Reversible Data Hiding Based on Two-level HDWT Coefficient Histograms

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1 Reversble Data Hdng Based on Two-level HDWT Coeffcent Hstograms Xu-Ren Luo 1, Chen-Hu Jerry Ln 2 and Te-Lung Y 3 1 Department of Electrcal and Electronc Engneerng, Chung Cheng Insttute of Technology, Natonal Defense Unversty, Tahs, Taoyuan 33509, Tawan, Republc of Chna nrgman.luo@gmal.com 2 Department of Electrcal and Electronc Engneerng, Chung Cheng Insttute of Technology, Natonal Defense Unversty, Tahs, Taoyuan 33509, Tawan, Republc of Chna jerryln@ndu.edu.tw 3 Department of Computer Scence and Informaton Engneerng, Chna Unversty of Technology, Hukou, Hsnchu 303, Tawan, Republc of Chna yntl@cute.edu.tw ABSTRACT In recent years, reversble data hdng has attracted much more attenton than before. Reversblty sgnfes that the orgnal meda can be recovered wthout any loss from the marked meda after extractng the embedded message. Ths paper presents a new method that adopts two-level wavelet transform and explots the feature of large wavelet coeffcent varance to acheve the goal of hgh capacty wth mperceptblty. Our method dffers from those of prevous ones n whch the wavelet coeffcents hstogram not gray-level hstogram s manpulated. Besdes, clever shftng rules are ntroduced nto hstogram to avod the decmal problem n pxel values after recovery to acheve reversblty. Wth small alteraton of the wavelet coeffcents n the embeddng process, and therefore low vsual dstorton s obtaned n the marked mage. In addton, an mportant feature of our desgn s that the use of threshold s much dfferent from prevous studes. The results ndcate that our desgn s superor to many other state-of-the-art reversble data hdng schemes. KEYWORDS Reversblty, Marked meda, Wavelet Transform, Wavelet Coeffcent, Dstorton, Hstogram 1. INTRODUCTION Known as lossless, nvertble, or dstorton-free data hdng, reversble data hdng s a type of delcate and vulnerable technque that s manly used for qualty-senstve applcatons such as multmeda content authentcaton, medcal magng systems, law enforcement, and mltary magery. The prmary goal n such applcatons s to recover the orgnal meda exactly. The key factors of reversble data hdng nclude the embeddng capacty and vsual qualty of the marked meda, whch are for achevng satsfactory performance n varous applcatons[1][2]. The scheme we present n ths paper s an attempt to acheve hgh-performance reversble data hdng, n whch embeddng and recoverng processes n the frequency doman are devsed. The partculartes of large wavelet coeffcent varance and mnor changes n wavelet coeffcents followng the embeddng process are exploted to acheve hgh capacty and mperceptble embeddng. The rest of ths paper s organzed as follows. In Secton 2, prevous reversble data DOI : /acj

2 hdng schemes and ther characterstcs wll be brefly revewed n terms of embeddng capacty and vsual qualty. Our proposed scheme s ntroduced n Secton 3. Expermental results and comparatve analyses are presented n Secton 4. Fnally, some conclusons are drawn n Secton PREVIOUS STUDIES The related works reported n the lterature can be classfed nto two major types accordng to the doman for hdng nformaton. In type-i, the schemes work on the transform doman. In 2002, Frdrch et al. [3][4] presented a novel RS scheme starts by dvdng the mage nto three dsjont blocks, and then classfes these blocks nto dfferent groups R, S, and U usng a dscrmnatng functon. The flppng functon s also ntroduced to convert an R-group to an S- group and vce versa. The scheme further compresses the R and S groups wthout loss, and embeds message bts nto the state of each group. Although t s a novel technque, the payload s stll nsuffcent for some applcatons and hghly dependent on the compresson algorthm. Subsequently, Xuan et al. [5] proposed a new scheme n the nteger wavelet transform (IWT) doman. In ths scheme, one or multple mddle bt-plan(s) n the hgh-frequency sub-bands s(are) chosen to embed data bts. In 2003, a dfference expanson (DE) scheme was proposed by Tan [6], who appled the nteger Haar wavelet transform to an mage and exploted the DE technque to embed data bts nto the hgh-frequency coeffcents. However, ths scheme suffers from the locaton map problem that t s dffcult to acheve capacty control. Alattar [7][8] extended Tan s scheme by generalzng the DE technque to the trplets and quads of adjacent pxels. Kamstra et al. [9][10] mproved the DE scheme by predctng the expandable locatons n the hgh-pass band. Ths scheme mproves the effcency of lossless compresson, although the embeddng capacty s small. In 2007, Thod et al. [11] proposed a new scheme combnng hstogram shftng and predcton-error expanson approaches to remedy the problems of Tan s scheme. In type-ii, most of the studes focus on the spatal doman. Frdrch et al. [12] proposed an nvertble method to authentcate dgtal mage usng the jont b-level mage experts group (JBIG) lossless compresson technque to save free space for data embeddng. However, some nosy mages may lead to the use of hgher bt-planes and result n hghly vsble dstortons. The payload s hghly dependent on the lossless compresson algorthm. Celk et al. [13][14] employed the generalzed least-sgnfcant-bt (G-LSB) technque and the context-based adaptve lossless mage codng (CALIC) to acheve lossless data hdng. In 2006, N et al. [15] utlzed multple pars of maxmum and mnmum ponts of mage hstogram to acheve reversblty. In the scheme, the pxels are modfed for data embeddng and extracton. The greater the number of pars that are selected, the larger the payload becomes. Besdes, ths scheme can acheve hgher embeddng capacty through usng a mult-level strategy. However, such a strategy may lead to sgnfcant overhead and nsuffcent vsual qualty. N s scheme was also extended by others usng a locaton map rather than the knowledge of the pars to acheve reversblty [16][17]. Although the scheme s smple comparng to other schemes, sgnfcant overhead and nsuffcent vsual qualty are crtcal problems. In 2009, Km et al. [18] utlzed the feature of hgh spatal correlaton between neghborng pxels to acheve hghperformance data hdng. The embeddng capacty n the paper ranges from 6 to 210 k. For all of the schemes above, addtonal overhead s the most dffcult problems n the restore process. Ths paper proposes a new hstogram shftng technque n the frequency doman and uses the actual payload to acheve hgh-performance lossless data hdng. 3. THE PROPOSED SCHEME Ths secton present a new scheme that combnes the two-level Haar dscrete wavelet transform (HDWT) algorthm and new hstogram shftng rules. The HDWT algorthm can produce a 2

3 complete and lossless reconstructon durng synthess wth approprate flters. Moreover, the hstogram shftng rules used n the frequency doman can provde hgher flexblty n terms of scalablty n resoluton and dstorton. In our scheme, an orgnal mage s frst transformed nto a frequency doman and sub-bands n the mddle- and hgh-frequency ranges are then used to create sub-band dfferences. Each hstogram of these sub-band dfferences s then shfted accordng to a selected threshold. Message bts can then be hdden n the empty bns of the shfted hstograms. Fnally, the marked mage s reconstructed wth the sub-bands carryng and non-carryng hdden message by performng the nverse HDWT algorthm to complete the embeddng process. In the extractng process, the correspondng nverse operatons can exactly extract the hdden message and recover the orgnal mage Segmentaton algorthm The two-level HDWT algorthm utlzes the four-band sub-band codng system to decompose an mage nto a set of dfferent frequency sub-bands. As llustrated n Fgures 1 and 2, the sze of each sub-band s one ethth of the orgnal mage n the spatal doman. The eght dfferent sub-bands can be classfed nto the low-, mddle-, and hgh-frequency sub-bands. Snce the low-frequency sub-band of an mage ncorporates more energy than the other sub-bands, ts coeffcents are the most fragle that f any of them are manpulated, a suspect can vsbly detect the changes on the spatal doman mage. However, f the coeffcents n the mddle- and/or hgh-frequency sub-bands are altered, the changes n the spatal doman mage wll be mperceptble to human eyes. Consequently, ths characterstc s generally exploted to hde secret message. Fgure 1. The decomposton process of two-level HDWT 3.2. Data embeddng algorthm Fgure 2. A tow-level HDWT four-band splt of Lena We assume that the secret message s a random bnary sequence of 0s and 1s. The hstograms of the sub-band dfferences between the reference sub-band and the other destnaton sub-bands are shfted to embed the secret message. Fgure 3 depcts the overall data embeddng process, whch s descrbed n detal below. 3

4 Fgure 3. Flowchart of data embeddng process Embeddng_process ( η, T, ϕ ) Input: η, the orgnal mage; T, the threshold accordng to whch the empty bns n each hstogram are prepared; φ, the secret message. Output: ψ, the marked mage, f, the mark of embeddng status. Advan Proceedngs: Step 1: Create sub-bands by performng two-level HDWT four-band sub-band codng system on an nput mageη. Fve of the sub-bands to be utlzed are denoted by L H ( x, y ), H L ( x, y ), H H ( x, y ), L H 2 ( x, y ), and H H 2 ( x, y ), where ( x, y) ndcates the coordnate of the coeffcents n each sub-band. Step 2: Create sub-band dfferences D, 1 D and 2 D between the reference sub-bands L H, 3 LH 2 and the other destnaton sub-bands HL, HH and HH 2 by the followng formulas: D ( x, y ) = L H ( x, y ) H L ( x, y ) 1, (1) D ( x, y ) = LH ( x, y ) H H ( x, y ) 2, (2) D 3 ( x, y ) = L H 2( x, y ) H H 2( x, y ). (3) 4

5 Step 3: Denote the hstograms of D as h, where = 1,2,3. Step 4: Shft hstogram h accordng to the threshold T selected. The shfted h can be calculated as follows: ( ) ( ) ( ) ( ) h j + 8, f h j T + 1, h h j 8, f h j ( T + 1 ), (4) where 1, 2,3 = and ( ) j ndcates the value of each bn. These can also be obtaned by the followng formulas: D ( x, y ) = L H ( x, y ) H L ( x, y ) 1, (5) D ( x, y ) = L H ( x, y ) H H ( x, y ) 2, (6) D ( x, y ) = L H 2 ( x, y ) H H 2 ( x, y ) 3. (7) where HL ( x, y), HH ( x, y) HL ( x, y) HH ( x, y) HH 2 ( x, y) and HH ( x, y) 2 can be expressed as: HL( x, y ) 8, f h1 T + 1, HL( x, y ) + 8, f h1 ( T + 1 ). (8) HH ( x, y ) 8, f h2 T + 1, HH ( x, y ) + 8, f h2 ( T + 1 ). (9) HH 2( x, y ) 8, f h3 T + 1, HH 2( x, y ) + 8, f h3 ( T + 1 ). (10) Embeddng Data nto HL, HH and HH2: Step 5: We frst set an nteraton ndex l to T and then embed message bts sequentally by modfyng h. Each h s shfted to become h, where = 1, 2 and 3by the followng rules: h h h h h for l > , f h + 4, f h 8, f h 4, f h = = l, l, = l, = l, ϕ( n) = 0, ϕ( n) = 1, ϕ( n) = 0, ϕ( n) = 1, (11) h h ( j ) + 8, f h = 0, φ( n) = 0, h ( j ) + 4, f h = 0, φ( n) = 1, (12) for l = 0. The changes n the dfference hstograms above result n changes n the coeffcents. Ths mples that the modfed sub-band dfference D ( x, y) s scanned and modfed agan. Once the 5

6 value of D ( x, y) s equal to ±l, the message bt s embedded. Ths procedure s repeated untl there are no D ( x, y) wth the value of ±l. We then decrease l by 1 and repeat the step untll < 0. These steps can be formulated as follows: D ( x, y ) = L H ( x, y ) H L ( x, y ) 1, (13) D ( x, y ) = L H ( x, y ) H H ( x, y ) 2, (14) D ( x, y ) = L H 2 ( x, y ) H H 2 ( x, y ) 3. (15) f l > 0, ( ) HL ( x, y ) + 4, f h1 j = l, φ( n) = 1, HL ( x, y ) 4, f h1 = l, φ( n) = 1, HL ( x, y) HL ( x, y ) + 8, f h1 = l, φ( n) = 0, HL ( x, y ) 8, f h1 = l, φ( n) = 0. ( ) HH ( x, y ) + 4, f h2 j = l, φ( n) = 1, HH ( x, y ) 4, f h2 = l, φ( n) = 1, HH ( x, y) HH ( x, y ) + 8, f h2 = l, φ( n) = 0, HH ( x, y ) 8, f h2 = l, φ( n) = 0. ( ) HH 2 ( x, y ) + 4, f h3 j = l, φ( n) = 1, HH 2 ( x, y ) 4, f h3 = l, φ( n) = 1, HH 2 ( x, y) HH 2 ( x, y ) + 8, f h3 = l, φ( n) = 0, HH 2 ( x, y ) 8, f h3 = l, φ( n) = 0. (16) (17) (18) f l = 0, HL ( x, y) HH ( x, y) HH 2 ( x, y) HL ( x, y ) 4, f h1( j) = 0, φ(n) = 1, HL ( x, y ) 8, f h1 = 0, φ(n) = 0. (19) HH ( x, y ) 4, f h2 = 0, φ(n) = 1, HH ( x, y ) 8, f h2 = 0, φ(n) = 0. (20) HH 2( x, y ) 4, f h3( j) = 0, φ(n) = 1, HH 2( x, y ) 8, f h3 = 0, φ(n) = 0. (21) Centralzng Hstogram Step 6: When all the bns n the dfference hstogram are exhausted to hde data, eght bns, valued from 4 to 3, wll become empty. In ths case, the mark f s set to be 1 and all bns on the rght sde wll be moved left 4 bns, and those on the left wll be moved rght 4 bns n order to mprove the mage qualty by decreasng the varance of the dfferences n the coeffcents. Otherwse, the mark f s set to be 0. Each h s shfted to become h by the followng rules: 6

7 h ( j ) 4, f h ( j ) 0, h ( j > ) h ( j ) + 4, f h ( j ) < 0, (22) where = 1, 2 and 3. Shftng hstograms as above creates coeffcent changes, whch can be formulated as follows: D ( x, y ) = LH ( x, y ) H L ( x, y ) 1, (23) D (, ) (, ) (, ) 2 x y = LH x y HH x y, (24) D (, ) 2(, ) 2 (, ) 3 x y = LH x y HH x y, (25) where HL ( x, y), HH ( x, y) and HH ( x, y) 2 can be expressed as: HL ( x, y) HH ( x, y) HH 2 ( x, y) HL ( x, y ) + 4, f h1 > 0, HL ( x, y ) 4, f h1 < 0. (26) HH ( x, y ) + 4, f h2 > 0, HH ( x, y ) 4, f h2 < 0. (27) HH 2 ( x, y ) + 4, f h3 > 0, HH 2 ( x, y ) 4, f h3 < 0. (28) Embeddng Data nto LH: Step 7: Usng the sub-band HL wth the hdden message as the reference, a fourth dfference hstogram s created wth the orgnal sub-band LH. The secret message s then hdden nto ths dfference hstogram accordng to steps 1 to 6; as a result, LH ( x, y) wll be created. Ths completes the embeddng process. Obtanng Marked Image: Step 8: Reconstruct the marked mage by utlzng the nverse of the two-level HDWT fourband sub-band codng on the sub-bands. We frst reconstruct the LL sub-band and then reconstruct the marked mage ψ. Ths procedure can be formulated as follows: LL IDW T S S S S = ( LL 2, LH 2, HL 2, HH 2 ), (29) ψ = IDWT ( S LL, S LH, S HL, S HH ). (30) Preventng overlap and over/underflow A flag-bt s used to ndcate whether the bn n the dfferent hstograms s overlap or not. The flag-bt s set to 1 f a bn value shfted by ± 8 overlaps wth one shfted by ± 4. The flag-bt s set to 0 f no overlap occurs. These flag-bts and the values of T and f n the btmap wll ultmately all be compressed wth an effcent compresson tool based on the LZMA algorthm. The compressed result s then hdden nto the reserved non-overlappng bns. Accordng to expermental results, ths process results n less than 2.74% overhead n full embeddng capacty for many dfferent types of mages. 7

8 Though the generated pxel values n the marked mage may be outsde the allowable range, the method n [12][18] could be used to deal wth the problem. The nterval range s dynamcally selected wth the mage characterstcs that t wll reduce dstortons to mnmum Data extractng and reversng algorthm Before extractng the hdden message, recever needs to verfy whether or not the marked mage ψ has been modfed. If there s more than one occurrence at h = 1, we can conclude that the marked mageψ has been tampered wth. The proposed scheme then stops the followng extracton steps mmedately. The extracton and recovery process s schematzed n Fgure 4. ψ Fgure 4. Flowchart of extracton and recovery process The detaled extracton and recovery process ncludes the followng steps: Extractng_process ( ψ, T, f ) Input: ψ, the marked mage; T, the threshold; f, the mark, accordng to whch the embeddng status s determned. Output: φ, the secret message; η, the orgnal mage. Advan Proceedngs: Step 1: Create sub-bands by performng two-level HDWT four-band codng on the marked mage ψ. Fve of the sub-bands to be utlzed are denoted by ψ ( x, y ), ψ ( x, y), ψ ( x, y), LH HL HL 8

9 x y ndcates the coordnate of the coeffcents n each sub- ψ (, ) LH 2 x y and (, ) HH 2 x y band. ψ, where (, ) Recoverng LL Sub-band Step 2: Create sub-band dfference Dψ 1( x, y) between the reference sub-band ψ LH 2 and the destnaton sub-band ψ HH 2 accordng to the followng formulas: D ψ ( x, y ) = ψ ( x, y ) ψ ( x, y ). (31) 1 L H 2 H H 2 Step 3: Denote the hstogram of D ( x, y) as ψ 1 hψ 1, where ndcates the value of each bn. Step 4: Check the dstrbuton of the hstogram hψ 1. If there s more than one occurrence at h =, the subsequent steps wll be stopped mmedately. ψ 1 1 Step 5: Check the embeddng status. Once the value of f s equal to 1, t can be concluded that the sub-band s completely flled wth hdden message bts. Subsequently, frst restore the orgnal dfference hstogram. The bns greater than or equal to zero wll be shfted to the rght by 4 and those less than zero to the left by 4. The restored hψ 1 can be calculated as follows: ( ) ( ) hψ 1 j + 4, f hψ 1 j 0, h ψ1 hψ 1 4, f hψ 1 < 0. (32) These can also be obtaned by the followng formulas: D ψ 1 ( x, y) = ψ LH 2 ( x, y) ψ HH 2 ( x, y), (33) where ψ (, ) 2 x y can be expressed as: HH ψ HH 2 ( x, y ) 4, f hψ 1 0, ψ HH 2 ( x, y) ψ HH 2 ( x, y ) + 4, f hψ 1 < 0. (34) Extractng Data: Step 6: Extract the hdden message φ ( n), where n denotes the ndex of a message bt, by shftng h 1 teraton ndex l s set to 0. Once a hψ 1 wth a value of ± ( + 4) 1 s retreved. On the other hand, a bnary bt 0 s retreved f h 1 l. Ths procedure s repeated untl there are no h ± ( + 8) ψ wth reference to the btmap and nvertng the embeddng process. Frst, the l s encountered, a bnary bt ψ 1 values of ± ( + 4) ψ has a value of l or ± ( l + 8). Subsequently, l s ncreased by 1. The same procedures as descrbed above are repeated untl l reaches T+1. The retrevng rule s as follows: ( ) ψ ( ) ( ) ( ) h ψ 1 j 8, f h 1 j = 8, h ψ 1 h j 4, f h j = 4, for l = 0. ψ 1 ψ 1 (35) 9

10 ( ) ψ ( ) ( ) ( ) h ψ1 j 8, f h 1 j = l+ 8, h ψ1 j 4, f h ψ1 j = l+ 4, h ψ1 h ψ1( j ) + 8, f h ψ1 = ( l+ 8), h ψ1( j ) + 4, f h ψ1 = ( l+ 4), for 1 l T. (36) Step 7: At the same tme, the modfed sub-band dfference D ψ ( x, y) 1 s also scanned and modfed. The extractng operaton can be expressed as the followng formula: φ ( n) 0, f D ( x, y) = ± ( l + 8 ), 1, f (, ) ( 4 ). ψ 1 D ψ 1 x y = ± l + (37) Ths procedure s executed untl l = T+1. Step 8: Remove the hdden message bts ( n) { 0,1} removng rule s gven by D ψ ( x, y) = ψ ( x, y) ψ ( x, y), (38) 1 LH 2 HH 2 where ψ (, ) 2 x y can be expressed as HH φ from the sub-band dfference. The ψ HH (, ) + 8, f = 8, = 0, ψ HH 2( x, y) ψ HH 2(, ) + 4, f ψ1 = 4, = 1, 2 x y hψ 1 x y h ϕ( n) (39) for l = 0, and ( ) l ) ( ) l ϕ( ) ψ HH 2( x, y ) + 8 f h ψ1 j = + 8, n = 0, ψ HH 2( x, y ) + 4 f h ψ1 j = + 4, n = 1, ψ HH 2( x, y) ψ HH 2( x, y ) 8 f h ψ1 = ( l+ 8), = 0, ψ HH 2( x, y ) 4 f h ψ1 = ( l+ 4), ϕ( n) = 1, (40) for 1 l T. Step 9: Restore the orgnal hstogram. The orgnal hstogram h ψ 1 can be calculated accordng to the followng rules: ( ) ψ ( ) ( ) ( ) h ψ 1 j 8 f h 1 j T + 1, h ψ 1 h ψ 1 j + 8 f h ψ 1 j ( T + 1). (41) for l L. The restoraton of the hstogram as descrbed above results n changes n the coeffcents. Ths can be descrbed by the followng formula: D ψ ( x, y) = ψ ( x, y) ψ ( x, y). (42) 1 LH 2 HH 2 10

11 Here, ψ (, ) 2 x y can be expressed as: HH ψhh ( x, y ) + 8, f h j T+ 1, ψhh 2( x, y) ψhh 2( x, y ) 8, f h ψ1 j ( T+ 1). 2 ψ1( ) ( ) (43) Obtanng the LL Sub-band: Step 10: Recover the orgnal Sub-band LL through the nverse operaton of the HDWT algorthm wth ψ (, ) LL2 x y, ψ (, ) LH 2 x y, ψ ( x HL, y ), and ψ (, ) HH 2 x y. Ths procedure can be formulated as follows: LL = IDWT ( ψ, ψ, ψ, ψ ). (44) LL2 LH 2 HL2 HH 2 Recoverng LH, HL and HH Sub-bands: Step 11: After recoverng the LL sub-band, steps 1 to 9 are repeated to recover the LH, HL and HH sub-bands as ψ ( x, y ), ψ ( x, y ) and ψ ( x, y ). LH Obtanng Orgnal Image: HL HH Step 12: Recover the orgnal mage η through the nverse operaton of the HDWT algorthm wth ψ ( x, y ), ψ ( x, y ), ψ ( x, y ) and ψ ( x, y ). Ths procedure can be formulated as follows: LH HL η = IDWT ( ψ, ψ, ψ, ψ ). (45) LL LH HL HH HH The above steps complete the extracton and recoverng procedure. 4. EXPERIMENTAL RESULTS AND COMPARISON LL In ths secton, a set of experments are conducted to evaluate the embeddng performance of our scheme. For these experments, we used many dfferent types of mages, ncludng some commonly used ones and two medcal mages (Fgure 5). The message bts to be embedded n our experments are randomly generated by a pseudo-random bnary generator. The threshold ranges from 0 to

12 Advanced Computng: An Internatonal Journal ( ACIJ ), Vol.2, No.1, January 2011 Fgure 5. 8-bt mages(a)lena, (b)baboon, (c)boat, (d)arplane, (e)aeral, (f)tank, (g)trucks, (h)medcal mage1, () Medcal mage2 Capacty versus Threshold Fgure 6 depcts relatonshp between the capacty n bpp and threshold. The embeddng rate almost reaches 0.78 bpp at threshold 100 for most the test mages. As expected the capacty s nearly proportonal to the threshold at the begnnng and saturates when the threshold s suffcently hgh. Fgure 6. Embeddng capacty at varous thresholds Vsual Qualty versus Threshold Fgure 7 llustrates the vsual qualty n PSNR of the marked mage versus threshold varyng from 0 to 100 for test mages on the premse that maxmal bts are embedded. The expermental result ndcates that the PSNR rses as the threshold ncreases and ths s not the case for the prevous works. The marked mage can acheve 43.3 db at the threshold 0, and above 46 db at the threshold of 100 for most test mages. It s noteworthy that the larger threshold T can contrbute less varaton n the hstogram of wavelet transform. Snce the mddle/hgh-frequency 12

13 sub-bands ncorporate less energy, the test mages wth larger varance between mddle and hgh-wavelet coeffcents such as MRI 1 and MRI 2 can acheve hgher vsual qualty than Baboon at the threshold 0. Fgure 7. PSNR at varous thresholds Comparson of vsual qualty wth other schemes In terms of actual embeddng capacty and vsual qualty, the proposed scheme was also compared wth the DE scheme [14], G-LSB scheme [5], Km et al. s scheme [9], and N et al. s scheme [6] for the Lena, Baboon, Boat, and Arplane mages as shown n Fgure 8. The embeddng capacty s the amount of embedded bts wth overhead subtracted. It can be observed that our scheme s stable and acheves hghest PSNR at the same bpp. 13

14 Fgure 8. Comparson of embeddng capacty n bpp versus dstorton wth exstng reversble schemes: DE scheme, G-LSB scheme, Km et al. s scheme, and N et al s scheme: (A) Baboon; (B) Lena; (C) Boat; (D) Arplane 5. CONCLUSIONS In ths paper, we propose a smple and hgh-performance reversble data hdng scheme, whch utlzes the large varance of wavelet coeffcents and ngenous hstogram shftng rules to 14

15 avod the decmal problem n pxel values durng recovery process. Our scheme, compared wth those reported prevously, can obtan better vsual qualty of the marked mages gven the same payload. The man reason s that the vsual qualty of our scheme does not decay wth ncreasng threshold as n the other schemes because the larger threshold can contrbute less varaton to the sub-band dfference hstograms. In addton, our scheme provdes the greatest embeddng capacty under nearly equvalent vsual qualty, as the partculartes of large wavelet coeffcent varance and mnor changes n the wavelet coeffcents followng the embeddng process are utlzed. It may be of nterest for future research that the threshold predctons, mult-round schemes, and fast algorthms wll be explored to meet real-tme applcaton requrements. REFERENCES [1] W. Bender, D. Gruhl, N. Mormoto, and A. Lu, (1996) Technques for data hdng, IBM systems Journal, vol.35, no.3, pp [2] M. Awrangjeb, An overvew of reversble data hdng, (December 2003) Proceedngs Sxth Internatonal Conference on Computer and Informaton Technology, Jahangrnagar Unversty, Bangladesh, pp [3] J. Frdrch, M. Goljan, and R. Du, Dstorton-free data embeddng, (2001) Proceedngs 4th Informaton Hdng Workshop, New York, vol.2137, pp.27 41, Lecture Notes n Computer Scence. [4] J. Frdrch, M. Goljan, and R. Du, (2002) Lossless data embeddng new paradgm n dgtal watermarkng, EURASIP J. Appl. Sgnal Process. vol.2, pp [5] G. Xuan, Y.Q. Sh, J. Chen, J. Zhu, and Z. N, W. Su, (2002) Lossless data hdng based on nteger wavelet transform, IEEE Internatonal Workshop on Multmeda Sgnal Processng, St. Thomas, Vrgn Islands, USA, December [6] J. Tan, (2003) Reversble data embeddng usng a dfference expanson, IEEE Transacton on Crcuts and Systems for Vdeo Technology,vol.13, no.8, pp [7] A.M. Alattar, (2003) Reversble watermark usng dfference expanson of trplets, Proceedngs IEEE Internatonal Conference on Image Processng, vol.1, Barcelona, Span, pp , September. [8] A.M. Alattar, (May 2004) Reversble watermark usng dfference expanson of quads, Proceedngs IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Processng, Montreal, Canada, vol.3, pp [9] L. Kamstra and H.J.A.M. Hejmans, (August 2004) Wavelet technques for reversble data embeddng nto mages, Centrum voorwskunde en Informatca Rep. [10] L. Kamstra and H.J.A.M. Hejmans, (December 2005) Reversble data embeddng nto mages usng wavelet technques and sortng, IEEE Transactons on Image Processng, vol.14, no.12, pp [11] D.M. Thod, J.J. Rodrguez, (2007) Expanson embeddng technques for reversble watermarkng, IEEE Transactons on Image Processng, vol.16, no.3, pp [12] J. Frdrch, M. Goljan, and R. Du, (January 2001) Invertble authentcaton, Proceedngs of the SPIE, Securty and Watermarkng of Multmeda Contents, vol.4314, San Jose, CA, pp [13] M.U. Celk, G. Sharma, and A.M. Tekalp, (2002) Reversble data hdng, Proceedngs IEEE Internatonal Conference on Image Processng, Rochester, NY, pp [14] M.U. Celk, G. Sharma, A.M. Tekalp, and E. Saber, (February 2005) Lossless generalzed-lsb data embeddng, IEEE Transactons on Image Proceedngs, vol.14, no.2, pp [15] Z. N, Y.Q. Sh, N. Ansar, and W. Su, (March 2006) Reversble data hdng, IEEE Transactons on Crcuts and Systems for Vdeo Technology, vol.16, no.3, pp

16 [16] J. Hwang, J.W. Km, and J.U. Cho, (2006) A reversble watermarkng based on hstogram shftng, Internatonal Workshop on Dgtal Watermarkng, Lecture Notes n Computer Scence, Sprnger-Verlag, Jeju Island, Korea,, vol.4283, pp [17] W.-C. Kuo, D.-J. Jang, and Y.-C. Huang, (2007) Reversble data hdng based on hstogram, Internatonal Conference on Intellgent Computng, Lecture Notes n Artfcal Intellgence, Sprnger-Verlag, Qng Dao, Chna, vol.4682, pp [18] K.-S. Km, M.-J. Lee, H.-Y. Lee, and H.-K. Lee, (2009) Reversble data hdng explotng spatal correlaton between sub-sampled mages, Pattern Recognton, vol.42, pp Authors Xu-Ren Luo receved the B.S. degree n Computer Scence and the M.S. degree n Electrcal and Electronc Engneerng, both from Chung Cheng Insttute of Technology (CCIT), Natonal Defense Unversty, Tawan, R.O.C., n 1997 and 2004, respectvely. He s currently pursung the Ph.D. degree n the area of nformaton assurance at the Electrcal and Electronc Engneerng Department, CCIT. Hs research nterests are focused on nformaton securty, data hdng, multmeda securty, and mage processng. Chen-Hu Jerry Ln receved the M.S. degree from the Department of Electrcal Engneerng, Unversty of Mssour at Rolla n He then began hs career of teachng computer programmng at several colleges and unverstes of technology. He receved the Ph.D. degree n electrcal engneerng from Natonal Tawan Unversty n He has joned the faculty of Natonal Defense Unversty as an assocate professor snce Hs research nterests nclude sgnal processng and computer programmng. Te-Lung Yn receved the B.S., M.S. and Ph.D. degree from the Chung Cheng Insttute of Technology, Natonal Defense Unversty, Tawan, R.O.C., n 1989, 1995 and 2001, respectvely, n electrcal engneerng. He now s an assocate professor of the Department of Computer Scence and Informaton Engneerng at the Chna Unversty of Technology, Tawan, R. O. C.. Dr. Yn s a member of the IEICE socety and hs research nterests nclude data hdng, cryptography and mage processng. 16