Steganography in JPEG2000 Compressed Images

Transcription

1 824 IEEE Transactons on Consumer Electroncs, Vol. 49, No. 4, NOVEMBER 2003 Steganography n JPEG2000 Compressed Images Po-Chy Su and C.-C. Jay Kuo, Fellow, IEEE Abstract Informaton hdng n JPEG2000 compressed mages s nvestgated n ths research. The challenges of covert communcaton n ths state-of-the-art mage codec are analyzed and a steganographc scheme s then proposed to relably embed hgh-volume data nto the JPEG2000 btstream. A specal mode of JPEG2000 s employed, and ts usage and functons are explaned and justfed. Expermental results are gven to demonstrate the performance of the proposed algorthm. Index Terms Informaton hdng, steganography, JPEG2000. I. INTRODUCTION INFORMATION hdng n dgtal mages, vdeo or audo clps has drawn much attenton n recent years [1]-[3]. Some auxlary nformaton s mplctly combned wth a pece of multmeda data,.e. the host sgnal, to form a composte sgnal for certan nterestng applcatons. Dgtal watermarkng s one type of nformaton hdng. The copyrght related nformaton about the meda data s nserted to enforce ntellectual property rght protecton. Castng a fragle sgnal nto the meda fle to assst detectng or locatng subsequent unauthorzed modfcaton may serve as a potental tool for data authentcaton. The other applcaton s to transmt a large volume of nformaton covertly n a multmeda fle va nformaton hdng technques. The objectve s to delver the data to the ntended recever relably and secretly. We can vew the nnocuous host meda fle as a camouflage to fool possble eavesdroppers or as a secret channel from a communcaton vewpont. The case of covert communcaton can also be termed as steganography, whch s derved from the Greek words meanng covered wrtng. In ths research, we wll focus on steganography n dgtal mages. Two nformaton hdng approaches have been commonly used. One s to cast the nformaton on the magery data wthout takng any fle format nto consderaton. The other s to explctly operate on a specfc mage format. Most of the prevous work n the latter category, such as the methods presented n [4] and [5], was based on JPEG. Ths s partly because that most of the stll mages crculated nowadays are compressed wth JPEG. The other reason s that, as a block DCT codec, JPEG lends tself to a good canddate for nformaton hdng due to ts fxed block structure. Gven that mages are usually compressed before transmsson or storage, nformaton hdng n a compressed data format should be a better choce. The authors are wth the Integrated Meda Systems Center and Department of Electrcal Engneerng-Systems, Unversty of Southern Calforna, Los Angeles, CA Emal: {pochysu,cckuo}@sp.usc.edu. JPEG2000 s an upcomng stll mage codng standard. Ths new standard complements JPEG by provdng several mportant features such as resoluton/qualty progressve mage transmsson, better reslence to bt-errors, and Regon of Interest (ROI) codng, etc. It s beleved that JPEG2000 wll be used wdely and ts rch features wll beneft many emergng applcatons. As many mages wll be compressed by JPEG2000 n the near future, t s worthwhle to nvestgate how to hde hgh-volume data n JPEG2000 compressed mages effcently. Ths s the man objectve of our research. Ths paper s organzed as follows. We frst provde a bref revew of the basc archtecture of JPEG2000 n Secton II, whch should offer suffcent nformaton to help understand our concerns n desgnng an nformaton hdng scheme n ths mage standard. Readers are referred to [6]-[8] for more detals. Then, we wll pont out some challengng ssues of nformaton hdng n JPEG2000 and present a steganographc scheme under ths compresson framework n Secton III to acheve relable covert communcaton. Expermental results wll be shown n Secton IV to demonstrate the feasblty of the proposed method. Fnally, concludng remarks are gven n Secton V. II. REVIEW OF JPEG2000 CODING The block dagram of JPEG2000 s shown n Fg. 1. In the encoder sde, the orgnal mage frst undergoes the forward mage transform, whch ncludes the nter-component transform and the ntra-component transform (.e. the wavelet transform). The resultng wavelet coeffcents are then quantzed and coded. Scalar or Trells Coded Quantzaton s used, whch may cause some nformaton loss f the mage s lossy compressed. The codng paradgm of JPEG2000 can be vewed as a two-tered structure as shown n Fg. 1 and wll be explaned n detal below. Rate control s appled n quantzaton and codng steps to acheve the targeted bt-rate. The decoder sde bascally reverses the operatons by decodng and dequantzng the bt-stream and applyng the nverse mage transform to reconstruct the mage. Now, let us take a closer look at the two-tered codng structure n JPEG2000. We llustrate the concept from the encoder part. In ter-1 codng, the quantzaton ndces for each subband are parttoned nto code blocks, whch are ndependently coded usng a bt-plane coder. More specfcally, the code block s coded one bt-plane at a tme startng from the most sgnfcant bt-plane to the least sgnfcant bt-plane. Each ndvdual bt-plane s coded wth three codng passes. The frst codng pass s the sgnfcance propagaton pass, whch conveys sgnfcance and necessary sgn nformaton for samples that have not yet been found to be sgnfcant and are predcted to become sgnfcant. The Contrbuted Paper Manuscrpt receved September 29, /00 $ IEEE

2 P.-C. Su and C.-C. J. Kuo: Steganography n JPEG2000 Compressed Images 825 second codng pass s the magntude refnement pass. All bts that became sgnfcant n a prevous bt-plane are conveyed n ths pass by usng bnary symbols. The fnal pass s the cleanup pass, n whch all bts that have not yet been coded durng the prevous two passes are encoded. The symbols generated from the sgnfcance propagaton and the magntude refnement passes can be ether raw coded or entropy coded by a context-based adaptve bnary arthmetc coder,.e. MQ coder. The cleanup pass s run-length coded and always processed by the MQ coder. The output of the ter-1 encodng process s therefore a collecton of compact representatons of codng passes for the code blocks. Source Image Expanded Image Forward Transform Inverse Transform Quantzaton Dequantzaton Ter-1 Encoder Ter-1 Decoder Fg. 1. The block dagram of JPEG2000. Ter-2 codng operates on the summary nformaton of code blocks, whch determnes block contrbutons to the fnal code stream. The bt-stream of each code-block s truncated n an optmal way so as to mnmze dstorton subject to the bt-rate constrant. Bascally, truncaton can only happen at the end of a codng pass. Feasble truncaton ponts have been further dentfed as those located wthn the convex hull of the ratedstorton curve. To mnmze the dstorton wth the targeted bt-rate constrant, the exact truncaton pont s chosen from these feasble ones n each block after the statstcs of a collecton of code blocks are avalable. The codng passes are then packaged nto packets and output to form the fnal code stream. The orderng of packets n the code stream facltates progressve transmsson of the mage by fdelty, resoluton or component. Snce the rate dstorton algorthm of the ter-2 codng s appled after all subband samples have been compressed n ter-1 codng, the rate-control mechansm of JPEG2000 can thus be referred to as Post-Compresson Rate- Dstorton (PCRD) optmzaton. Besdes, t should be noted that some codng passes may be dscarded by ths optmzed truncaton procedure so that the ter-2 codng s another prmary source of nformaton loss n the codng path besdes quantzaton. III. INFORMATION HIDING IN JPEG2000 Ter-2 Encoder Ter-2 Decoder Compressed Bt-stream A. Challenges of Informaton Hdng Our objectve s to develop an nformaton hdng scheme under the framework of JPEG2000 so that a hgh volume of data can be secretly transmtted to the ntended recpent n a more relable fashon. Frst, we have to determne an approprate poston n JPEG2000 codng flow for nformaton hdng. From the structure gven n Fg. 1, there are three postons to be consdered. We examne ther sutablty for nformaton hdng below. (1) Image Transform After the ntra-component mage transform, the mage data are transformed to wavelet coeffcents. If we modfy the data at ths stage, the scheme wll be equvalent to many exstng wavelet-based watermarkng algorthms, whch may take other wavelet-based codecs as attacks. For dgtal watermarkng, the payload s usually low, and multple embeddng wth the majorty detecton or the spread-spectrum concept can be appled. The embedded nformaton can thus have suffcent robustness aganst lossy compresson of another codec. However, multple embeddng s not sutable n the data hdng applcaton as the requred payload s hgh and we have to make effcent use of the already lmted bandwdth. (2) Quantzaton Quantzaton s an mportant step n mage compresson, whch reduces certan vsual redundancy for effcent codng. As mentoned n Secton II, quantzaton s the prmary source of nformaton loss. We can avod losng the hdden data due to coarser quantzaton by embeddng them n the quantzaton ndces. Ths soluton works for JPEG (as many JPEG-based nformaton hdng schemes operate on the quantzaton ndces), but s not good for JPEG2000. It should be noted that wavelet-based coders usually truncate the compressed btstream to fulfll the targeted bt-rate. In JPEG2000, PCRD optmzaton strategy s adopted so that the truncaton mechansm s actvated after the whole mage has been compressed. If embeddng the nformaton at ths stage, we cannot predct exactly whch quantzaton ndex or bt-plane of an ndex wll be ncluded n the fnal code stream. The embedded nformaton wll not be perfectly recovered unless the lossless compresson mode s chosen (3) Codng If the nformaton s embedded n the output of ter-2 codng,.e. the JPEG2000 packets, t can be guaranteed that all the embedded nformaton wll be receved wthout error and n a correct order because we avod the two major sources of nformaton loss,.e. quantzaton and bt-stream truncaton. However, we wll have dffculty n modfyng the packets for nformaton embeddng snce the bt-streams may have been compactly compressed by the arthmetc coder. Careless modfcaton could result n falure of expandng the compressed mage. B. Progressvely Embeddng a Hdden Image and Its Drawbacks There does exst a soluton to partally acheve hgh-volume nformaton hdng n wavelet-based codecs. From the prevous dscusson, we know that the hdden nformaton could be lost after the subsequent truncaton of the compressed bt-stream f t s embedded n the quantzaton ndex. However, an ntutve concept ndcates that certan ndces may have a better chance of survval snce they are of more sgnfcance. To be more specfc, wavelet coeffcents n lower frequency subbands are

3 826 usually more mportant than those n hgher frequency bands. An extreme example s resoluton progressve transmsson, n whch lower frequency subbands wll be sent pror to hgher ones. In ths case, lower frequency bands should be preserved well at hgh bt-rates. On the other hand, although some portons of the embedded nformaton may be lost, the recpent can stll receve enough nformaton f the sgnfcant portons are transmtted successfully. Therefore, f the hdden nformaton s a dgtal mage of a smaller sze, we may transmt t by embeddng n the quantzaton ndces. Ths general dea should work n most of the wavelet codecs. We brefly descrbe the dea and factors that should be consdered. Frst of all, we decompose the hdden mage wth the wavelet transform. The number of wavelet decomposng levels and the mage sze should be related to the host mage. For example, f the host mage s 512 by 512 and decomposed wth 3 levels, we may set the rule that the hdden mage s onefourth the sze,.e. 256 by 256, wth the same decomposng levels. We may need to pad the sdes of the hdden mage when ts sze s smaller than requred. Ths strategy s to make sure that no mage specfc nformaton should be necessarly known by the recpent. Besdes, t should be noted that coeffcents n each level be represented by a fxed number of bts, whch s also known by both sdes. Then we embed the wavelet subbands of the hdden mage accordng to ther mportance nto the counterparts n the host mage. Bascally, lower (hgher) frequency subbands of the hdden mage wll be embedded n the lower (hgher) frequency subbands of the host mage. Embeddng s based on modfcaton of lower btplanes of the host quantzaton ndex,.e. replacng ts least sgnfcant bts wth the bts of the hdden nformaton. The number of the bt-planes used for nformaton embeddng wll affect both capacty and qualty of the resultng mage. Embeddng follows certan predefned agreements between the nformaton embedder and the recpent. A rule of thumb s that the sgn of a coeffcent, whch s comparatvely mportant than the magntude, should be embedded more carefully. In addton, bt-planes of lower frequency subbands of the hdden mage should also be better embedded than those of the hgher frequency subbands. Permutaton can be appled to the hdden nformaton before embeddng to ncrease uncertanty. The recpent should be able to permute t back correctly to reconstruct the hdden mage. We should not embed any data n the lowest frequency band,.e. the DC band, of the host mage to avod generatng unpleasant artfacts. Many exstng wavelet-based watermarkng schemes, such as [9] and [10], may emphasze the functon of progressve embeddng/detecton. However, there are some drawbacks n the dea of progressve hdden mage transmsson. Frst of all, we know from the prevous dscusson that many parameters have to be known n advance by both the sender and the recever so that the hdden mage can be correctly extracted and perceved. Nevertheless, f a lot of nformaton has to be shared beforehand between the sender and the recever through a certan sde channel, the steganographc scheme becomes IEEE Transactons on Consumer Electroncs, Vol. 49, No. 4, NOVEMBER 2003 mpractcal. Besdes, f the hdden nformaton s an mage, the eavesdropper may have more chances to detect ts exstence, gven that the characterstcs of an mage are qute dfferent from that of the host sgnal. Encrypton mght not be applcable here snce we cannot guarantee that the hdden nformaton be transmtted wthout errors due to the truncaton of JPEG2000 and the fact that an encrypted bt-stream s usually not robust to any error. The most we can do to ncrease the securty level s to permute the poston of the wavelet coeffcents of the hdden mage as mentoned above. It s not clear how ths permutaton procedure wll prevent the eavesdropper from detectng the hdden mage. Fnally, the requrement of embeddng an mage as the hdden nformaton sgnfcantly lmts the usage of ths algorthm. The embedded nformaton should be general bnary data, n any form such as texts, encrypted bt-streams, raw/compressed mages, or else, to acheve practcal covert communcaton. It s apparent that the method presented above may not meet our requrements. In the followng sectons, we would lke to develop a practcal steganographc scheme to convey hgh-volume general bnary data n a more secret and relable manner. C. Informaton Hdng wth Lazy Mode Codng As analyzed n Secton III-A, n order to transmt general bnary data secretly wthout error, we should embed the hdden nformaton n the JPEG2000 packets. However, we have to avod modfyng the bt-stream that s entropy coded for ts correct decodng. In JPEG2000, a so-called lazy mode codng opton s ntroduced, n whch the arthmetc codng procedure s completely bypassed for most of the sgnfcance and the magntude refnement codng passes. To be more specfc, except for the four most sgnfcant bt-planes, the sgnfcance and magntude refnement passes n the remanng bt-planes are raw coded. Thanks to ths lazy mode codng opton, we propose a steganographc scheme, whch solves all the abovementoned problems to acheve relable covert communcaton n JPEG2000. Ths lazy mode choce for the proposed scheme can be justfed below. It has been observed that, at hgh bt-rates, the symbols produced by the sgnfcance and magntude refnement passes have dstrbutons close to a unform one so that there s no substantal beneft from arthmetc codng. Bypassng the MQ coder can thus reduce the complexty and mprove the executon speed wthout degradng the codng performance. For nformaton hdng, the mages used to host a large volume of data are usually compressed at hgh bt-rates. Therefore, t s approprate to embed the nformaton n JPEG2000 compressed bt-stream wth the lazy mode enabled. Besdes, the hdden nformaton may also be unformly dstrbuted gven that encrypton s usually appled. It turns out that the data n these passes are pretty good canddates for nformaton hdng wth less chance of beng notced. Informaton hdng s acheved by modfyng the data n the codng passes. Among the three types of codng passes, only the magntude refnement passes are chosen n our steganographc scheme. The cleanup passes are defntely

4 P.-C. Su and C.-C. J. Kuo: Steganography n JPEG2000 Compressed Images 827 prohbted snce they are always entropy/run-length coded and modfcaton of them wll cause errors n expandng the btstream. The sgnfcant passes carry the sgnfcance and necessary sgn nformaton. Although the sgnfcant passes may be raw coded, the modfcaton may cause ether sgn flppng or decodng errors as well. The magntude refnement passes carry subsequent bts after the most sgnfcant bt for each sample. When the magntude refnement passes are raw coded, modfcaton of them wll not cause problems. Besdes, the sgnfcant bts or MSB of each sample can act as vsual maskng so that the change of these subsequent bts can be made less obvous. Furthermore, the amount of raw coded magntude refnement passes s qute large so carryng a large payload s achevable. By consderng these factors, we conclude that only the magntude refnement pass s sutable for steganographc purposes. D. Selecton of Refnement Passes for Embeddng In order to avod degradng the composte mage severely, we may only use a subset of the raw coded magntude refnement passes for nformaton embeddng. We descrbe three scenaros of selectng sutable magntude refnement passes as follows. (1) Fxed number of the lowest bt-planes The most straghtforward method s to examne the bt-planes where these raw coded magntude refnement passes are located. Gven that the total number of meanngful bt-planes n a subband s K, whch s sgnaled explctly n the code stream, the modfcaton for nformaton hdng s restraned to those btplanes lower than K-G. The smaller G s assgned, the more btplanes can be modfed so that more hdden nformaton can be carred. Bascally, ths dea s smlar to the common LSB-based nformaton-hdng methodologes, n whch only the lowest few bt-planes are modfed to avod ntroducng vsble artfacts. The subtle dfference s that, n ths steganographc scheme, not all the data n those bt-planes but the data ncluded n the magntude refnement passes are affected by the embeddng process. The advantage of ths embeddng scenaro s ts smple mplementaton snce both the nformaton embeddng and extracton can be done effcently n the ter-2 codng. Besdes, both of the nformaton embedder and extractor only need to know the parameter G to acheve successful secret communcaton. The amount of the nformaton that has to be transmtted through other subsdary channels s thus sgnfcantly reduced. (2) Bt-planes below the MSB A more sophstcated way s to take the MSB of the quantzaton ndex nto account. In ths embeddng scenaro, the dgt of a quantzaton ndex s allowed to be modfed for nformaton hdng f t s located at the bt-plane that s below the MSB of a sample by at least $P$ bt-planes. Ths dea s somewhat analogous to those watermarkng schemes that use the magntude of a host coeffcent to scale the embedded watermark [11]. If a host sgnal s large n magntude, we may modfy t wth a greater scale so that more nformaton or a stronger watermark can be embedded owng to the maskng effect. Therefore, the capacty of the steganographc scheme may thus be mproved wthout further affectng the vsual qualty. In addton, we can ntentonally gnore some bt-planes of certan coeffcents for embeddng due to a more advanced vsual maskng model or ncreased securty concerns. However, the complexty of the mplementaton ncreases accordngly snce the nformaton embeddng/extracton processes become coeffcent-wse, nstead of smply vewng the whole bt-planes as a group. In ths way, the ter-1 codng has to be nvolved n the nformaton embeddng/extracton processes. Besdes, we have to deal wth such problems as the varyng length of the codng passes and the specal patterns reserved for error reslence n a more careful manner. (3) Backward embeddng A better way of selectng sutable magntude refnement passes for steganography s to consder the mportance of these passes to the overall qualty of the compressed mage. The ter-2 codng acheves rate scalablty through multple qualty layers. Each codng pass s ether assgned to one of the layers or dscarded accordng to ts rate-dstorton slope, whch s calculated n the ter-1 codng and passed to the ter-2 codng for organzng the code stream. The codng passes wth larger rate-dstorton slopes are ncluded earler n the lower layers, whle the codng passes wth smaller rate-dstorton slopes are ncluded later n the hgher layers. Our goal s to hde as much nformaton as possble wth the mnmal mpact on the mage qualty. Obvously, the embeddng process should functon n the opposte order of the ter-2 codng by selectng less mportant codng passes earler for modfyng. Therefore, we propose the dea of backward embeddng to take account of the mportance of the passes to the overall mage qualty. After the ter-2 codng determnes the passes that wll be ncluded nto the code stream, an extra procedure embeds the nformaton backward, startng from the last ncluded refnement pass. On one hand, modfyng these nsgnfcant passes may be smlar to dscardng them, whch does not severely affect the mage, compared to those passes ncluded earler n the lower layers. On the other hand, the length of these passes could be larger so that we can actually hde more nformaton. The embeddng procedure can be carred out untl the mage qualty has been degraded wthn an acceptable level. A termnaton pattern may be necessary to sgnal the end of embeddng so that the decoder can learn when to stop extractng the hdden nformaton. E. Issues on Backward Embeddng By consderng the complexty and the performance, we adopt backward embeddng n the proposed steganographc scheme. Wth multple layers beng employed n JPEG2000, backward embeddng can easly select those passes that are less mportant to the compressed mage for nformaton hdng wthout consderng the locaton of the bt-plane and the assocated coeffcent. The embeddng process can thus be done very effcently snce only the ter-2 codng s nvolved n the embeddng process and the codng structure of JPEG2000 can be kept almost the same except that an extra procedure to embed the data n a backward fashon s necessary. It s noteworthy that a major beneft of the proposed JPEG2000

5 828 steganographc scheme over the exstng JPEG schemes s ts controllable rate-dstorton trade-off. Here, the rate means the capacty of the hdden nformaton whle the dstorton s referred to as the addtonal degradaton resultng from the nformaton hdng process. In the exstng JPEG embeddng schemes, the effect on mage qualty due to nformaton hdng s usually unpredctable snce t s dffcult to acheve good rate-control n the JPEG standard. In contrast, our scheme may explot the characterstcs of wavelet-codecs to acheve a better balance between the payload of the hdden nformaton and the resultng mage qualty. As the embeddng process starts from the last ncluded magntude refnement pass, the endng pont of embeddng wll decde the dstorton of the composte mage. A smple scenaro for controllng capacty and dstorton goes as follows. If the mage wll be compressed wth the bt-rate equal to B bpp, we can guarantee that the composte mage wll have the qualty of the mage compressed wth C bpp, where C<B, by embeddng the raw coded magntude refnement passes untl the one that s ncluded n both the bt-stream wth B bpp and the bt-stream wth C bpp. The dea s easy to mplement but the estmaton of the qualty s conservatve snce we do not modfy all the three codng passes n a bt-plane but magntude refnement passes, whch may only occupy a small porton. We can see ths argument from an extreme case that C s equal to 0 whle the resultng composte mage wll stll have a reasonably good qualty. Therefore, to demonstrate the advantages of the proposed JPEG2000 steganographc scheme over other exstng schemes based on the JPEG standard, a more accurate qualty measurement s necessary. If MSE s used as the qualty measure, the most accurate way s to calculate the addtonal dstorton n the spatal (or the mage) doman. However, the complexty s too hgh n ths approach snce we have to expand the compressed btstream several tmes after each embeddng of a pass. A more practcal way s to evaluate the addtonal dstorton n the wavelet doman along wth the generaton of the bt-stream. In JPEG2000, the overall dstorton n terms of MSE of the compressed mage and the orgnal mage can be estmated n the wavelet doman drectly. For each code block, B, the n embedded bt-stream s truncated to the rates, R, wth the truncaton pont, n. The contrbuton from B to the dstorton mprovement n the reconstructed mage s denoted by D n. The overall mage dstorton, D, can be calculated by, n 2 n 2 D = D = { ω ( s [ k] s [ k]) }, (1) b k B where s [k] denotes the subband samples n the code block B, s n [k] denotes the quantzed representaton of these samples assocated wth the truncaton pont n, and ω denotes the b L2-norm of the wavelet bass functon for the subband, b, to whch the code block belongs. Ths approxmaton s vald provded the wavelet transform's bass functons are orthogonal and the quantzaton errors n each of the samples IEEE Transactons on Consumer Electroncs, Vol. 49, No. 4, NOVEMBER 2003 are uncorrelated. Although nether of the assumptons s held perfectly, the estmaton s acceptable n the case of compresson. Followng the same route, we can calculate the addtonal dstorton ntroduced by nformaton hdng. Durng the embeddng process, dstorton happens when the bt flps from 0 to 1 or from 1 to 0,.e. when the orgnal bt and the embeddng bt are dfferent. The addtonal dstorton can then be calculated by the sum of the dfference between the orgnal quantzaton ndex and the ndex after possble bt flppng and scaled wth the quantzaton step sze and the L-2 norm of the wavelet base functon. In the mplementaton, we need not keep the orgnal quantzaton ndex or the resultng ndex to calculate ther dfference but evaluate the dstorton on the fly wth each bt-plane processed. For the same ndex, f a bt n a certan bt-plane changes from 1 to 0, we record t as a negatve change whle f a bt changes from 0 to 1, we vew t as a postve change. The dfference between the ndex values before and after nformaton hdng can be calculated by takng the sum of the postve changes subtracted by the sum of the negatve changes. We gve a quck example. If the orgnal value s 44 (101100) and the value after embeddng s 50 (110010). Each of the postve change and negatve change happens twce. The sum of postve changes wll be = 18 and the sum of negatve changes wll be = 12 so the dfference wll be 6. Ths way of calculaton s straghtforward, and the beneft s ts adaptaton to the bt-plane codng structure. However, the exact determnaton of dstorton comes wth a few drawbacks, whch ncrease the complexty of the mplementaton. Frst of all, the nformaton embeddng process s carred out n the ter-2 codng. At ths stage, what the ter-2 encoder sees s only a bt-stream. It knows nothng more than the poston of the bt-plane or the code-block to whch the pass belongs. When flppng a bt n a pass, we may not know exactly whch coeffcent wll be affected. Ths problem may be solved by passng more nformaton from ter- 1 codng to ter-2 codng. Snce only the raw coded magntude refnement passes wll be embedded wth the hdden nformaton, the ter-1 encoder may have to send extra nformaton to the ter-2 encoder, ndcatng the correspondence between the bt n the pass and ts assocated coeffcent. For a 64 by 64 block, the extra nformaton may be 64 by 64 bts long for each pass wth 1 representng that the pass ncludes the bt nformaton and 0 representng the null nformaton. The encoder s then able to scan wth the same order to dentfy whch coeffcent wll be affected by a certan bt flppng to evaluate the dstorton. Nevertheless, the other problem exsts. We have to keep the dstorton value for each coeffcent n each code block, whch ncreases the memory consumpton sgnfcantly and contradcts the requrement of effcent memory usage n the ter-2 codng. Next, we provde two rough evaluaton methods, whch smply operate n the btplane level and we wll then valdate ther feasblty by comparng them wth the exact dstorton approach. The frst method s to calculate the dstorton by summng

6 P.-C. Su and C.-C. J. Kuo: Steganography n JPEG2000 Compressed Images 829 up MSE of bt flppng n each bt-plane. If a bt flppng happens, we add t to the overall dstorton wthout takng account of the coeffcent. The addtonal dstorton D wth one bt flppng s expressed as 2 2 p 2 D = ω b ( b ) (2 ), (2) where ω s the L-2 norm of the wavelet bass functon, b s the quantzaton step sze assocated wth subband b and p s the bt-plane poston. It s apparent that the dstorton calculated n ths way s only a rough estmaton snce the exact change of the dstorton wth each coeffcent s not recorded and we smply use the sum of the square of the dfference n each bt-plane to estmate the square of the sum of the dfference n each btplane. However, n most of the common cases, we found that many ntermedate terms between bt-planes tend to cancel each other. Besdes, the overestmate and underestmate compensate each other, as the number of the bt-planes s large. Ths method wll thus provde us a pretty good estmaton of the addtonal dstorton ntroduced by nformaton embeddng. The second estmaton method s to utlze the dstorton of each pass calculated durng the ter-1 encodng. The dstorton mprovement of each pass s estmated by the dfference between the dstorton measured before and after ncludng the pass. The dstorton s recorded and then evaluated wth the rate ncrease of ths pass for rate control. We can vew ths step as a measurement of mportance of the pass snce the ncluson of the pass wth large dstorton mprovement makes great mpact on the compressed mage. We beleve that, n nformaton embeddng, f the host sgnal and the hdden sgnal are both of the unform dstrbuton, the dstorton ntroduced by embeddng or modfyng the content of the pass would be very smlar to dscardng the whole pass. Therefore, we may also use ths dstorton measurement of a pass as an estmaton of the dstorton resultng from nformaton embeddng. A clear beneft of ths method s that the overhead of nformaton hdng s made as small as possble snce the embeddng process shares the same procedure of dstorton measurement n the codng process. Besdes, ths estmaton method allows us to measure the dstorton of the host mage even before the secret nformaton s embedded. By usng ths estmaton method, we may predct the dstorton of many mages n advance and choose a more approprate one for hdng the targeted nformaton. It should be noted that the md-pont reconstructon rule s often employed n the dstorton measurement n the ter-1 codng. Informaton hdng, however, results n bt flppng wthout md-pont reconstructon as done n the dequantzaton step. Therefore, we multply the dstorton estmated n the ter-1 codng by 2 as a measurement of the dstorton ntroduced by the modfcaton of ths pass. F. Steganalyss of the Proposed Informaton-Hdng Scheme Unlke dgtal mage watermarkng, robustness s not the man ssue of steganographc applcatons snce we do not b expect the attacker wll modfy the mage content by ether transcodng or other sgnal processng procedures, especally n the case that the secret nformaton s hdden n a compressed fle for storage or crculaton. Capacty, relablty and securty are the three major concerns. In our nformatonhdng scheme wth the JPEG2000 standard, we can guarantee that the secret transmsson be carred out wthout errors by embeddng the nformaton n raw coded magntude refnement passes. We can acheve hgh-volume covert communcaton by choosng an approprate amount of passes for nformaton embeddng. The remanng ssue to be dscussed s the securty of the proposed scheme. In ths secton, we try to play the role of an eavesdropper to clarfy some securty ssues to whch we should pay attenton when desgnng a steganographc scheme. The frst step the eavesdropper may take s to analyze the bt-stream structure. One drawback of the proposed scheme s that the nformaton-hdng procedure s operated n a specal mode of JPEG2000,.e. the lazy mode. Some people may queston that the attacker may suspect the exstence of certan hdden nformaton n the JPEG2000 bt-stream f t s compressed wth the lazy mode. Eventually, ths problem depends on how popular the lazy mode wll be. From our vewpont, the lazy mode codng operaton s very useful n hgh bt-rate mage compresson. The complexty can be sgnfcantly reduced by employng the lazy mode codng because the computatonally expensve MQ codng s bypassed whle codng effcency wll not be affected much, especally n the hgh bt-rate codng, whch s a very possble case for nformaton hdng. The ROI codng may be the only scenaro that the lazy mode s not approprate to be appled. Therefore, we do not see many reasons for not adoptng the lazy mode codng n a broad range of magery applcatons. Next, the eavesdropper may analyze the data n the magntude refnement passes to see f any unusual dstrbuton appears. As mentoned before, the reason why the MQ coder does not mprove codng effcency n the magntude refnement passes n the lower few bt-planes s that the dstrbuton of these data s close to a unform one. Therefore, f we can encrypt or scramble the data n some way so that the hdden nformaton also has a unform dstrbuton, the chance that the eavesdropper can tell the dfference wll be small. However, we have to make sure that some specal patterns desgned for ncreased error reslence n JPEG2000 should not appear n the modfed bt-stream. Asde from the purpose of correct expandng the compressed bt-stream, ths cautous strategy can prevent that the appearance of the mark at the wrong poston reveals the exstence of the hdden nformaton. The eavesdropper may further expand the compressed btstream to see f any abnormal stuaton happens. In the proposed steganographc scheme, we do not change the length of the magntude refnement passes but modfy the bnary content. In general cases, the modfed magntude refnement passes generate the same number of symbols wth the orgnal passes. However, some specal stuatons may happen when more symbols or less symbols are generated than expected.

7 830 Ths comes from the fact that extra bts are added by the encoder to avod generatng error reslence patterns as descrbed before. The naccurate number of symbols wll not affect the normal operaton of the codng but may gve a loophole for the eavesdropper to sense the exstence of the hdden nformaton. Besdes, the bt-stuffng at the end of the pass to comply wth the byte boundary may appear dfferently f embeddng s done n a careless way. We may not embed nformaton nto the bts that are used for bt-stuffng f a unfed bt-stuffng byte s adopted n most of the JPEG2000 coders. In other words, we should only modfy the bts that come from the magntude refnement passes and avod the bts used n the smplfed mplementaton or certan markers to ensure better securty. A more advanced eavesdropper may examne the behavor of wavelet coeffcents to see f possble hdden nformaton exsts. Ths s actually an nterestng topc to nvestgate f nformaton hdng has dfferent effects on wavelet coeffcents from the quantzaton process. We beleve that modfyng the JPEG2000 packets may result n some ntrgung phenomenon on the nverse wavelet transform. We may study ths subject by avod the quantzaton step,.e. by operatng the nformaton-hdng process n the lossless compresson mode. We leave ths part as future research. IV. EXPERIMENTAL RESULTS The mplementaton of our steganographc scheme was based on JASPER [8]. JASPER s a free reference code of JPEG2000 offerng the baselne codng wth an excellent performance and thus serves as a good framework. In the experment, we used the four well-known gray-level mages, Lena, Boat, Peppers and Baboon, as the host mages, all wth the same sze of 512 by 512, to carry the generalzed bnary nformaton. We assume that the mage wll be compressed nto the bt-stream wth a hgh bt-rate,.e. 2 bpp. It should be noted that the length of the bt-stream s not changed by the nformaton-hdng process. In other words, the embeddng process wll only affect the qualty of the mage by modfyng the bt-stream content,.e. certan magntude refnement passes, as descrbed n Secton III-C. Frst of all, we would lke to justfy the clam that the lazy mode codng does not gve an nferor performance compared wth the normal mode n the case of hgh bt-rate mage codng. We compressed Lena, Baboon, Boat and Peppers mages from 0.5 bpp to 2 bpp wth the normal mode and the lazy mode and then compared the PSNR values of the expanded mages n each case. The results are shown n Table I. We see that the dfference of PSNR values s very lmted. It should be noted that the larger dfference, such as Peppers n 2 bpp, comes from the fact that the two compressed bt-streams are dfferent n ther lengths although we have tred to make them as close to the target bt-rate as possble. Ths result may suggest that the lazy mode s applcable n many cases and the compresson/decompresson speed s thus tremendously mproved wthout much qualty degradaton. IEEE Transactons on Consumer Electroncs, Vol. 49, No. 4, NOVEMBER 2003 One of the man advantages of ths steganography scheme over other JPEG-based schemes s ts controllable dstorton durng the process of nformaton embeddng. As we mentoned before, we can estmate the addtonal dstorton n MSE n the wavelet doman qute precsely. However, n order TABLE I THE COMPARISON OF PSNR (DB) USING THE LAZY AND THE NORMAL MODES UNDER VARIOUS BIT-RATES (BPP) Bt-rate Lena n Lena z Boat n Boat z Peppers n Peppers z Baboon n Baboon z Image n : mage compressed wth the normal mode. Image z : mage compressed wth the lazy mode. to smplfy the structure wthout ncreasng memory consumpton, we presented two methods to roughly estmate the dstorton ntroduced by nformaton embeddng,.e. the method one estmatng the overall MSE by addng up errors n each bt-plane and the method two utlzng the exstng dstorton value calculated n the ter-1 codng. We would lke to verfy ther applcablty by some experments. Fgure 2 shows the addtonal MSE measured n Lena, Boat, Peppers and Baboon. The horzontal axs represents the number of magntude refnement passes that are chosen for nformaton hdng. As more passes are modfed for embeddng the secret data, the MSE ncreases accordngly. The dash lnes are the actual MSE whle the plus marks and cross marks show the estmated MSE values calculated by the method one and method two respectvely. We can see that the two methods track the actual dstorton pretty well. They both perform better at the begnnng of the estmaton but worse at the end snce the errors accumulate as more passes are processed. Some calbratng steps may need to be taken to acheve a more accurate measurement. In steganographc applcatons, we are nterested n the relatonshp between the capacty and the resultng composte mage. We embedded the four mages wth the same bnary data and examned the MSE ncrease of the mage due to the embeddng process assocated wth the payload of the hdden nformaton. We can see from Fg. 3 that the capacty vares n the four mages even though they are compressed wth the same rato. Ths phenomenon should not be too surprsng snce the compresson affects mages n dfferent ways. In our scheme, the capacty s eventually determned by the number of magntude refnement passes that are raw coded so the dstrbuton of the data across the three passes wll affect the payload. Fg. 3 also shows that, wth more nformaton beng embedded, the MSE value grows as expected. However, they do not relate to each other lnearly. We take Lena as an example. Embeddng the frst 3000 bytes of the bnary data only results n about 1 addtonal MSE of each pxel n average

8 P.-C. Su and C.-C. J. Kuo: Steganography n JPEG2000 Compressed Images 831 but embeddng the next 1000 bytes quckly ncreases the MSE to 2. The last 100 bytes even cause the MSE to change by more than 9. Therefore, the embeddng process should evaluate ths curve to decde how much nformaton s approprate to be embedded. It should be noted that the MSE ncrease may be roughly estmated n conjuncton wth the embeddng process so that we can stop embeddng at the pont that a mnmal acceptable qualty s reached. result demonstrates the benefts of backward embeddng, n whch the less mportant refnement passes are used to carry the more mportant nformaton of the hdden mage owng to the layered structure of JPEG2000. Progressve transmsson of the hdden mage can thus be acheved. At the begnnng of the embeddng, the composte mage degrades lttle whle the PSNR of the hdden mage boosts quckly. At the latter part of the embeddng, the large sacrfce of the composte mage only helps to mprove the fner detal of the hdden mage so the ncrease of the PSNR value s lmted. Under ths scenaro, the embeddng process should proceed untl both the composte and the hdden mages have an acceptable qualty. (a) (b) V. CONCLUSION A steganographc scheme was proposed to hde a large volume of data nto JPEG2000 compressed mages for covert communcaton. Several desgn ssues were examned to help acheve relable nformaton hdng n ths state-of-the-art mage codng standard. Expermental results showed the practcablty of the proposed algorthms and the decent performance. Progressve transmsson of the hdden nformaton was also demonstrated. As future extenson, we would lke to apply a more rgorous steganalyss to the proposed scheme to further ensure ts securty. (c) (d) Fg. 2. Addtonal MSE estmaton of (a) Lena, (b) Boat, (c) Peppers and (d) Baboon. Fg. 4. PSNR of the composte mage vs. PSNR of the hdden mage Fg. 3. Capacty vs. addtonal MSE of the composte mage. Snce the payload s qute large n our experment, we may consder usng an mage wth a smaller sze as the ntended bnary data for nformaton embeddng. We compressed the mage, F-16 (128 by 128), nto a JPEG2000 bt-stream and embedded t nto the four host mages. The relatonshp between the PSNR of the composte mage and that of the hdden mage along wth embeddng s shown n Fg. 4. The REFERENCES [1] W. Bender, D. Gruhl, N. Mormoto and A. Lu, Technques for data hdng, IBM System Journal, vol. 35, no. 3, pp , [2] M. D. Swanson, M. Kobayash and A. H. Tewfk, Multmeda data embeddng and watermarkng technologes, Proc. IEEE, vol. 86, pp , [3] F. Hartung and M. Kutter, Multmeda watermarkng technques, Proc IEEE, vol. 87, no. 2, pp , [4] M. Hollman, N. Memon, B.-L. Yeo and M. Yeung, Adaptve publc watermarkng of DCT-based compressed mages, n Proc. SPIE Photoncs West, Securty and Watermarkng of Multmeda Contents, San Jose, CA, Jan [5] C. I. Podlchuk and W. Zeng, Watermarkng of the JPEG bt-stream, n Proc.Internatonal Conference Image Scence, Systems and Technology, Las Vegas, NV, June 1997.

9 832 [6] D. Taubman, Hgh performance scalable mage compresson wth EBCOT, IEEE Trans. on Image Processng, vol. 9, no. 7 pp , July [7] C. Chrstopoulos, A. Skodras and T. Ebrahm, The JPEG2000 stll mage codng system: An overvew, IEEE Trans. on Consumer Electroncs, vol. 46, no. 4, pp , Nov [8] M. D. Adams, The JPEG-2000 stll mage compresson standard, ISO/IEC JTC 1/SC 29/WG 1, Tech. Rep., Sep [9] X. G. Xa, C. G. Boncelet and G.R. Arce, A multresoluton watermark for dgtal mages, n Proc. IEEE Internatonal Conference on Image Processng, vol. 1, Santa Barbara, CA, July [10] M.D. Swanson, B. Zhu and A. H. Tewfk, Multresoluton scene-based vdeo watermarkng usng perceptual models, IEEE Journal Selected Areas n Communcatons, vol. 16, pp , May [11] I. J. Cox, F. T. Leghton and T. Shamoon, Secure spread spectrum watermarkng for multmeda, IEEE Trans. on Image Processng, vol. 6, no. 12, IEEE Transactons on Consumer Electroncs, Vol. 49, No. 4, NOVEMBER 2003 Po-Chy Su was born n Tape, Tawan n He receved the B.S. degree from the Natonal Tawan Unversty, Tape, Tawan, n 1995 and the M.S. and Ph.D. degrees from the Unversty of Southern Calforna, Los Angeles, n 1998 and 2003, respectvely, all n Electrcal Engneerng. Hs research nterests nclude nformaton hdng, dgtal mage processng and mage/vdeo compresson. C.-C. Jay Kuo receved the B.S. degree from the Natonal Tawan Unversty, Tape, n 1980 and the M.S. and Ph.D. degrees from the Massachusetts Insttute of Technology, Cambrdge, n 1985 and 1987, respectvely, all n Electrcal Engneerng. Dr. Kuo was Computatonal and Appled Mathematcs (CAM) Research Assstant Professor n the Department of Mathematcs at the Unversty of Calforna, Los Angeles, from October 1987 to December Snce January 1989, he has been wth the Department of Electrcal Engneerng-Systems and the Sgnal and Image Processng Insttute at the Unversty of Southern Calforna, where he currently has a jont appontment as Professor of Electrcal Engneerng and Mathematcs. Hs research nterests are n the areas of dgtal sgnal and mage processng, audo and vdeo codng, wavelet theory and applcatons, multmeda technologes and large-scale scentfc computng. He has authored around 500 techncal publcatons n nternatonal conferences and journals, and guded more than 50 students to ther Ph.D. degrees. Dr. Kuo s a member of SIAM, ACM, a Fellow of IEEE and SPIE. He s the Edtor-n- Chef for the Journal of Vsual Communcaton and Image Representaton. Dr. Kuo receved the Natonal Scence Foundaton Young Investgator Award (NYI) and Presdental Faculty Fellow (PFF) Award n 1992 and 1993, respectvely.