Spread Spectrum based M-ary Modulated Robust Image Watermarking

Transcription

1 54 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.7 o., October 27 Spread Spectrum based M-ary Modulated Robust Image atermarng T. S. Das, V. H. Manar 2 and S. K. Sarar 3, Dept. of Electroncs & Telecommuncaton, Jadavpur Unversty, Kolata-732 IDIA Summary Spread Spectrum (SS) modulaton prncple has been wdely used n dgtal watermarng due to ts dstngushng characterstcs vz. excellent securty and robustness n performance. The use of wde spectrum of the host sgnal n message hdng process puts a lmt on the data rate subect to a gven embeddng dstorton. In SS communcaton the use of M ary modulaton s a popular extenson to bnary antpodal sgnalng usually resultng n a sgnfcant performance mprovement. Moreover, wth the ncreasng M and for certan schemes, M ary modulaton wors at the channel capacty. The present wor nvestgates on how to use M ary modulaton n the context of transform doman SS watermarng for performance mprovement over bnary sgnalng schemes. Furthermore, relevant computatonal complexty ssue of M ary watermarng s also reduced to a greater extent by the mplementaton of M ary phase modulaton. The present wor also suggests data embeddng n selected sub bands (DT) or channels (M band) of wavelet transform decomposton. Performance mprovement of M ary sgnalng prncple n SS scheme wth respect to error rate, complexty and superorty of wavelet doman embeddng approach are supported by expermental results aganst lossy compressons. Key words: Spread Spectrum atermarng, M ary modulaton, Dscrete avelet Transform.. Introducton Dgtal watermarng, the art of hdng nformaton n multmeda data, can be consdered as communcaton scheme where an auxlary message s embedded n dgtal multmeda sgnals and are avalable wherever latter sgnals move. The decoded message latter on serves the purpose of copyrght protecton, content authentcaton, broadcast montorng, and securty n communcaton etc. Robustness, mperceptblty, payload, computatonal cost, complexty and oblvous extracton are essental crtera n dgtal watermarng schemes needed for data hdng and recovery process. But all these requrements are related n conflctng manner and the partcular applcaton based algorthm emphaszes on one or more such requrements to a greater extent []. The SS modulaton technque n dgtal communcaton offers ant-ammng and nterference reecton property. These had motvated the several researchers for developng SS watermarng algorthms for multmeda sgnals ether n spatal doman or n transform doman by usng Dscrete Cosne Transform (DCT), Fourer-Melln, Dscrete Hlbert Transform (DHT), and wavelet decomposton [2-5]. SS watermarng schemes, although can be mplemented n varous dfferent way, the method that uses dstnct pseudo nose () spreadng codes for embeddng each bnary dgt s popular and proven to be effcent, robust and cryptographcally secured. At ths pont the use of varous channel codng schemes and M ary modulaton technques can be found effcent for robustness mprovement as they are wdely used n dgtal communcaton for mprovng data transmsson relablty. In the applcatons of dgtal mage watermarng the concept of channel codng scheme becomes neffcent due to dffculty n fndng the approprate code lengths. The problem arses because of the varable nature of channel dstorton that depends on host data sze, content and the nature of delberate attacs appled to the stego data. For a gven length of bnary message and fxed embeddng dstorton, M ary sgnalng schemes offer hgher reslency over bnary modulaton scheme snce less number of modulaton functons wll be requred n the latter case that gves rse to the scope of choosng hgher modulaton ndex values. M ary prncple of certan modulaton schemes mprove detecton performance also by ncreasng the number of transmtted symbols. In the channel codng and M ary modulaton, computatonal cost and complexty s much hgher over the bnary sgnalng scheme. evertheless, ths complexty can be greatly reduced n case of M ary modulaton wthout affectng the performance. Ths complexty les n the message decodng and sequence generaton. By crcular shftng and phase modulaton, sequence generaton can be made qute smpler and number of correlator detectors can be sgnfcantly reduced. The paper s organzed as follows: Secton 2 ntroduces proposed M-ary modulaton and demodulaton n SS watermarng. atermarng archtecture s gven n Secton 3. Secton 4 shows the mplementaton results of 6 X 6 bnary watermar and fnally secton 5 concludes and remars about the mportant fndngs of the present wor. Manuscrpt receved October 5, 27 Manuscrpt revsed October 2, 27

2 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.7 o., October M-ary Modulaton and Demodulaton n SS atermarng 2. Embeddng Let B denotes the bnary valued watermar bt strng as a sequence of bt long nformaton. B b, b, K, b n }, b {,} { 2 To proect the host sgnal or cover mage I nto watermarng space ξ the mage transformaton χ s appled to the mage.e. χ : (I L ) [C L ] where C s the proected mage and L, L are length of vector I and C respectvely. For bnary sgnalng, optmal modulaton functons are antpodal sgnal pars. For embeddng of bt watermar, a set of two dmensonal orthogonal sequence, {,2,,} s used where defnes the secret ey used as ntalzng seed to generate the set. These sequences/ code patterns can be consdered as unformly dstrbuted random sets of ndependent random varables havng a zero mean, unt varance b-level dstrbuton. Hence, n order not to ntroduce nter symbol nterference (ISI). {(x,y), (x,y) }, φ The watermar s defned as the superposton of all modulated and weghted sequence or code patterns : () [ L' ] ( b ') α[ ], L' where α s the weghtng factor or modulaton ndex and b represents the bt value mapped from {,} to {-,}. The watermared or stego mage s now gven by addng watermar to mage representaton n embeddng space ξ and applyng nverse transformaton: [ I ] ([ ] [ ] L C + (2) χ L' L' Optmal modulaton ndex depends on the vsual characterstcs of the host mage, watermar embeddng space and the metrc used to measure the dstorton. Sophstcated modulaton ndex functons ncrease watermar energy by mantanng vsual dstorton and hence results ncrease of overall performance of the system. Accordngly, SS watermarng schemes can be called as sgnal adaptve tme SS watermarng. 2.2 Detecton The ntroduced watermarng scheme can be seen as a modulaton system n whch mage acts as addtve nose. evertheless, t s a common method n dgtal watermarng to use a lnear correlator as detecton statstcs. Let the watermared/ stego mage s proected nto watermarng space by applyng the mage transform: χ :[ I ] [ C L ] (3) ow the detecton statstcs or decson varable t s obtaned by evaluatng the zero lag cross-covarance functon between the sgnal features of proected stego mage and each sequence/ code pattern t m ( ), C m ( C ) () where m (X) represents the average of the sequence X. If X represents the elements of X wth, 2,, L m (X) can be mathematcally expressed as follows: m s (4) () (5) s The symbol () n equaton (4) ndcates the zero lag cross-correlaton and for two sequences S and R, the zero lag cross-correlaton s gven by S, R () ' s r L where s and r are the elements of sequence S and R respectvely wth, 2,,L. The bt b s detected as - f t > and as otherwse. Therefore, the computaton of t becomes, m m (, C m ( m ( ( C ) ), [ C + m ( C )] ), C + α. b ), C b + α. ' ' m ( C ). The above analyss ndcates that code patterns used for spread spectrum watermarng should posses some specfc propertes. atermar detecton s mproved f the followng condtons are satsfed. ),, 2,... L should be dstnct sequences wth zero average. ) The spatal correlaton, should be mnmzed. Ideally, sequences and should be orthogonal. ) Each for, 2,..., L should be uncorrelated wth mage coeffcent bloc C when mage predcton (for estmatng mage dstorton) s not used before evaluatng the cross correlaton. Snce, code patterns are zero mean and nonoverlappng orthogonal sequences, so above propertes () and () are satsfed. (6)

3 56 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.7 o., October Desgn of the Experment The proposed wor consders a bnary mage of sze (6 X 6) as watermar and (256 X 256), 8 bts/pxel gray mage as host/ cover mage. ow, the queston s what features of cover sgnal s sutable for robust watermarng? There s probably no answer to ths queston as dfferent features have dfferent levels of robustness to certan attacs. Therefore, n order to show better robustness of M-ary modulaton scheme data s embedded n wavelet transform doman as t provdes mportant class of features for data hdng. avelet transform provdes the co-ont representaton of smultaneous space-frequency resoluton of mage sgnal. avelet coeffcents are more effcent n representng perceptually mportant sgnal features and thus potentally more robust to dstorton. avelet transform also attracts attenton n varous mage processng applcatons ncludng de-nosng and upcomng compresson standard JPEG-2 due to ts specfc level of robustness. The host mage can be modeled as approxmately..d., sequence wth gaussan dstrbuton by ths wavelet transform. Here lnear, addtve modulaton functon s used for data embeddng. Therefore, all watermar features are treated equally and spread over them evenly. ow, n order to accomplsh better spectrum spreadng data s embedded n LL and HH sub bands of DT decomposton whle the same s done nto few selected channels wth low and hgh varance value n M-Band T decomposton doman. A sngle or a set of bnary valued sequence equal to the sze of sub band/ channel are generated and for each matrx, the orthogonal code s obtaned by complementng the bts of code. If code s used for data embeddng n LL sub band (H 2, H 3, H 4, H 24 n M-Band), the orthogonal code ( ) s used for data embeddng n HH sub band (H 4, H 42, H 43, H 3 ). The varance of dfferent sub-bands and channels along wth cross-correlaton propertes of sequences are depcted n fg Embedder Archtecture Case I: Message as combnaton of sngle/ several symbols bt long watermar of two symbols s mapped to total number of symbols n the symbol message where each symbol s represented my m bts (m ). Therefore, dstnct symbol n symbol message s M 2 m, formed by groupng log 2 M bts of orgnal message to one symbol. Each symbol s represented by a b-level spread spectrum modulaton functon. Hence, M dfferent sets of code pattern each havng numbers of b-level modulaton functon are requred for M-ary embeddng n the watermarng space. Case II: M-ary Phase Modulator In M-ary modulaton case I, a total (M X ) number of b-level code patterns are requred where and M 2 m, m,2,,l, L s the length of watermar bt strng. Here a set of (M X ) reference patterns are formed from a sngle reference b-level modulaton functon n the followng way: A reference pseudo nose sequence (s) r s generated as an..d., (ndependent & dentcally dstrbuted) gaussan dstrbuted sequence: [] ~ (,),,2, L, where L s the length of the feature vector C or [] ~ (,),,2, (M X ), M dstnct symbol, total symbol. Based on r, a set of (M X ) s are generated to be crcular shft versons of r, satsfyng Case I: If (M X ) < L r [+m] f < L -m; [] (7) r [+m-l ] otherwse m,,,(m X )-; Case II: If (M X ) L,2,,L. r [+m] f <(M X )-m [] (8) r [+m-(m X )] otherwse m,,,(m X )-;,2,,L. Snce watermared feature vector C and reference modulaton functon r has dfferent lengths, therefore zeros are appended to C r : so that t has the same length as C [] C [] for L for L+ (MX) (9) 3.2 Detector Structure Case I: Lnear Correlators (Matched flter) To extract/ decode a symbol at one partcular poston, lnear correlaton between the test sgnal (embedded mage bloc) and reference modulaton functon/ code pattern of that partcular poston for all the sets of eys are computed. th a maxmum lelhood (ML) estmator, the embedded symbol s decoded as the ndex number of the reference code pattern, whch has the maxmum correlaton wth the test sgnal.

4 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.7 o., October m arg maxc( C, ) () ε {,, M-} f m L M M (snce ) m arg maxc( C, ) () ε {,, M-} f m < L M > M Case II: Method of Elmnaton (based on tree structure) To detect the embedded reference modulaton functon at one partcular poston, all the relevant code patterns are frst dvded nto two groups. {, K } {, K } { K, },( ) 2 ε {,2,,}, 2 (2) Then the test sgnal C s correlated wth the sum of all code patterns n each group: 2 C C ( C, ) C ε {,2,,} 2 C ( C, ) (3) ε {,2,,} If C > C 2, the embedded pattern m must be n the frst group and otherwse n the second group. The group wth m s then dvded nto two ¼ sze groups to decde the locaton of m. Ths process contnues untl the exact poston of m s located; whose ndex number s the estmate of the embedded message. Case III: th the crcular versons of s as reference set, t s no longer need to compute (M X ) correlatons between the watermared feature vector C and (M X ) s desred from r can be computed by a smple method as follows: by: The lnear correlaton between C C [ ] C [ C ] [ ] [ ]) and s gven [ ]),,,L - L L (M X < L ) M X (M X > L ) It s DFT C [ y ] ( [ ]) e C [ ] [ C [ C [ ] 2 [ ] e ' ( y 2 [ [ ]) e y ]) e 2 y 2 y [ ] * F ( C ) F ( ), y,,, L - Ths becomes (4) * c[ ] F [ F ( C ) F ( )],,,,L - where F(.) and F - (.) denote DFT and IDFT operatons respectvely. Therefore, usng equaton (4), symbol decodng can be computed convenently and effcently. Here c(c[], c[],,c[l ]), c[] s the correlaton between C and wth c[], c[],, c[-] calculated accordng to equaton (4), one can mmedately estmate the embedded message through maxmum lelhood estmaton. 4. Results and Dscusson The Spread spectrum (SS) M-ary watermarng scheme s appled n wavelet transform doman (DT & M-Band T) over large number of benchmar mages. It s qute clear that mperceptblty and robustness effcency are mproved wth the ncrease of payload amount.e. M value but at the same tme computatonal cost and complexty regardng code pattern and decodng process are also ncreased. The reason for the latter pont s that for data hdng we need two steps: () code pattern generaton for embeddng and (2) detecton statstcs computaton by correlators. Both the steps ncorporate sgnfcant computatonal complexty. That s why the embeddng algorthm-case I at the condton > M provdes relatvely low computatonal complexty but at the cost of comparatvely low robustness whch s agan better than bnary antpodal sgnalng. The same algorthm s maxmally mproved n respect to robustness effcency at the condton M wth hghest level of computatonal cost. Ths s because the number of code pattern ncreases wth the decreasng number of embeddng thereby ncreasng the number of correlators also. Ths problem of computatonal cost and complexty s relatvely solved n the detecton algorthm-case II: method of elmnaton type correlators but wth relatvely hgher detecton errors.

5 58 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.7 o., October 27 Therefore, t s a general expectaton to evolve wth M-ary method where robustness and computatonal complexty wll be mproved wth ncrease n payload (.e. M values). M-ary phase modulaton satsfes our requrement towards code generaton and detecton to a greater extent. The robustness performance for any value of M n M-ary modulaton s better for both DT and M-Band T decomposton than spatal doman M-ary SS watermarng. Ths s because code patterns are of gaussan nature (..d.) but the host mage dstrbuton s not that type. But DT and M-Band T can approxmate the host features to a gaussan one so that correlator detector can decode at optmally best. The result s reported aganst lossy compresson operaton. However, the result s also vald for other types of ntentonal and delberate mage mparment operatons. In order to substantate our clam for the present wor numercal results are shown n fg. 4-9 and n Table & Concluson The paper crtcally analyzes the usage of M-ary modulaton prncple n SS watermarng scheme. It s found that M-ary modulaton sgnfcantly mproves the robustness performance of SS watermarng scheme for values of M larger than 4. The nherent computatonal cost and complexty ssues wth ncreasng value of M (e.g. M > 256) s also mtgated by the mplementaton of M-ary phase modulaton SS watermarng and method of elmnaton type detecton statstcs. M-ary modulaton scheme s found to be more effcent compared to channel codng scheme because of non-avalablty of proper code length. Ths s because of the varable nature of channel dstorton, whch depends on the sze, content and varous types of operaton appled on the watermared data. It s also found that, the robustness performance of wavelet transform (DT and M-Band T) s better over spatal doman as wavelet transform models the host data towards gaussan..d. (ndependent & dentcally dstrbuted) nature. But wavelet coeffcents are never gaussan dstrbuton n a strct sense thereby correlator functons (matched flter) wor at the sub optmally best level. Durng embeddng, lnear addtve, non-adaptve modulaton functon s used. But the problem s that dfferent host features have dfferent capabltes n carryng a watermar due to ther perceptual roles and magntudes. Therefore these areas of SS watermarng need further mprovement n the context of M-ary modulaton. atermarng, IEEE Trans on sgnal processng, pp , Aprl 23. [2] I. J. Cox, J. Kllan, F. T. Leghton, T. Shamoon, Secured Spread Spectrum atermarng for Multmeda, IEEE Trans on Image Processng, vol. 6, pp 6-6, June 2. [3] R. Grobos, T. Ebrahm, atermarng n JPEG-2 Doman, Proc. of IEEE orshop on Multmeda Sgnal Processng, pp. 3-5, 2. [4] J. Mayer, A. V. Slvero, J. C. M. Bermudez, On the Desgn of Pattern Sequences for Spread Spectrum Image atermarng, Internatonal Telecommuncatons Symposum, Brazl. [5] S. P. Maty, M. K. Kundu, T. S. Das, P. K. and, Robustness Improvement n Spread Spectrum atermarng usng M-ary Modulaton, Proc. of at. conf. on Communcaton, pp , Jan 25. [6] M. Kutter, Performance Improvements of Spread Spectrum Based Image atermarng Schemes Through M-ary Modulaton, Prelmnary Proceedngs of the Thrd Internatonal Informaton Hdng Informaton Hdng orshop, pp , Dresden, 999. [7] I. Daubechs, Orthogonal bases for Compactly Supported avelets, Comm., Pure Appl. Math, Vol. 4, pp , 988. [8] M.K.Kundu and M.Acharya, M-Band avelets: Applcaton to Texture Segmentaton for Real Lfe Image Analyss, Internatonal ournal of wavelets, Multresoluton and Informaton proceedng, vol, pp5-49, 23. [9] C. S. Burrus, R. A. Gopnath, H. Guo, Introducton to avelets and avelet Transform, A Prmer, Prentce Hall, J, 997. [] I. Selesne, Hlbert Transform Pars of avelet Bases, IEEE Sgnal Processng Letters Vol. 8, o.6, 2. [] C-S. Lu, S-K. Huang, C-J. Sze, H-Y. M. Lao, Coctal atermarng for Dgtal Image Protecton, IEEE Transacton on Multmeda Vol. 2, o. 4, 2. [2] D. V. Sarwate, M. B. Purseley, Correlaton Propertes of Pseudorandom and Related Sequences, Proceedngs of IEEE Vol. 68, o. 5, pp , 98. Trtha Sanar Das receved hs B. Tech. n Electroncs and Telecommuncaton Engneerng from Vdysagar Unversty n year 22 and M. E. from Bengal Engneerng & Scence Unversty, Shbpore, B, Inda n 24. At present he s a Lecturer n Electroncs and Communcaton at Gurunana Insttute of Technology, Panhat, Kolata, Inda. He s currently dong hs Ph.D from Jadavpur Unversty. Hs feld of nterest spans dgtal mage processng, sgnal processng, watermarng, communcaton and VLSI. References [] H. S. Malvar and D. A. F Florenco, Improved Spread Spectrum: A new Modulaton Technque for Robust

6 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.7 o., October Vay Harshchandra Manar receved the B. E. degree from agpur Unversty and M. Tech. n Electroncs Engneerng from VIT agpur, (formerly agpur Unversty) MS, Inda n 992 and 995, respectvely. Presently he s worng as a Lecturer n Government Resdental omen s Polytechnc, Yavatmal (MS), Inda. He s currently deputed to Jadavpur Unversty to carry out hs Ph. D. under QIP. Hs feld of nterest ncludes dgtal sgnal processng, dgtal mage processng, data hdng and watermarng. Dr. Subr Kumar Sarar receved hs B. Tech. From Unversty of Calcutta, Inda n 98, M. Tech. from Unversty of Calcutta, Inda n 983 and Ph. D (Tech) from Insttute of Rado Physcs and Electroncs, Unversty of Calcutta n 999. From 992 to 999 he was lecturer n Bengal Engneerng and Scence Unversty, Shbpore, Howrah. Currently he s Professor n Jadavpur Unversty, Kolata, Inda. Hs present feld of nterest s applcaton of soft computng tools n smulatons of devce models and also n the feld of Hgh Frequency and Low Power Consumng Devces and wreless moble communcaton. Hs research nterests also nclude sngle electron devces and next generaton dgtal electroncs and mage processng. Fg. 3. Cross-correlaton of Crcular shfted sequences Fg. 4. Comparsons of Conventonal & Proposed M-ary scheme Fg.. Covarance of dfferent sub-band combnatons of DT decompostons Fg. 2. Varance of dfferent channels of M-band T decomposton Fg. 5. Probablty of Error Vs Symbol length (M)

7 6 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.7 o., October 27 Table : umercal Results of Robustness aganst dfferent mage mparments Fg. 6. Robustness aganst Addtve hte Gaussan nose (AG) wth ncreasng symbol rate Type of Attac hte Gaussan ose Salt & Pepper ose Hstogram Equalzaton Medan Flterng ener Flterng Sharpenng Parameter of Attac Bt-Error Rate (BER) σ 5 σ σ 5 D. D.3 D x -2 /A f.sze 2 x 2 f.sze 3 x 3 f.sze 4 x x -2 f.sze 2 x 2 f.sze 3 x 3 f.sze 4 x x -4 Moderate Hgh Table 2: Strmar Test Results Fg. 7. Gaussan Flterng Fg. 8. Image Croppng wth ncreasng symbol rate Attac Type Remove 7 rows and 5 columns Remove 5 rows and columns JPEG 5 JPEG 2 JPEG 25-9 Change aspect rato x:.8 y:. Change aspect rato x:.9 y:. Change aspect rato x:. y:. Rotaton -.25 Rotaton -2. Rotaton. Rotaton 9. Scale.25 Scale.5 Scale.75 Scale.9 Scale.5 Scale 2. Sharpenng 3x3 Shearng x: 5. y:. Strmar random bend Average BER Fg. 9. JPEG-2 wth varyng symbol rate