed lossy and lossless codec. It s also of nterest for hardware mplementatons, where the use of floatng pont s stll a costly operaton. In software mplementatons, many processors now offers multmeda nstructons whch can execute multple nteger operatons n parallel, lke the MMX nstructon set n the Pentum processor [9]. The use of IWT s also a means to reduce the memory demands of the compresson algorthm as ntegers are used nstead of real numbers. We present an nformaton hdng method based on IWT oned wth the use of assgnment algorthm [10-13]. We hde secret mage nto the nteger wavelet coeffcents of the orgnal mage n order to provde hgher data mperceptblty and ncrease the robustness of our steganography method. IWT avods the floatng pont precson problems of the wavelet flter. Also, we also used an assgnment algorthm to select the best embeddng locatons of the nteger wavelet coeffcents to ncrease the system securty and stego-nformaton can have hgh vsual qualty The authors - Publshed by Atlants Press 564

2 The remander of ths paper s organzed as follows. IWT and the Hungaran's assgnment algorthm are presented n Secton II. The proposed method s detaled presented n Secton III. Expermental results and performance evaluaton are presented n Secton IV. The concluson s drawn n Secton V. Integer Wavelet Transform and Hungaran Algorthm A. Integer Wavelet Transform For the forward transform, typcally the data s splt nto the even and odd samples have been replaced by low pass and hgh pass coeffcents, respectvely. The nverse transform s calculated by reversng the order of the lftng steps and flppng the sgns. But reversble nteger wavelet transforms can be constructed by roundng or truncatng the output of the lftng step pror to addng. The lftng scheme s a spatal doman constructon of borthogonal wavelets developed by Sweldens [5]. Lftng allows a wavelet transform to be computed quckly through a seres of ndvdual lftng steps. Several reversble nteger wavelet transforms based on the lftng scheme have been used extensvely n the lterature and are descrbed n the remander of ths secton. In each case, one dmensonal sgnal{ x }, the lftng steps are descrbed as follows. sl = x dl = dl + α sl + sl, dl = x + 1 sl = sl + β dl + dl ( + 1 ( 1 ( 1 ( 1 ( 1 ( 1 ( + 1 ( 1 ( 2 ( 1 ( 1 ( 1 ( 2 dl = dl + γ sl + sl sl = ζsl ( 2 ( 1 ( 2 ( 2, ( 2 sl = sl + δ dl + d d l l = dl ζ (2 α = , β = , γ = , δ = , ζ = (3 where s l and d l are generally referred to as lower frequency and detal coeffcents, respectvely. ( ( sl, dl ( = 012,, are md-output. Accordng to nteger wavelet theory [7], we construct nteger wavelet transform based on the framework mentoned above. That s: sl = x ( 1 dl = dl + nt ( α( sl + sl+ 1, (4 dl = x ( 1 ( 1 ( sl = sl + nt ( β( dl + dl 1 ( γ ( + 1 δ ( 1 (( ( 2 ( 1 ( 1 ( 1 dl = dl + nt sl + sl ( 3 ( 2 2 ( 2 dl = dl + nt ζ ζ sl, (5 ( 2 ( 1 ( 2 ( 2 ( 3 ( 2 ( 3 sl = sl + nt ( dl + dl sl = sl + nt( ( 1 ζ d l ( 4 ( 3 (( 1 ( 3 ( 4 dl = dl + nt ζ sl sl = sl, ( 4 ( 3 ( 4 ( 4 (6 sl = sl + d d l l = dl where means nteger part of x. The values of parameters α, βγ,, δζare, gven n formula (3. Equaton (5 s an extra lftng step dfferent from Equaton (2. We adopt t here because t can acheve reversble transform accordng to [7] whle Equaton (2 cannot. Wavelet transform decomposes an mage nto a set of band lmted components whch can be reassembled to reconstruct the orgnal data wthout error. In general most of the mage energy s concentrated at the lower frequency coeffcent sets (approxmaton coeffcents and therefore embeddng secret data n these coeffcent sets may degrade the mage sgnfcantly. Embeddng n the low frequency coeffcent sets, however, could ncrease robustness sgnfcantly. On the other hand, the hgh frequency coeffcent sets (dagonal detal coeffcents nclude the edges and textures of the mage and the human eye s not generally senstve to changes n such coeffcent sets. Ths allows the secret mage to be embedded wthout beng perceved by the human eye. The agreement adopted by many wavelet-based mage hdng methods, s to embed the secret mage n the 565 l l Z (1

3 mddle frequency coeffcent sets (horzontal detal coeffcents and vertcal detal coeffcents s better n perspectve of mperceptblty and robustness. Lftng schemes whch we have used n ths paper s one of many technques that can be used to perform nteger wavelet transform. The wavelet lftng scheme s a method for decomposng wavelet transform nto a set of stages. An advantage of lftng schemes s that they do not requre temporary storage n the calculaton steps and have requred less no of computaton steps. B. Hungaran Algorthm The Hungaran algorthm assumes the exstence of a bpartte graph G = { VU,, E} as llustrated n Fgure 1, where V and U are the sets of nodes n each partton of the graph, and E s the set of edges. The edge weghts may be stored n a matrx C ost.the method mantans feasble values for all theδ and γ from ntalzaton through termnaton. An edge n the bpartte graph s called admssble δ + γ c. when Algorthm nput: Fg.1 Bpartte graph showng matched and unmatched edges An assgnment problem comprsng a bpartte graph G { VU,, E} = (where V = U = n and an n n matrx of edge costs C ost. An optmal soluton to the above assgnment problem, comprsng a complete matchng M, and the fnal values of all dual varablesδ and γ. Each of whch can be a row c *, a column c * or a sngle entryc of the cost matrx C ost. Algorthm output: A new complete matchng M, representng an optmal soluton to the problem wth the changed edge costs. The hungaran algorthm steps are descrbed as follows. Step.1 Begn wth an empty matchng M 0 = φ. Assgn feasble values to the dual varablesδ and γ as follows: v V, δ = 0 ( u U, γ = mn c Step.2 Desgnate each exposed (unmatched node n V as the root of a Hungaran tree. Step.3 Grow the Hungaran trees rooted at the exposed nodes n the equalty subgraph. Desgnate the ndces of nodes v encountered n the Hungaran tree by the set I,and the ndces of nodes u encountered n the Hungaran tree by the set J. If an augmentng path s found, go to step 5. If not, and the Hungaran trees cannot be grown further, proceed to step 4. Step.4 Modfy the dual varablesδ and γ as follows to add new edges to the equalty subgraph. Then go to step 3 to contnue the search for an augmentng path. 566 (7

4 1 θ = mn δ γ 2 I, J ( c δ+ θ, I δ δ θ, I (8 γ + θ, J γ γ θ, J Step.5 Augment the current matchng by flppng matched and unmatched edges along the selected augmentng path. That s, M k (the new matchng at stage k s gven by ( Mk 1 P U ( P Mk 1, where M k 1 s the matchng from the prevous stage and P s the set of edges on the selected augmentng path. Step.6 Output the matchng after the n th stage: M = M. n Adaptve Reversble Jont Processng In the adaptve reversble ont processng method, the orgnal and secret mages are decomposed nto 4 sub-mages such as approxmaton coeffcents (WC, horzontal detal coeffcents (WH, vertcal detal coeffcents (WV and dagonal detal coeffcents (WD usng nteger wavelet transform. These sub-mages are dvded nto non-overlappng blocks. The blocks of approxmaton coeffcents of orgnal mage are subtracted from approxmaton coeffcents of secret mage. The dfferences of these coeffcents are called error blocks. By applyng assgnment algorthm, matchng and dstrbuton could be optmzed. Thus, by usng Hungaran's assgnment algorthm, we fnd the best matched blocks between resulted error blocks and the 3 3 non-overlappng blocks that belong to WH sub-mage of orgnal mage. We fnd best embeddng locatons of orgnal mage and then replace these error blocks wth related matched blocks of orgnal mage. In addton, n ths scheme we have two secret keys that we have made them n two dfferent ways. Therefore, we have partly ncreased the securty. Also, n ths method matchng and dstrbuton have been optmzed. Fgure 2 shows the block dagram of the adaptve reversble ont processng method, left: data embeddng, rght: data extracton. A. Embeddng Procedure The steps of embeddng procedure are as follows. Step.1 Usng nteger wavelet transform, decompose the orgnal mage C and the secret mage S nto nne sub-mages C 2 2and S 2 2,respectvely. CWC CWH C2 2= CWV CWD, SWC SWH S 2 = 2 SWV SWD (9 Step.2 Each of SWC, CWC, and CWH are parttoned nto blocks of 3 3 pxels and can be represented by: SWC = SS, { } {, 1 9} CWC = CC {, 1 9} CWH = HH k k where SS, CC and HH k represent the th block n SWC, the th block n CWC and the k th block n CWH, respectvely. Step.3 For each block SS n SWC, the best matched block CC of mnmum error n CWC s searched by usng the root mean squared error (RMSE. Calculate the error block RMSE between SS and CC as follows: SC (10 567

5 { } RMSE = E SS CC (11 SC The frst secret key K conssts of the addresses of the best matched blocks n CWC. Step.4 After fndng all of the error blocks n step3, then for each error block RMSE SC, the best matched block HHk n CWH s searched by Hungaran's algorthm. So, we frst create 3 3 matrx, called the cost matrx. In whch each element represents the RMSE between each of RMSE blocks and HH k blocks. In fact, the mnmal cost perfect matchng s the set of HH k blocks correspondng to these RMSESC blocks. In ths way, we can fnd the best blocks of HH k that have best matchng wth RMSE blocks, the second secret key K k conssts of the addresses k of the best matched blocks n SC CWH. Therefore, now we have the best opton for embeddng. So, we replace these matched RMSE blocks. SC Step.5 After embeddng all of RMSE SC SC HH k blocks wth blocks n step 4, apply the nverse IWT to the CWC, CWV, CWD, and the modfed sub-mage CWH to obtan the stego-data D. B. Extracton Procedure The steps of secret mage extracton procedure are as follows. Step.1 Decompose the stego-data D nto four sub-mages [DWC, DWH; DWV, DWD] usng nteger wavelet transform. Step.2 Extract the block CC from the sub-mage DWC by usng frst secret key K.Use the second secret key k K to extract the error block. The secret block SS can be obtaned by: { } SS = E CC RMSE (12 SC Repeat step 2 untl all secret blocks are extracted and form the sub-mage CWC. Step.3 Usng detal coeffcents from sender such as CWD,CWV,CWH and extracted CWC from above step, apply the nverse IWT to obtan the embedded secret mage whch s vsually smlar to the orgnal data Fg.2 Block dagram of the presented method, Fg.3 Hstogram of one detal subband Left: data ofembeddng, Rght:data extracton Expermental Results grayscale mage Lena Expermental results of a wde range of natural mages show that hstogram of IWT detal subband has approxmate shape of dscrete Gaussan dstrbuton functon lkewse. Moreover, study on human 568

6 vsual system n dgtal wavelet transform doman ndcates that modfcaton on wavelet coeffcents under detecton threshold can t be detected by human eyes. Fgure 3 shows hstogram of a detal subband of grayscale mage Lena. Ths work presented a partcular property of wavelet detal coeffcents of almost every natural textured mage that they have a hstogram correspondng to a Generalzed Gaussan Densty (GGD. 48 adaptve reversble ont processng dfference expanson method PSNR Fg. 4 Vsual mpact of the presented method n Lena, Payload (bpp Fg.5 Comparson results on Lena (a PSNR = 44.3dB, 0.121bpp (b PSNR = 41.6dB, 0.306bpp We appled the presented reversble nformaton hdng algorthm to a grayscale level mages of Lena of sze shown n Fgure 4. For an mage of sze of , a payload 1 bpp (bts per pxel means that 262,144 (namely bts are embedded n the mage. The results ndcate that the adaptve reversble ont processng algorthm can hdden a large payload, whle mantan the hgh peak sgnal-to-nose-rato (PSNR of the marked mage versus the orgnal mage. In Fgure 5, the comparson results between the dfference expanson method [6] and our proposed method are shown. It s observed that our proposed method can obtan better vsual qualty n the same payload. More than 2dB mprovement n PSNR has been acheved. Conclusons Ths paper presents an adaptve reversble nformaton hdng method based on nteger wavelet transform and assgnment algorthm. Expermental results and the comparson wth the dfference expanson method demonstrate that ths ont processng method can obtan a better vsual qualty of the marked mage at the same payload. It s expected that ths reversble data hdng technque wll be deployed for a wde range of applcatons n secure data system. Acknowledgement The authors deeply thank several colleagues who helped them at dfferent stages durng the preparaton of ths paper. In partcular, the authors thank the anonymous revewers for ther helpful comments and suggestons. The proect supported n part by Natural Scence Basc Research Plan n Shaanx Provnce of Chna (Program No.2014JM2-6101, 2015JM6325. References [1] Sad, W.A.Pearlman, New fast andeffcent mage codec based on set parttonng n herarchcal trees. IEEE Transacton on Crcut System Vdeo Technology, Vol.6,pp ,1996. [2] D.Taubman, Hgh performance scalable mage compresson wth EBCOT. Proceedng of IEEE, IEEE Internatonal Conference on Image Processng, pp.24-28,

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