Difference expansion and prediction for high bit-rate reversible data hiding

Difference expansion and prediction forhigh bit-rate reversible data hiding

Giulia BoatoMarco CarliFederica BattistiMarco AzzoniKaren Egiazarian

Difference expansion and prediction for high bit-ratereversible data hiding

Giulia BoatoUniversity of Trento

Department of Information Engineering and Computer ScienceTrento 38121, Italy

E-mail: [email protected]

Marco CarliFederica Battisti

University of Roma TREDepartment of Applied Electronics

Roma 00146, Italy

Marco AzzoniUniversity of Trento

Department of Information Engineering and Computer ScienceTrento 38121, Italy

Karen EgiazarianTampere University of TechnologyDepartment of Signal Processing

Tampere 33720, Finland

Abstract. Reversible data hiding deals with the insertion of auxiliaryinformation into a host data without causing any permanent degrada-tion to the original signal. In this contribution a high capacity reversibledata hiding scheme, based on the classical difference expansioninsertion algorithm, is presented. The method exploits a predictionstage, followed by prediction errors modification, both in the spatialdomain and in the S-transform domain. Such two step embeddingallows us to achieve high embedding capacity while preservinga high image quality, as demonstrated in the experimental results.© 2012 SPIE and IS&T. [DOI: 10.1117/1.JEI.21.3.033013]

1 IntroductionDigital watermarking schemes are usually adopted for pro-tecting rights of both digital data and their correspondingowners.1,2 Such methods invisibly embed a watermarkinto the data to be protected, thus allowing copyright protec-tion and illegal copies or illegal distributors identification viathe embedded information recovery. In particular, classicalwatermarking applications consist of copy control, broadcastmonitoring, fingerprinting, authentication, copyright pro-tection, and access control (see for instance Refs. 3 and 4).This technology can be used also for different purposes,such as multimedia indexing, enrichment, quality assess-ment, error concealment, and others. In general, the imposed

requirements are 1. robustness: the hidden data should bedetectable after classical signal processing, 2. imperceptibil-ity: the watermarked signal has to be perceptually similar tothe original one, and 3. capacity: the number of bits that canbe embedded should be as high as possible. In particularapplication scenarios (e.g., medical or military) anothercrucial constraint has to be considered 4. integrity of therecovered signal: the watermarking process has to be inver-tible, allowing the reconstruction of the original data after thewatermark extraction. This last requirement is achieved bythe so-called reversible watermarking techniques.

Many reversible watermarking algorithms have been pro-posed in the literature. The main difference among existingschemes lies in the particular method adopted for achievingreversibility. A first class of techniques exploits datacompression, which was introduced in Ref. 5 by Fridrichet al. by embedding with the watermark also the losslesscompressed original data as well as the correspondinglocation map. Celik et al. follow this idea in Ref. 6 bypresenting a generalized-LSB data hiding method. Xuanet al.7 propose an algorithm based on integer wavelettransform.

Another class of methods is based on histogram shifting.The basic idea to embed the watermark through histogrammodification was presented by Ni et al.8 where the pixelvalues in the range between peak and zero points are mod-ified. This technique is extended in, Ref. 9, where Hwanget al. propose to use two zero points and one peak pointof the histogram as triplets to insert the data, and more

Paper 11296 received Nov. 3, 2011; revised manuscript received May 7,2012; accepted for publication Jul. 9, 2012; published online Aug. 14, 2012.

0091-3286/2012/$25.00 © 2012 SPIE and IS&T

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recently by Tai et al.10 Bo et al.11 and Yoo et al.12 to extendhistogram shifting using small blocks of the image toembed data.

A third class of algorithms uses difference expansion toachieve reversibility. The first proposal is due to Tian13 andembeds the watermark by modifying the difference betweena pair of pixels, thus exploiting the redundancy among neigh-boring pixel values. Following Tian’s intuition, many exten-sions were proposed, which extend this approach totriplets,14 quads,15 three-pixel blocks,16 or n-pixel blocks,17,18

therefore allowing a reduction of the location map and anincrease in both efficiency and capacity. Further modifica-tions are presented in Ref. 19 by Thodi et al.20 by Kamstraet al.21 by Hu et al. while novel techniques based on otherinteger transforms are proposed by Coltuc et al.22 and byChen et al.23

Finally, a new idea based on pixel prediction is elaboratedin a set of recent contributions. The median edge detectorpredictor is used by Thodi et al.24 by Hong et al.25 and byYang et al.26 while the gradient adjusted prediction isexploited by Fallahpour et al.27 Kuribayashi et al.28 applydifference expansion and prediction, while Tsai et al.29

and Pan et al.30 apply predictive coding and histogram shift-ing in the specific domain of medical imaging. In Ref. 31,prediction and histogram shifting are dynamically applieddepending on human visual system characteristic while inRefs. 32 to 34, interpolation is used as prediction to calculatethe error band. Xuan et al.35 and Kuo et al.36 apply error con-trol and histogram shifting to embed data keeping goodstego-image quality. Tseng et al.37 study various predictors,while Hu et al.38 improve the location map compressibility,Sachnev et al.39 reduce its size, and Fujiyoshi et al.40 avoidany image-dependent parameter or location map. In Ref. 41,Yang et al. propose a data hiding technique in both the spatialand frequency domain which seems to be robust againstJPEG and JPEG2000. In this context, the authors proposedin Ref. 42 to exploit both local dependency and non-localsimilarity for prediction, by employing block-matchingtechniques, while in Ref. 43 histogram shifting was com-bined with a particular prediction exploiting directionaldifferences.

In this work a double embedding scheme is proposed,where a prediction stage, followed by prediction errorsmodification, is applied both 1. in the spatial domain and in2. the S-transform domain. The adoption of this multilayerapproach allow us to achieve very high capacity while pre-serving good image quality. A preliminary study on multi-resolution approaches was presented in Ref. 44 Recently,high capacity was achieved by in Refs. 45 and 46, whichwe compare the performances with in the experimentalsection.

The rest of the work is organized as follows: details on theproposed algorithm are given in Sec. 2, while the experimen-tal results are reported in Sec. 4, and finally in Sec. 5 someconclusions are drawn.

2 EmbeddingAs depicted in Fig. 1 the proposed scheme works as follows:the spatial prediction is first applied to the original image anda first embedding is performed exploiting the obtained pre-diction error. Then, an integer transform is applied to theresulting image, and a novel prediction scheme is appliedto the low-and high-frequency subbands. Thus, a secondembedding is performed on the prediction errors. Let usdetail all steps of the scheme:

1. Prediction is applied to the original image X ! fxi;jgi,j ! 1; : : : ; n in the spatial domain, thus obtaining Xas described in Sec. 2.1 and correspondingly thespatial prediction error

Esp ! X ! X: (1)

2. Embedding via difference expansion into predictionerror Esp as detailed in Sec. 2.4:

• Definition of positions used for embedding and ofthe corresponding location map (required at thedetector side to perform watermark extractionand original image reconstruction).

• Watermark and overhead information embeddingthus defining a new watermarked predictionerror E 0

sp.

The watermarked image X 0 is defined as follows

X 0 ! X " E 0sp: (2)

3. S-transform is applied to the watermarked image X 0,thus obtaining low-and high-frequency bands L andH, respectively (see details in Sec. 2.2). Startingfrom L, prediction is applied to get H and the trans-form prediction error is calculated as follows

Etr ! H ! H; (3)

as described in Sec. 2.3.4. Embedding via difference expansion into prediction

error Etr defining a new watermarked predictionerror E 0

tr, as in step 2. The watermarked high-frequency band H 0 is defined as follows

Fig. 1 Proposed scheme for watermark embedding.

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H 0 ! H " E 0tr: (4)

5. Finally, the inverse S-transform is applied to L and H 0

to obtain the watermarked image X 0.

Let us notice that the watermark and the required over-head information are embedded into two steps (2 and 4)and will be denoted as W ! #Wsp;Wtr$.

2.1 Prediction in Spatial DomainThe gradient adjust predictor (GAP)27 considers seven neigh-bors of the to-be-predicted pixel xi;j as follows:

dv ! jxi!1;j ! xi!1;j!1j" jxi;j!1 ! xi;j!2j

" jxi"1;j!1 ! xi"1;j!2j

dh ! jxi!1;j ! xi!2;jj" jxi;j!1 ! xi!1;j!1j" jxi;j!1 ! xi"1;j!1j

D ! dv ! dh xi;j !xi!1;j " xi;j!1

2"xi"1;j!1 " xi!1;j!1

4

xi;j !

8>>>>>>>>>><

>>>>>>>>>>:

xi;j!1 if D < !80xi;j"xi;j!1

2 if ! 80 " D < !323xi;j"xi;j!1

4 if ! 32 " D < !8xi;j if ! 8 " D < 8

3xi;j"xi!1;j4 if 8 " D < 32

xi;j"xi!1;j2 if 32 " D < 80xi!1;j if D # 80

:

(5)

This defines X ! fxi;jgi, j ! 1; : : : ; n and the spatial pre-diction error Esp ! X ! X that will be used for watermarkembedding via difference expansion.

2.2 S-TransformThe S-transform47 is an invertible time-frequency spectrallocalization technique often called also integer Haar wavelettransform. Let us consider the image X 0 of size n ! n. Thelow-frequency L and the high-frequencyH sub-band decom-position of X can be computed as follows:

li"1;j !!x 02i"1;j " x 0

2i"2;j

2

"hi"1;j ! x 0

2i"1;j ! x 02i"2;j; (6)

where i ! 0; : : : ; n2 ! 1, j ! 1; : : : ; n and L ! fli"1;jg whileH ! fhi"1;jg. The corresponding inverse transformation isgiven by

x 02i"1;j ! li"1;j"

!hi"1;j"1

2

"x 02i"2;j ! x 0

2i"1;j!hi"1;j: (7)

Notice that in this case we are applying the S-transform in thevertical direction. Horizontal decomposition can be per-formed just by defining L ! flj;i"1g and H ! fhj;i"1g.

2.3 Prediction in Transform DomainTo guarantee the reversibility of the watermarking method,the proposed prediction scheme aims at predicting high-

frequency sub-band starting from the low frequency onein a way all required information will be available also atthe detection side. The prediction scheme can be summarizedas follows. Given the low frequency coefficients we definerelative differences

Δli"1;j ! li;j ! li"1;j; (8)

where i ! 1; : : : ; n2 ! 1. Notice that differences can be calcu-lated starting from the second row, thus we imposeΔl1;j ! 0.The predicted high-frequency sub-band H is estimated asfollowing:

hi"1;j !1

4li;j "

1

8li"1;j !

1

2li"2;j "

1

8li"3;j; (9)

where i ! 1; : : : ; n2 ! 3 represent the range of coefficientsused in the prediction. Notice that this prediction differsfrom the one presented in Ref. 44 since a new combinationof weights is used exploring also second order differences.

The prediction error is finally given by

ei"1;j ! hi"1;j !#hi"1;j "

1

2

$; (10)

where i ! 1; : : : ; n2 ! 3, j ! 1; : : : ; n. This defines the trans-form prediction error Etr ! fei"1;jg that will be used forwatermark embedding via difference expansion.

2.4 Embedding Via Difference ExpansionThe main idea of difference expansion is to hide informationinto a set of values, in two slightly different ways accordingto their characteristics. Once Esp and Etr are defined, thewatermark W ! #Wsp;Wtr$ insertion is performed by apply-ing Tian’s method13 to Esp and Etr, thus defining the water-marked prediction error E 0

sp and E 0tr, used in Eqs. (2) and (4),

respectively. For simplicity and coherence with the originalTian’s method we describe the process in the transformdomain but the same procedure is applied in the spatialdomain.

In particular, following Eq. (4) E 0tr is used to define the

watermarked values of H 0 (similarly E 0sp allows to define

the watermarked values of X 0), which have to satisfy follow-ing rules in order to avoid overflow and underflow problems.Indeed, X, X 0, and X 0 0 values should be bounded in the range%0; 255&

0 " li"1;j "!h 0i"1;j " 1

2

"" 255

0 " li"1;j !!h 0i"1;j

2

"" 255: (11)

Since both l and h 0 are integer values

jh 0i"1;jj " 2#255 ! li"1;j$ ! a;

jh 0i"1;jj " 2li"1;j " 1 ! b:

(12)

Now we can define two different types of values in Etr (simi-larly in Esp):

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• The error is expandable if for both the watermarkentries wm ! 0 and wm ! 1

jh 0i"1;jj ! jhi"1;j " e 0

i"1;jj " min#a; b$: (13)

In this case we can perform the embedding of the bitwm of the watermark W by expanding the error anddefine the watermarked value as follows:

e 0i"1;j ! 2ei"1;j " wm: (14)

• The error is changeable if for both the watermarkentries wm ! 0 and wm ! 1

jh 0i"1;jj !

%%%%hi"1;j " 2

!ei"1;j

2

"" wm

%%%% " min#a; b$:

(15)

In this case embedding is performed just by substitut-ing the least significant bit (LSB) of ei"1;j with the bitwm of the watermark W.

Notice that an expandable value is also changeable, asdepicted in Fig. 2(a). Therefore, it can be used in bothways. This property will be exploited in the following sub-sets definition. Indeed, before embedding error values arepartitioned into four sets:

• E1 which contains all expandable differences withei"1;j ! 0 or ei"1;j ! !1.

• E2 which contains all expandable differences that donot belong to E1 and are used as expandable.

• E3 which contains all expandable differences that donot belong to E1 and are used as changeable.

• C which contains all changeable differences that do notbelong to E1 or E2 or E3.

• NC which contains all non-changeable differences.

Embedding is now performed in E1 $ E2 and E3 $ C fol-lowing the two different rules, expansion and LSB substitu-tion, respectively.

2.5 Overhead InformationIn order to design a reversible method some informationmust be sent to the detector: such extra information is com-posed by original LSB of every error value changed throughLSB substitution, and the so-called location map that is usedto identify the positions of the bits that have been modified

and the particular embedding adopted. The location map is abinary matrix of same size of the original image with value 1in the position corresponding to differences belonging toE1 $ E2 and with value 0 in the position belonging to E3 $C $ NC [see Fig. 2(a)]. It is worth noticing that a changeablevalue remains changeable also after embedding, thus it isalways distinguishable from a value in NC. This way, duringthe detection stage it is possible to distinguish placeswhere a bit of mark was introduced, and where not [seeFig. 2(b)].

The location map is lossless compressed defining theoverhead information LM which has to be sent to the detec-tor together with the mark. The compression ratio dependson the applied technique and affects the capacity of the algo-rithm. For each value of ei"1;j in E3 and C, LSB values haveto be collected since bit insertion change them. Such valuesare stored into a bit-stream called LSB. Therefore, the com-plete streamW ! fWsp;Wtrg which is embedded consists ofLM $ LSB $ watermark for both Wsp and Wtr. Thus, thewatermark payload size is defined depending on the sizeof E2 and on the compression rate of the location map.

3 DetectionLet us now describe in detail all phases of the detection pro-cess, illustrated also in Fig. 3:

1. The S-transform is applied to the watermarked imageX 0 0, resulting in L and H 0 decomposition.

2. Starting from L, prediction is applied thus recoveringH. The modified prediction error is calculated as

E 0tr ! H 0 ! H: (16)

Since the L sub-band coefficients used for predictingH have not been modified (bitwise equal), the pre-dicted H is exactly the same as in the embedd-ing phase. Thus, information extracted from E 0

tr isbitwise identical to the one inserted (thanks to thereversibility of the difference expansion method, seefor instance Ref. 13).

3. Bit-stream Wtr is extracted from E 0tr from all change-

able values. Now from the recovered LM it is possibleto differentiate among differences used as expandableE1 $ E2, changeable E3 $ C, and non-changeableNC. From LSB it is then possible to recover alloriginal LSB values of changeable differences.Finally, the watermark can be extracted and all originalvalues of Etr can be restored. The original high-frequency sub-bandH can be recovered by calculating

Fig. 2 (a) Distinction between values used as expandable and non-expandable positions within the location map; and (b) distinction betweenchangeable positions and non-changeable positions recognizable at the detector side without any side information.

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H ! H " Etr: (17)

4. The image X 0 can be restored by computing theinverse S-transform of L and H.

5. Starting from X 0, prediction is applied thus recoveringX. The modified prediction error is calculated as

E 0sp ! X 0 ! X: (18)

Also in this case, prediction is defined in order to bereversible: starting from the same input, the predictedset of coefficients will be exactly the same, indepen-dently from coefficients modified by the watermak(inserted only into high frequencies), see for instanceRef. 27.

6. Bit-stream Wsp is extracted from E 0sp as in step 3 and

all original values of Esp can be restored. Finally, theoriginal image X can be recovered by calculating

X ! X " Esp: (19)

Since both extraction steps (3 and 5) are reversible, thewhole process can be inverted and the original image bitwiseperfectly recovered.

4 Experimental ResultsTo evaluate the effectiveness of the proposed schemes sev-eral experimental tests have been performed. The achievedresults are reported by considering both capacity (payloadof the watermark inserted without considering the overheadinformation: location map bit-stream LM and LSB ofdifferences used as changeable, as described in Sec. 2.5),measured in bit per pixel (bpp) and quality of the water-marked image measured with different perceptual metrics:PSNR, PSNR-HVS, and PNSR-HVS-M.48 All tests havebeen computed on a set of 32 images taken from theGrayScale Set 2 image repository of the University ofWaterloo (http://links.uwaterloo.ca/Repository.html) andthe Tampere Image Database 2008 (http://www.ponomarenko.info/tid2008.htm), considering the gray-scaled version oforiginal images only.

Although the reversibility of the exploited techniques isalready proved in the literature (see for instance Ref. 27),first of all we have verified that both the original imageand the embedded data can be perfectly recovered fromthe watermarked one, after the hidden information extractionprocedure.

As far as the spatial prediction is concerned, differenttypes of prediction have been tested and combined withthe prediction in the transform domain described in

Sec. 2.3. In Figs. 4 to 7 results are reported for six differentwell known spatial predictors: GAP, median edge detector(MED), DARK, PAETH, simple average (SA), and previouspixel (DIFF). In all cases (we report here results for fourimages) GAP gives the best results and this motivates ourchoice in the algorithm design.

Results reported in Figs. 8 to 11 present the detailed per-formances achieved by the proposed method for four images

Fig. 3 Proposed scheme for watermark extraction and original image recovery.

Fig. 4 Spatial predictors performances in terms of PSNR for the Lenaimage.

Fig. 5 Spatial predictors performances in terms of PSNR for theBarbara image.

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Fig. 6 Spatial predictors performances in terms of PSNR for the Boatimage.

Fig. 7 Spatial predictors performances in terms of PSNR for theGoldhill image. Fig. 10 Performances of the proposed approach in terms of different

perceptual metrics for the Boat image.

Fig. 9 Performances of the proposed approach in terms of differentperceptual metrics for the Barbara image.

Fig. 8 Performances of the proposed approach in terms of differentperceptual metrics for the Lena image.

Fig. 11 Performances of the proposed approach in terms of differentperceptual metrics for the Goldhill image.

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(due to lack of space) in terms of different quality metrics:PSNR, PSNR-HVS, and PNSR-HVS-M. This way, we donot only have the information about classical PSNR measureof quality but also about state-of-art perceptual qualitymetrics which allow to better understand the real user eva-luation of distortion introduced with the watermark. It isworth noticing that the proposed method allows us to achievehigh capacity by keeping the quality of the watermarkedimages pretty high. With respect to Ref. 45, we achieve betterresults: for example, for Lena45 reports 1,70 bpp with19,60 dB of PSNR while we reach a lower maximum capa-city (1,47 bpp) but with much higher quality (27,54 dB); forBarbara for capacity 1 bpp.45 gets a PSNR of 18,82 dB whilewe have 26,37 dB; for Boat45 reports 1,56 bpp with 19,52 dBwhile we reach a 1,46 bpp with 27,01 dB. As far as Ref. 46is concerned, the proposed technique achieves very similarresults for high-capacity ranges (see for example Lena andBarbara images). Comparison with high-capacity techniquescannot be done in terms of perceptual quality metrics dueto the fact that results are usually reported just in terms ofPSNR.

The maximum capacity achieved and the correspondingperceptual quality of the watermarked image in terms of thethree metrics are shown in Table 1 for all 32 tested images. Itis evident that the proposed technique allows us to embed ahigh number of bits for the watermark without impacting toomuch on the quality of the data. In particular, capacity higherthat 1 bpp can be achieved for Mandrill whereas Refs. 45and 46 present maximum capacity lower than 1 bpp.

5 ConclusionsIn this work a reversible data hiding method has been pre-sented. It is based on the combination of prediction anddifference expansion insertion algorithms and on the use ofsuch combination both in the spatial and in the transformdomain. The adoption of a multilayer technique results inhigh capacity and good image quality as demonstrated inthe performed simulations.

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Table 1 Maximum capacity and corresponding quality of water-marked images for the whole dataset.

ImageMax payload

(bpp)PSNR(dB)

PSNR-HVS-M(dB)

PSNR-HVS(dB)

Zelda 1.47 30.87 37.46 33.02

Washsat 1.48 27.76 34.16 29.75

Peppers2 1.31 25.71 33.23 28.41

Mandrill 1.09 18.8 25.63 20.93

Lena2 1.46 27.54 32.84 28.47

Goldhill2 1.46 24.76 30.82 26.42

Frog 1.32 17.5 27.89 22.5

France 1.35 28.58 34.63 29.34

Boat 1.45 27.01 31.08 27

Barb 1.41 23.25 30.37 25.62

I01 0.96 20.1 26.30 21.88

I02 1.06 25.7 31.45 27.03

I03 1.05 26.34 32.71 28.15

I04 1.09 28.1 34.24 29.85

I05 0.93 20.60 25.44 21.6

I06 1.04 26.2 31.12 26.72

I07 0.75 21.52 26.56 22.23

I08 1.03 25.75 30.8 26.5

I09 1.01 26.12 31 26.7

I10 0.92 22.67 28.27 24

I11 1 26 30.3 26.67

I12 0.92 22 27.78 23.23

I13 0.95 26.36 33.6 28.6

I14 1.05 24.57 29.4 25.77

I15 1 25.78 31.83 27.12

I16 0.89 23 28.96 24.16

I17 0.92 24.1 29.96 25

I18 0.9 22.1 28 23.34

I19 0.97 23.32 29.9 25.3

I20 1 27.73 33 28.3

I21 0.98 24.12 29.2 25

I22 0.7 25.73 30.7 26.24

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Giulia Boato received the MSc degree inmathematics in 2002, and the PhD degreein information and communication technolo-gies in 2005, both from the University ofTrento, Italy. In 2006, she was a visitingresearcher at the University of Vigo, Spain,and in 2009 and 2010 she was a visitingresearcher at the Tampere University ofTechnology, Finland. Currently, she is anassistant professor of telecommunicationsat the University of Trento, working within

the Multimedia Signal Processing and Understanding Laboratory.Her research interests are focused on image and signal processing,with particular attention to multimedia data protection, data hiding, anddigital forensics.

Marco Carli received the “Laurea” degree intelecommunication engineering from the Uni-versity of Rome, “La Sapienza,” Rome, Italy,in 1996. He joined Datamat—Systems Engi-neering Company until 1997. Since 1997, heis involved in the European Union interna-tional programs in Distance Education.Since 2000, he is a visiting researcher withthe Image Processing Laboratory directedby S.Mitra, UCSB, University of California,Santa Barbara, California, USA. He currently

holds an assistant professor position at the University of Rome,“Roma TRE.” His research interests are in the area of digital signaland image processing, in multimedia communications, and in securityof telecommunication systems. He is an IEEE senior member and aSPIE member; he is a reviewer for many conferences and for IEEETransactions.

Federica Battisti received the MSc degreein electronic engineering in 2006, and thePhD degree in telecommunication engineer-ing in 2010, from the Università degli StudiRoma TRE, Italy. In 2008, she was a visitingresearcher in the Groupe Multimedia at Tele-com ParisTech, France. In 2009, she was avisiting researcher in the signal processing incommunications group at the University ofVigo, Spain. Currently, she is an assistantprofessor in the telecommunication group

at Università degli Studi Roma TRE, Italy. Her research interests

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Boato et al.: Difference expansion and prediction for high bit-rate reversible data hiding

are focused on image and video processing, with particular attentionto data hiding and multimedia quality assessment.

Marco Azzoni received the Bachelor degreein telecommunication engineering in 2006and the MSc degree in telecommunicationengineering in 2010 both from the Universityof Trento, Italy. From November 2010 toDecember 2010 he was a visiting researcherin the signal processing group in theTampere University of Technology.

Karen Egiazarian received the PhD degreefromMoscowM. V. Lomonosov State Univer-sity, Russia, in 1986, and Doctor of Technol-ogy degree from Tampere University ofTechnology (TUT), Finland, in 1994. He isa professor of signal processing leadingthe computational imaging and transformsgroup at TUT. He has published over 500refereed journal and conference articles,books, and patents. His main interests arein the field of image and video denoising

and compression, transforms, efficient algorithms, and digital logic.He is an associate editor of several journals, including the SPIE Jour-nal of Electronic Imaging and Research Letters in Signal Processing.He is a member of the DSP Technical Committee of the IEEE Circuitsand Systems Society and a senior member of the IEEE.

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Boato et al.: Difference expansion and prediction for high bit-rate reversible data hiding