IEEE TRANSACTIONS ON CYBERNETICS 1 Rate and...

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IEEE TRANSACTIONS ON CYBERNETICS 1

Rate and Distortion Optimization for ReversibleData Hiding Using Multiple Histogram Shifting

Junxiang Wang, Jiangqun Ni, Member, IEEE, Xing Zhang, and Yun-Qing Shi, Fellow, IEEE

Abstract—Histogram shifting (HS) embedding as a typicalreversible data hiding scheme is widely investigated due to its highquality of stego-image. For HS-based embedding, the selected sideinformation, i.e., peak and zero bins, usually greatly affects therate and distortion performance of the stego-image. Due to themassive solution space and burden in distortion computation,conventional HS-based schemes utilize some empirical criterionto determine those side information, which generally could notlead to a globally optimal solution for reversible embedding. Inthis paper, based on the developed rate and distortion model,the problem of HS-based multiple embedding is formulated asthe one of rate and distortion optimization. Two key propo-sitions are then derived to facilitate the fast computation ofdistortion due to multiple shifting and narrow down the solutionspace, respectively. Finally, an evolutionary optimization algo-rithm, i.e., genetic algorithm is employed to search the nearlyoptimal zero and peak bins. For a given data payload, the pro-posed scheme could not only adaptively determine the propernumber of peak and zero bin pairs but also their correspondingvalues for HS-based multiple reversible embedding. Comparedwith previous approaches, experimental results demonstrate thesuperiority of the proposed scheme in the terms of embeddingcapacity and stego-image quality.

Index Terms—Genetic algorithm (GA), histogram shift-ing (HS), rate and distortion optimization, reversible datahiding.

Manuscript received June 10, 2015; revised September 20, 2015 andDecember 20, 2015; accepted December 21, 2015. This work was supportedin part by the National Natural Science Foundation of China under Grant61379156 and Grant 61402209, in part by the National Research Foundationfor the Doctoral Program of Higher Education of China under Grant20120171110037, in part by the Key Program of Natural Science Foundationof Guangdong under Grant S2012020011114, and in part by Invention Patentand Industrialization Technology Demonstration Project of Jiangxi Provinceunder Grant 20143BBM26113. This paper was recommended by AssociateEditor Q. Zhao. (Corresponding author: Jiangqun Ni.)

J. Wang is with the School of Information Science and Technology,Sun Yat-sen University, Guangdong 510006, China, and also with the Schoolof Mechanical and Electronic Engineering, Jingdezhen Ceramic Institute,Jiangxi 333403, China (e-mail: [email protected]).

J. Ni is with the School of Information Science and Technology,Sun Yat-sen University, Guangdong 510006, China, and also with theState Key Laboratory of Information Security, Institute of InformationEngineering, Chinese Academy of Sciences, Beijing 100093, China (e-mail:[email protected]).

X. Zhang is with the School of Information Science andTechnology, Sun Yat-sen University, Guangdong 510006, China (e-mail:[email protected]).

Y.-Q. Shi is with the Department of Electronics and Computer Engineering,New Jersey Institute of Technology, Newark, NJ 07102, USA (e-mail:[email protected]).

This paper has supplementary downloadable multimedia material availableat http://ieeexplore.ieee.org provided by the authors. This includes a PDF file,which shows the proof of Propositions 1 and 2. This material is 213 KB insize.

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCYB.2015.2514110

I. INTRODUCTION

IN RECENT years, data hiding techniques have found wideapplications in copyright protection and content authentica-

tion of digital multimedia [1], [2]. The inherent defect of theconventional data hiding schemes is that they can usually notcompletely recover the original image after the image has beenmodified for data hiding. For some specific scenarios, such asmilitary, medical, and legal applications, even the slight dis-tortion in images is not tolerated. Therefore, reversible datahiding techniques are developed, which enable the decoderto not only extract the secret data as traditional schemes, butalso perfectly reconstruct the original cover image without anydistortion.

Many reversible data hiding schemes have been reported inliterature since Barton [3] proposed his first reversible datahiding scheme in 1997. In general, the existing reversibledata hiding schemes explore the correlation among pixels ina cover image and can be mainly classified into three cate-gories: 1) lossless compression [4], [5]; 2) difference expan-sion (DE) [6]–[12]; and 3) histogram shifting (HS) [13]–[23].DE-based scheme was first proposed by Tian [6]. Later, sev-eral improved techniques for DE-based embedding are putforward, which includes the prediction and sorting [7], [9],and location map reduction [8], [10]. HS-based reversible datahiding was initially proposed by Ni et al. [13] in 2006, whichselected a pair of peak and zero bins in histogram and thenshifted the bins between the two bins by 1 toward zero bin forreversible data embedding. In principle, DE can be regardedas a special case of HS with peak and zero bins selected fromthe center and tail of the histogram, respectively. Therefore,we concentrate on the HS-based approach throughoutthe paper.

The rate and distortion performance of HS-based reversibledata hiding depends heavily on the sharpness of histogramand the way to determine the peak and zero bin pairs.To sharpen the histogram, integer digital wavelet trans-form coefficients [14], pixel differences [15], [16], predictionerrors [9], [17], [18] and interpolation errors [19] have beensuccessively employed to generate the carrier image (to dis-tinguish the cover images, we use carrier images throughoutthe paper to refer to the ones into which data are directlyembedded, e.g., prediction and interpolation errors of coverimages, etc.) for HS-based embedding and relatively highembedding capacity are obtained. Among them, by takingadvantage of the four adjacent neighbors around current pixel,Sachnev et al.’s [9] prediction model gives the sharpest his-togram of prediction errors. Recently, to further improve the

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2 IEEE TRANSACTIONS ON CYBERNETICS

embedding capacity of carrier image, the concepts of statisti-cal quantity histogram [20] and 2-D difference-histogram [21]have also been introduced, and the later is shown to bevery suitable for low payload reversible data hiding. In addi-tion to the generation of carrier images and their histograms,the determination of peak and zero bins is also critical forHS-based embedding. For the small payload, single pair ofpeak and zero bins is sufficient and the optimal solution couldbe obtained through brute-force search. When relatively largepayload is required, however, multiple embedding scheme asmentioned in [16] should be employed, which uses multi-ple pairs of different peak and zero bins from the histogramat a time, and performs multiple HS-based embedding con-secutively based on the resulting histogram. Generally, withgiven data payload and carrier image, the design of HS-basedmultiple reversible embedding can be formulated as the opti-mization problem to find a set of optimal peak and zerobins while minimizing its distortion. To solve the optimiza-tion problem, however, several key issues as follows shouldbe addressed.

1) To develop the rate and distortion model for HS-basedmultiple embedding.

2) To fast evaluate the distortion for multiple embedding.Note that, during multiple embedding, only one pair ofpeak and zero bins is selected for each embedding level,consequently the other peak and zero bins in the follow-ing embedding levels may be inevitably affected andchanged to other values. To evaluate the distortion, theactual multiple embedding should be performed, whichis heavily dependent on the relative location of the mul-tiple peak and zero bins in the histogram and quitecumbersome and time-consuming.

3) To efficiently solve the optimization problem, i.e., todetermine the number of optimal peak and zero binpairs and their corresponding values. Due to the massivesolution space, conventional HS-based schemes usuallyfollow some empirical search paths to find the peak andzero bin pairs, which generally do not ensure globallyoptimal solution for multiple reversible embedding.

Ni et al. [13] orderly selected the highest frequency binsand their closest zero frequency bins as the peak and zerobins for HS-based embedding. Based on the assumption thatone peak bin should be on the left of the corresponding zerobin, Yang et al. [22] proposed a general model for the distor-tion estimation. Unfortunately, they did not provide an efficientsolution to find the optimal peak and zero bins. Moreover, theassumption itself may not always be true for practical applica-tions. Xuan et al. [23] proposed another HS-based scheme tofind the appropriate peak and zero bin pairs, which aimed tominimizing the possible histogram modification for given datapayload. They utilized a pair of beginning and end thresholdsto determine the interval around zero for successive assign-ment of peak bins. Although considerable improvement inperformance was obtained, their scheme could not alwaysguarantee the optimal peak bins be selected from the predeter-mined interval. In addition, the scheme in [23] implied the zerobins be located at the tail of the histogram, which may leadto relatively large distortion due to HS and further sacrifice

the performance. To our best knowledge, no practical rate anddistortion optimization scheme for HS-based multiple embed-ding has been reported in literature due to the massive solutionspace and the burden of distortion computation.

This paper presents a systematic framework to designHS-based multiple reversible data hiding system with nearlyoptimal rate and distortion performance, which is indepen-dent of carrier images. And the contributions of the paper areas follows. First, we develop the rate and distortion modelfor HS-based multiple embedding, then present Proposition 1for fast evaluation of the possible distortion due to HS-basedmultiple embedding without actually implementing the embed-ding process. We further provide Proposition 2 to significantlysimplify the process of distortion evaluation when differentpeak and zero bins are paired for given candidate peak andzero bin sets. It is noted that there is no explicit expres-sion of the rate and distortion in terms of multiple pairs ofpeak and zero bins, consequently the conventional optimiza-tion algorithms, such as gradient descent method etc., are notappropriate for application. In addition, the massive solutionspace of peak and zero bins also prohibit the direct use ofexhaustive search in the design of optimal HS-based multipleembedding. In [24], the evolutionary optimization algorithm,i.e., genetic algorithm (GA) was utilized to design a robuststeganographic scheme that can break the inspection of ste-ganalytic tools. In this paper, however, we also employ theGA with powerful global search capability and fast conver-gence, to automatically search the nearly optimal peak andzero bin pairs for HS-based multiple embedding. Finally, therhombus prediction in [9] is also incorporated to generate thecarrier image for efficient reversible data embedding.

The rest of the paper is organized as follows. The rate anddistortion model for HS-based multiple embedding and theassociated fast algorithm for distortion computation are devel-oped in Section II. The specific GA is then designed to solvethe optimization problem in Section III. The proposed embed-ding and extraction schemes are described in Section IV,which are followed by the experimental results and analy-sis in Section V. Finally, the conclusions are summarized inSection VI.

II. RATE AND DISTORTION MODEL FOR

HS-BASED MULTIPLE EMBEDDING

In the section, the rate and distortion model and the associ-ated algorithm for fast distortion computation are developed.Based on these, the HS-based multiple embedding is then for-mulated as the rate and distortion optimization problem interms of multiple peak and zero bin pairs.

A. Rate and Distortion Model for HS-Based Embedding

HS algorithm is usually implemented on the histogram ofgrayscale values or predictive errors of the pixels. The pre-cise rhombus predictor developed in [9] is employed in ourproposed scheme to generate a much shaper histogram forefficient HS-based embedding, which will be illustrated inSection IV. In the section, we concentrate on the development


WANG et al.: RATE AND DISTORTION OPTIMIZATION FOR REVERSIBLE DATA HIDING USING MULTIPLE HS 3

Fig. 1. HS embedding process in the case of P1 < Z1.

of the rate and distortion model for HS-based multipleembedding.

1) HS Embedding With Single Pair of Peak and Zero Bins:Based on a histogram of predictive errors, HS is performedto hide secret data. Before HS embedding, a peak bin withnonzero frequency and a zero bin with zero frequency in thehistogram should be determined and denoted as (P1, Z1). HSthen shifts the histogram bins between P1 and Z1 toward Z1direction by one unit to create a vacant position near P1.Finally, each predictive error is scanned to embed 1-bit mes-sage w when P1 is encountered. Let pe(r, s) and pe′(r, s)represent an original predictive error and the correspondingmarked one at (r, s), respectively. As illustrated in Fig. 1, whenP1 < Z1, HS is performed by

pe′(r, s) =⎧⎨

⎩

pe(r, s) + 1, pe(r, s) ∈ [P1 + 1, Z1 − 1]pe(r, s) + w, pe(r, s) = P1pe(r, s), otherwise.

(1)

In the case of P1 > Z1, HS is similarly implemented.For the HS process with (P1, Z1) as side information, the

embedding payload (rate) is calculated as

Payload = h(P1) (2)

where h(P) denotes the frequency of occurrence for value Pin histogram.

For an 8-bit grayscale image, predictive errors are located inthe range [−255, 255]. To compute the distortion due to HS,the shift of each shifted bin for single embedding denoted as�(i) should be evaluated. For the secret message w = {w}of length C, when P1 < Z1, the actual HS embedding canbe well illustrated in Fig. 1, where all the bins located in therange [P1 +1, Z1 −1] are shifted toward positive infinity by 1.With the assumption that the “0” and “1” in the message w areequally distributed, only half of the peak bins P1 are shiftedby 1, we then have the average shift at peak bin P1

δ(P1) = +1

2P1 < Z1. (3)

Therefore, when P1 < Z1, the shift for HS single embed-ding is

�(i) =⎧⎨

⎩

δ(P1) i = P11 i ∈ [P1 + 1, Z1 − 1]0 otherwise.

(4-1)

Similarly, we have the shift evaluation for P1 > Z1

�(i) =⎧⎨

⎩

−δ(P1) i = P1−1 i ∈ [Z1 + 1, P1 − 1]0 otherwise.

(4-2)

Fig. 2. Example of multiple embedding with two pairs of peak and zero bins.

With the evaluated shift �(i), it is readily seen that thedistortion D corresponding to the HS-based single embeddingas shown in Fig. 1 can be computed as

D =∑

i∈[P1,Z1−1]

h(i) × (�(i))2 =∑

i∈[P1+1,Z1−1]

h(i) + 1

2× C

(5)

where∑

h(i) and (1/2)×C in (5) denote the shifting distortionfor bins in the range [P1 +1, Z1 −1] and embedding distortionat peak bin P1, respectively.

2) HS-Based Multiple Embedding: When data payload islarge, multiple embedding method is introduced, which utilizesseveral pairs of different peak and zero bins at a time andperforms several levels of HS embedding consecutively basedon the resulting histogram until all the selected peak and zerobin pairs are exhausted. For the several pairs of peak and zerobins involved in the HS-based multiple embedding, each pairof peak and zero bins corresponds to one embedding level andaffects one another, which should be taken into account andwell tracked in distortion evaluation.

Fig. 2 shows an example of HS-based multiple embeddingwith two pairs of peak and zero bins. Firstly, two pairs of dif-ferent peak and zero bins in the histogram are determined at atime and defined as {(Pk, Zk) |k∈ [1, 2], P1 �=P2 and Z1 �=Z2}.Then one pair of peak and zero bins, i.e., (P1, Z1), is cho-sen to perform the first level embedding, which makes P2shift to P′

2 = (P2 + 1) in that P2 locates in [P1 + 1, Z1 − 1].Consequently, the peak bin for next embedding level shouldbe replaced by P′

2 = (P2 + 1) instead of P2, which is referredto as “peak-bin drift” in our paper. Similarly we have “zero-bin drift.” Based on (P′

2, Z2), the second level embedding isperformed on the resulting histogram.

It is observed that each bin including the peak and zero inthe histogram may experience several shifting for HS-basedmultiple embedding, and the distortion introduced by eachshifting should be processed separately through tracking thecorresponding peak and zero bin “drift” caused by previousshifting. To compute the distortion with two-level embeddingas shown in Fig. 2 (the same for m-level embedding, m > 2),however, the accumulated shifts of each shifted bin should beevaluated, which is defined as

�bin = {�bini | i ∈ [−255, 255]} (6)

where �bini represents the accumulated shifts of the ith bin.By consecutively implementing two single HS embedding

with (P1, Z1) and (P2 + 1, Z2), and taking into account of the



bin shifts arising from each single HS embedding, we have

�bini =

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

+δ(P1) i = P1+1 i ∈ [P1 + 1, P2 − 1]+1 + δ(P2) i = P2+1 + 1 i ∈ [P2 + 1, Z1 − 1]+1 i ∈ [Z1 + 1, Z2 − 1]0 otherwise.

(7)

It is noted that, to compute the accumulated shifts of eachbin, the peak bin drift for P2 is required to be tracked and itseffects should be taken into account. Thus, the distortion Dcaused by the two-level embedding process is computed by

D =∑

i∈[−255,255]

h(i) × (�bini)2

=∑

i∈[−255,255]�bini=Fix(�bini)

h(i) × (�bini)2 +

∑

�bini �=Fix(�bini)

Di

=∑

i∈[−255,255]i/∈{P1,P2}

h(i) × (�bini)2 + (

DP1 + DP2

)(8)

where DPk(k = 1, 2) denotes the embedding distortion at thepeak bin Pk and Fix(•) is the round function that rounds itsinputs toward zero, e.g., Fix(3.6) = 3 and Fix(−3.6) = −3.With Fix(•), it is easy to identify bin i as peak bin if thecondition �bini �= Fix(�bini) is met [Note that accumulateshift in peak bin is not integer as shown in (7)]. Without lossof generality, let d = Fix(�bini), (i = Pk) for the peak binPk, DPk(k = 1, 2) can be individually computed by

DPk =

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

12 × h(Pi) × (d)2

+ 12 × h(Pi) × (d + 1)2, �bini > Fix(�bini)

12 × h(Pi) × (d)2

+ 12 × h(Pi) × (d − 1)2, �bini < Fix(�bini)

(9)

where k ∈ [1, 2].For an HS-based multiple embedding with m pairs of peak

and zero bins as side information, i.e., {(Pk, Zk) | 1 ≤ k ≤ m},its embedding payload (rate) is

Payload =m∑

i=1

h(Pi). (10)

While the distortion for m-level multiple embedding can beevaluated based on its accumulated shift array �bin, that is

D =∑

i∈[−255,255]

h(i) × (�bini)2

=∑

i∈[−255,255]i/∈{Pk|k∈[1,m]}

h(i) × (�bini)2 +

m∑

k=1

DPk (11)

where the distortion DPk(k = 1, 2, . . . , m) due to peak binshift can be similarly obtained as (9).

According to aforementioned, to exactly evaluate the dis-tortion for multiple embedding with fixed m pairs of peakand zero bins, the accumulated shifts for each bin, i.e., theshift array �bin should be computed, which is cumbersome

and time-consuming. The computation involves the trackingof both peak-bin drift and zero-bin drift, dynamically updat-ing the peak and zero bins for each embedding level and theactual implementation of m-level multiple shifting. A closeobservation of the two-level embedding process as shown inFig. 2, however, suggests that the accumulated shifts of eachbin for HS-based multiple embedding looks like to be obtainedin a “de-coupled” way. Proposition 1, in the next section willbe put forward to confirm the conjecture and the associatedfast algorithm will then be developed in the next section tocompute the distortion for HS-based multiple embedding. Forgiven m peak and zero bins, another important issue in rate anddistortion optimization is the evaluation of distortion when dif-ferent peak and zero bins are paired and sequentially arrangedin the process of multiple embedding. The problem is highlychallenging since the inherent combinatorial nature often bearsprohibitive computational complexity and renders the problemintractable. And Proposition 2 will also be proposed to tacklethe issue for rate and distortion optimization of HS-basedmultiple embedding.

B. Main Results of Fast Distortion Computation forHS-Based Multiple Embedding

In this section, two propositions and the associated algo-rithms are presented to cope with the issues of fast distortioncomputation for HS-based multiple embedding with fixed mpairs of peak and zero bins, and the fast distortion evaluationwhen different peak and zero bins are paired and sequentiallyarranged for given m peak and zero bins, respectively.

Proposition 1: For an HS-based multiple embedding withhistogram H, and fixed m pairs of peak and zero bins as sideinformation, denoted as {(Pk, Zk)|1≤k≤m}, Pi �=Pj, Zi �=Zj,i �= j and i, j ∈ [1, m], the accumulated shifts �bini forbin i after m-level embedding are equivalent to the sum ofm independent shift �k(i) due to HS single embedding withinitial histogram H and (Pk, Zk), i.e., �bini = ∑m

k=1 �k(i),where �k(i) denotes the shift of the kth-level embedding with(Pk, Zk) and is calculated with (4-1) or (4-2).

In the interest of focused presentation, the strict mathemat-ical proof for Proposition 1 is included in the supplementaryfile (available at http://ieeexplore.ieee.org). Based on that, afast algorithm can be developed to evaluate the accumulatedshifts of each bin for HS-based multiple embedding. Instead ofactually performing the multiple embedding and dynamicallytracking the peak-bin drift and zero-bin drift, our approachonly involves the computation of the bin shift for m inde-pendent HS single embedding with the same initial histogramH using (4-1) or (4-2), and finally adds the shifts together toobtain the accumulated shifts. With the accumulated shifts, theoverall distortion is then obtained using (11).

We then proceed to investigate the distortion computa-tion for HS-based multiple embedding with given m peakand zero bins when different peak and zero bins are pairedand sequentially arranged, which is effectively resolved withProposition 2 below.

Proposition 2: Let P = {P1, P2, . . . , Pm} and Z ={Z1, Z2, . . . , Zm}, Pi �= Pj, Zi �= Zj, i �= j and i, j ∈ [1, m], be




the given m peak and zero bins. For HS-based multiple embed-ding with m pairs of peak and zero bins, different permutationof P and Z leads to an identical distortion.

Note that the P and Z above are ordered sets with their ele-ments in the set from left to right indicating the sequentialorder in the implementation of HS-based multiple embed-ding. With Proposition 2, the computational complexity ofdistortion evaluation for the HS-based multiple embeddingwith given m peak and zero bins is substantially decreasedby Am

m × Amm, where Ak

n is the number of k permutationsof n. Therefore, the solution space is significantly reducedaccordingly. Proposition 2 itself can also be strictly provedusing mathematical induction. Since it is rather technical, thedetails are presented in the supplementary file (available athttp://ieeexplore.ieee.org).

C. Rate and Distortion Optimization

On the basis of the developed rate and distortion modelfor HS-based multiple embedding, we have the rate and dis-tortion optimization for payload-limited embedding. Beforeformulating the optimization problem, the range for the tun-able parameters, i.e., Pk, Zk, and m, should be defined. Letthe number of peak and zero bin pairs m in the predefinedrange [1, Mmax]. For the histogram of a carrier image (pre-diction errors) with bins located in the range [−255, 255], allthe bins with zero frequency are candidates for zero bins, i.e.,Zero_Set = {Zk | k ∈ [1, l]}, where l denotes the number of thecandidate zero bins in the histogram. While other bins exceptzero ones are considered as the candidates for peak bins anddenoted as Peak_Set = {Pk | k ∈ [1, 511 − l]}.

1) Payload-Limited Embedding: In practice, the HS-basedmultiple reversible data hiding can usually be formulated asthe payload-limited embedding, that is⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

min{(Pk,Zk),m|k∈[1,m]} D[(Pk, Zk)k=1,...,m]

Pk ∈ Peak_Set, Zk ∈ Zero_Set, m ∈ [1, Mmax]

s.t.m∑

k=1h(Pk) ≥ C

Pi �= Pj, Zi �= Zj, i �= j and i, j ∈ [1, m]

(12)

where D is the distortion calculated with the Proposition 1(for accumulated shifts) and distortion model (11). The rateand distortion optimization problem in (12) is to determine thenumber of peak and zero bin pairs m among the predefinedrange [1, Mmax] and the corresponding values of peak andzero bins {(Pk, Zk)|k ∈ [1, m]} from Peak_Set and Zero_Setthat embeds a given payload C while minimizing the distor-tion D. Therefore, if m is fixed, the size of solution spacefor (12) is Am

l × Am511−l. Take the predictive errors of Lena

image as example, where l = 92, the size of solution spaceis approximately A10

92 × A10511−92 = 3.0466 × 1032 in the case

of m = 10. In addition, to optimize the rate and distortionperformance, it is desirable to try all the possible pair numberm among the range (m ∈ [1, Mmax]) and thus the size of totalsolution space is

∑Mmaxm=1 Am

l × Am511−l. On the other hand, the

combinatorial nature of the problem also makes the conven-tional approaches, such as gradient based or numerical searchmethods, fail to achieve good results. Therefore, the evolution-ary optimization algorithm, such as GA, is adopted to solve

the rate and distortion optimization problem in (12) in nextsection. It is worth noting that, although other evolutionaryalgorithms, such as particle swarm optimization (PSO), couldalso be utilized, our simulation results indicate that both GAand PSO have comparable rate and distortion performance forHS-based multiple reversible embedding. If a specific optimal(or suboptimal) solution with given m pairs of peak and zerobins exists, then according to Proposition 2 and (10), differentcombinations between these peak and zero bins lead to thesame rate and distortion performance. Therefore, the chanceto find an optimal solution is substantially increased for GA,or equivalently the solution space size is reduced dramaticallyto

∑Mmaxm=1 Cm

l × Cm511−l (Ck

n is the number of k combinationsof n), which is more preferable for practical application of GA.By taking advantage of fast convergence and powerful globalsearch ability of GA, we could not only adaptively determinethe nearly optimal number of peak and zero bin pairs but alsotheir corresponding values for a given payload.

III. RATE AND DISTORTION OPTIMIZATION USING GA

A. Framework of the Proposed GA

Aiming to optimize the rate and distortion performancedescribed in (12), we design a GA to automatically determinethe tunable parameters, i.e., the number of peak and zero binpairs m and their corresponding values. During the GA pro-cess, the two constraints on payload and assignment of peakand zero bins as shown in (12) should be specially considered.

Our GA follows the framework of conventional geneticmethodology as described in [25], which includes severalproblem oriented designs. Starting with an initial randomlygenerated pool of population, into which some specifi-cally designed empirical chromosomes with good genes areadded to ensure better convergence for GA implementa-tion. Let g, Gmax, N, and Mmax denote the current generationnumber, the maximum generation number, the amount of indi-viduals in the initial population, and the predefined upperbound of peak and zero bin number m, respectively. The over-all structure of the proposed GA includes: 1) initialization;2) empirical chromosomes addition; 3) evaluation of the pop-ulation; 4) parents’ selection for reproduction; 5) crossoverand mutation; and 6) selection for next generation construc-tion, which is well illustrated in Fig. 3. In the next section,we will describe some problem oriented designs for our GAscheme different from the conventional ones.

B. Chromosome Encoding

To solve the rate and distortion optimization problemdescribed in (12) using GA, all the tunable parameters, i.e.,the number of peak and zero bin pairs and the correspondingvalues of peak and zero bins should be represented with chro-mosome encoding. The chromosome vector consists of 3 Mmaxelements (genes) and is defined as

Ct = (It, Pt, Zt)

It = {ik | ik ∈ {0, 1} and k ∈ [1, Mmax]}Pt = {Pk | Pk ∈ Peak_Set and k ∈ [1, Mmax]}Zt = {Zk | Zk ∈ Zero_Set and k ∈ [1, Mmax]} (13)




Fig. 3. Flowchart of the proposed GA scheme.

where Ct refers to the tth individual chromosome in a pop-ulation. It is actually a composite chromosome consisting ofthree different types of chromosomes. The first section of Ct,i.e., It is designed for indicating bits, while Pt and Zt eachincludes at most Mmax different peak and zero bins chosenfrom the Peak_Set and Zero_Set, respectively.

The element ik = ‘1’ in It indicates that kth pair of peakand zero bins (Pk, Zk) from Pt and Zt would be activated forHS-based multiple embedding, otherwise, the pair (Pk, Zk) isignored. With the adoption of indication bits It in the chro-mosome, the number of involved peak and zero bin pairsfor multiple embedding could be dynamically adjusted in therange [1, Mmax].

C. Empirical Chromosomes Addition

We then proceed to investigate the way to improve the capa-bility of the proposed GA to find the nearly optimal solutionby introducing some empirical chromosomes with good genes.When the payload C is large, the constraint

∑mi=1 h(Pi) ≥ C

specifies a relatively tiny feasible solution space comparedwith the entire solution space

∑Mmaxm=1 Cm

l × Cm511−l, it is usu-

ally difficult to find even the feasible solution, let alone theoptimal one based on the randomly selected initial chromo-somes through limited generations of evolution with GA. LetF_C denote the feasible solution space size corresponding tothe constraint

∑mi=1 h(Pi) ≥ C, the probability of reaching the

feasible solutions by randomly selected initial chromosomes is

prob = F_C∑Mmax

m=1 Cml × Cm

511−l

(14)

where the denominator∑Mmax

m=1 Cml × Cm

511−l is the size of theentire solution space as mentioned in Section II-C. Accordingto our experiments, it is usually difficult for GA to find thefeasible solutions within finite generations of evolution withrandomly selected initial chromosomes when the payload isrelative large, e.g., C ≥ 2 × 105 bits for cover image Lena of512 × 512 × 8 bit.

To solve the problem, we manually construct a group ofempirical individuals (chromosomes), which include the peakand zero bins determined using some existing criterion [13]and are adopted in the initial population. In our implementa-tion, at most Mmax empirical individuals are introduced, wherethe chromosome Ct, t ∈ [1, Mmax] includes t different peakbins with highest frequency from Peak_Set and t different zerobins closest to the corresponding peak bins from Zero_Set,respectively.

The adoption of empirical chromosomes shows some advan-tages. One is that, rather than a completely random search,these chromosomes indicate the search direction toward thefeasible solutions space (i.e.,

∑mi=1 h(Pi)≥C) and ensure sta-

ble convergence for GA when the payload is large. Next, theevolution mechanism of GA generally guarantees to achieve abetter performance than the ones with the empirical peak andzero bins in the initial population.

D. Fitness Evaluation

The objective of the proposed GA process is to find thenearly optimal solution in terms of multiple pairs of peakand zero bins associated with the minimal distortion D. Theinvolved selection scheme, such as roulette wheel selection,however, tends to choose the chromosome with higher fit-ness value. Thus, the distortion D itself cannot be takendirectly as the fitness value. Let Dmax be the possible max-imal distortion for the given HS-based multiple embeddingin one generation, a proper fitness value can be defined asfollows:

fitness = Dmax − D. (15)

In addition, to ensure the feasible output satisfying the pay-load constraint

∑mi=1 h(Pi) ≥ C in (12), the penalty with

predefined large value, say 107, is assigned to the distor-tion D of the infeasible chromosomes, which makes thembe eliminated with high probability during the selectionprocess.

IV. EMBEDDING AND EXTRACTION PROCESSES

In general, our GA-based rate and distortion optimizationscheme is independent of the carrier images, either in pixel orprediction domain. The accurate rhombus prediction proposedin [9] is incorporated in this paper to generate the predic-tion errors with much shaper histogram which would lead tosignificant performance improvement for HS-based multipleembedding. To perform rhombus prediction, the pixels in animage are divided into two sets, i.e., the cross set (X) and theround set (O) as shown in Fig. 4(a). Hereinafter, we denotethe pixels and prediction errors in these two sets as PZ andPEZ(Z = ‘X’ or ‘O’), respectively. Each pixel in cross set is



Fig. 4. Sketch of rhombus prediction. (a) The distribution of cross (X) andround (O) sets. (b) The prediction pattern for the pixel in cross set.

predicted with its four neighboring pixels in dot set as shownin Fig. 4(b) and vice versa

PX(i, j)

= round

[PO(i − 1, j) + PO(i + 1, j) + PO(i, j − 1) + PO(i, j + 1)

4

]

(16)

where round(•) is the function that returns the nearest integerof the input. The corresponding prediction error PEX(i, j) iscomputed as follows:

PEX(i, j) = PX(i, j) − PX(i, j). (17)

As the performance of the proposed GA scheme depends heav-ily on the carrier image, we also sort the prediction errorsin their local variances ascending order [9] and take the topχ(%) of the prediction errors for HS-based multiple embed-ding. According to our experiments, the optimum χ(%) is inthe collections �1 = {10, 20, 30, 40, 50} for low data payload(< 0.1 bits per pixel) and �2 = {50, 60, 70, 80, 90, 100} formedium to high payload applications (≥ 0.1 bits per pixel),respectively.

A. Embedding Process

For a 8-bit grayscale cover image and the binary secret mes-sage w of length C, the embedding process is described brieflyas follows.

1) Initialization: With the cover image in cross and roundsets as shown in Fig. 4(a), assign half of the secretmessage of length 1/2 × C for cross and round setsembedding, respectively.

2) Rhombus Prediction of the Cross Set: As shown inFig. 4(b), each pixel in the cross set is predicted byits four neighboring pixels in round set to obtain thePX(r, s) and then the prediction error PEX(r, s) in thecross set.

3) Optimal Peak and Zero Bins Selection: Based onthe histogram of prediction errors in the cross set,i.e., PEX = {PEX(r, s)}, the GA-based rate and dis-tortion optimization is carried out to determine thenearly optimal number of peak and zero bin pairsand their corresponding values for the payload oflength (1/2)C.

4) Cross Set Embedding: To hide the message intothe prediction errors PEX , the accumulated shifts�bin = {�bini} for each bin after the multiple embed-ding are calculated by application of Proposition 1 to

generate the marked prediction errors in cross set. LetPEX(r, s) = i, we have

PE′X(r, s)

=⎧⎨

⎩

PEX(r, s) + �bini, �bini = Fix(�bini)

PEX(r, s) + Fix(�bini) + w, �bini > Fix(�bini)

PEX(r, s) + Fix(�bini) − w, �bini < Fix(�bini)

(18)

where w denotes 1-bit secret data, �bini is the accumu-lated shifts of bin i.

5) Stego-Pixels Generation in the Cross Set: With markedprediction errors, we have the stego-pixels in thecross set

P′X(r, s) = PE′

X(r, s) + PX(r, s). (19)

6) Stego-Pixels Generation in the Round Set: Utilize thegenerated stego-pixels in the cross set to predict thepixels in round set as mentioned in step 2) and repeatsteps 3)–5) to generate the stego-pixels P′

O(r, s) in theround set.

7) Stego Image Generation: Combine the stego-pixels inboth cross and round sets, i.e., P′

X and P′O to obtain the

whole stego-image.Note that, the above GA-based multiple embedding should

be tested for the possible χ in �(�1 or �2) to determine theoptimum χopt in terms of rate and distortion performance. Fora given payload, we take the same percentage χ in both crossand round sets to simplify the implementation. Besides, Luo’smethod [19] is also employed in the embedding process toavoid the possible overflow/underflow for the generated stegoimage, in which, a location map is introduced to indicate theoverflowed/underflowed pixels and then hidden in the carrierimages as the additional side information.

B. Extraction Process

Based on the received optimal χopt, peak and zero bins andthe stego-image, we extract the secret message and recoverthe original image in the inverse order as embedding pro-cess, namely the marked round set is recovered and messageis extracted first, which is then used to reconstruct the markedcross set and extract the corresponding hidden message.

V. EXPERIMENTAL RESULTS AND ANALYSIS

To evaluate the proposed rate and distortion optimizationscheme, we test several 512 × 512 × 8 bits grayscale imageswith different texture characteristics from SIPI database [26]and 100 512 × 512 × 8 bits grayscale images randomlyselected from Bossbase ver.1.01 [27]. By comparing the pro-posed scheme with some state-of-the-art reversible data hidingmethods, the superiority of our scheme is verified.

A. Parameters’ Setting and Empirical ChromosomesAddition for GA

Before comparing it to prior works, we first discuss theparameters’ setting of our GA based multiple embeddingscheme. To simplify the analysis, we set most of the GA



TABLE IPARAMETERS’ SETTING OF THE PROPOSED GA

Fig. 5. Distortion versus the number of generation for test image Lena atsmall payload (0.076 bits per pixel).

parameters experimentally, e.g., population size, crossoverrate, mutation rate, maximum pair number Mmax, and themaximum generation number Gmax, as shown in Table I. Inaddition, the effectiveness of empirical chromosomes additionis also investigated.

For a small payload of C/2 = 104 bits (i.e., 0.076 bitsper pixel) embedded in the cross set of Lena, Fig. 5 givesthe convergence results when initial empirical chromosomes(good seeds) are not included /and included, respectively. TheMmax = 20 pairs of different peak and zero bins describedin Section III-C [13] are utilized as the initial “good” chro-mosomes in our implementation. It is observed that, whetherthe initial empirical chromosomes are included or not, theGA-based multiple embedding scheme converges within ratherlimited generations of evolution. The adoption of some initialgood seeds, however, would speed up considerably the conver-gence and achieve a better performance in terms of distortion.This is because, compared with the randomly selected seeds(chromosomes), the introduction of those good seeds into theinitial population can provide better genes for evolution andthus a better solution is easier to be reached with higher prob-ability. For a large payload, say C/2 ≥ 105 (i.e., 0.763 bits perpixel), however, the implementation of the proposed schemeis heavily dependent on the help of some initial good seeds.The payload constraint itself, i.e.,

∑mi=1 h(Pi) ≥ C, makes it

difficult for the GA-based scheme to find a payload feasiblesolution based on the randomly selected initial seeds withinlimited generations of evolution. Fig. 6 includes the corre-sponding convergence performance, where the distortions areconsistently around the predefined penalty value, i.e., 107, evenafter 100 generations of evolution. In contrast, the additionof specifically designed seeds in the initial population can

Fig. 6. Distortion versus the number of generation for test image Lena atlarge payload (0.763 bits per pixel).

not only meet the payload constraint but also quickly reachthe nearly optimal solution and ensure the stable convergenceas shown in Fig. 6. Therefore, the effectiveness of empiri-cal chromosomes addition is verified. In addition, accordingto our experimental results, the maximum generation numberGmax = 70 is sufficient to obtain the stable convergence formedium textured images, such as Lena. While Gmax is a lit-tle bit larger in the range [70, 100] for other highly texturedimages, such as Baboon, owing to the slower convergencespeed.

B. Comparison With Other Related Schemes

We first compare our GA-based multiple embedding schemewith three typical methods [9], [13], [23] in terms of peak andzero bins selection for various payloads. In the interest of faircomparison, our scheme [with χ(%) ∈ �1 ∪ �2] and otherrelated methods are implemented on the same cross set of testimages with rhombus prediction. Table II summarizes the rate(payload) and distortion performance of the involved schemesand the corresponding values of peak and zero bins for imageLena.

It is noted that the distortion performance of our scheme inTable II is the average over ten experiments for each payloadand represents in the form “mean ± standard deviation” whilethe listed peak and zero bins of our scheme correspond to thesolution whose distortion is closest to the average one for eachpayload.

It is demonstrated in Table II that our GA-based schemeachieves the best rate and distortion performance for variousdata payloads. Compared with the proposed scheme, both themethods in [9] and [13] determine the peak bins based on someempirical rules. Ni et al.’s [13] method uses in priority thepeak bins with higher frequency, while the DE method in [9]is actually a special case of HS with the peak bins fixedlyselected from an interval [Tn, 0] ∪ [0, Tp], (Tn < 0 and Tp ≥0) around zero, where Tn and Tp are predefined thresholds.Although the method in [23] shows some adaptability in peakbin selection, the employed peak bins are also confined andsuccessively assigned from an interval determined. Moreover,the peak bins employed in [9], [13], and [23] are generallylocated around 0 and the zero bins in [9] and [23] are selected



TABLE IISELECTED PEAK AND ZERO BINS FOR INVOLVED SCHEMES IN THE CROSS SET OF IMAGE Lena WITH 512 × 512 × 8 BITS

Fig. 7. Illustration of bin shift cancellation.

from the tail of histogram, therefore the corresponding shiftingdistortion is further increased.

According to our understanding, the good rate and distor-tion performance of our GA-based multiple embedding can beachieved in two aspects. For one thing, instead of utilizing oneor two high frequency bins as peak bins which correspondsto high shifting distortions, several relatively low frequencybins may be a better choice in the case of small data pay-load. For another, those two peak and zero bin pairs shouldbe determined in priority, i.e.: 1) their associated shiftings arein the reverse direction with each other and 2) their associatedshiftings share as much overlapped bins with high frequencyas possible. For this example, the (P1, Z1) and (P2, Z2) asshown in Fig. 7 are two peak and zero bin pairs shifting inreverse direction. According to Proposition 1 in Section II-B,the accumulated shifts in the overlapped bins between [P1, P2]can be eliminated, which gives rise to reduced shifting distor-tions. It is also observed in Table II that, for low data payload(0.076 bits per pixel), rather than the high frequency bin 0, ourscheme selects two low frequency bins 3 and −3 as the peak

bins and the bin shifts in reverse direction between [−3, 3]would offset each other. As the prediction errors of naturalimages are Laplacian distributed, and the highest frequencybins are located close to bin 0, the shifting distortions are thussignificantly reduced. The same happened to the medium pay-load embedding (0.23 and 0.458 bits per pixel in Table II).Note that, for the case of 0.076 and 0.23 bits per pixel,although the peak and zero bins in (−3, −136)1 and (6, 81)are far apart from each other, the bins in between each of thesetwo peak and zero bin pairs are sparse and have low frequency,which corresponds to much less shifting distortions.

We then proceed to compare the comprehensive per-formance between our scheme and some state-of-the-artreversible data hiding methods, which include two DE-basedmethods in predictive errors [9], [12], three HS-based meth-ods [18], [19], [23]. In our implementation of the GA-basedembedding scheme, both the cross and round sets of coverimages are utilized with rhombus prediction and sorting toensure the better rate and distortion performance (refer toSection IV-A). Note that the embedding payload is the effec-tive one except the location (boundary) map and multiplepeak and zero bins. For small to medium data payload, i.e.,embedding rate (ER) ≤ 0.4 bits per pixel, which is idealfor HS-based multiple embedding and most commonly usedin practical applications, our scheme achieves the best rateand distortion performance among all the methods, for thetest images Lena, Baboon, F16, and Peppers as shown inFig. 8. The same happened to the average performance com-parison with 100 test images randomly selected from image

1The original peak and zero bin pair is (3, −136), and the shifts in [−3, 3]are canceled.



Fig. 8. Performance comparison between the proposed scheme and other related schemes.

database BOSSbase ver. 1.01 [27], as illustrated in Fig. 9.It is observed that, for large data payload (ER > 0.4 bitsper pixel), although our scheme outperforms consistently theother three HS-based methods [18], [23], [25], its performancetends to be similar to Sachnev et al.’s [9] method. This isbecause the proposed scheme and the method in [9] are allimplemented on the errors of rhombus prediction. At highER, the important bins with high frequency in the histogramshould be utilized by all the involved schemes to hide largepayload. Under these circumstances, our scheme could notexemplify its advantage in peak and zero bin selection. Itis also observed that the proposed scheme cannot competeLi et al.’s [12] method for Pepper image at high data pay-load. This is because the Pepper image has many potentiallyoverflowed/underflowed pixels located around both sides of thehistogram, i.e., 0 and 255. Instead of embedding only 1 bit at apixel with our scheme, Li et al.’s [12] method could choose theappropriate smooth areas in images to hide more than 1 bit dataat a pixel, thus Li et al.’s [12] method may utilize much lesspotentially overflowed/underflowed pixels than our scheme,which leads to a less sized location map. Consequently,Li et al.’s [12] method may outperform ours for some images

with much more boundary pixels, such as Pepper, at highdata payload.

For small data payload (ER < 0.1 bits per pixel), we fur-ther compare the performance of our GA-based scheme withthe one of Li et al.’s [21] method, which is summarized inTable III. Note that, for small data payload embedding, wetake the top χ (%)(χ ∈ �1) of the sorted prediction errors ofboth the cross and round sets as carrier images and the “–” inTable III denotes that there is no result reported for the corre-sponding bits per pixel. It is observed that, although we onlymake use of a few fixed percentage χ in �1, the performanceof the proposed scheme is still slightly better than the one ofLi et al.’s [21] method, which is the state-of-the-art for smalldata payload embedding.

C. Practical Evaluation of Computational Complexity

In this section, we further evaluate the practical com-putation cost in terms of computation time (CmpTime) ofour GA based multiple reversible embedding scheme ondifferent image sizes, and briefly analyze the practical com-putational complexity of our scheme and other involved



TABLE IIICOMPARISON BETWEEN OUR PROPOSED SCHEME AND LI et al.’S [21] METHOD FOR SMALL PAYLOAD

Fig. 9. Average performance comparison for 100 test images fromBossbase [27].

schemes [9], [12], [18], [19], [21], [23]. Since any HS-based embedding process needs to undergo three similarsteps, i.e., generation of carrier images, peak and zero binselection, and reversible embedding, we only compare theCmpTime of peak and zero bin determination, which isthe major difference between our scheme and others. Forschemes [9], [12], and [21], since the peak and zero bins arefixedly selected, their CmpTimes are negligible. While thepeak and zero bin pairs for schemes in [18], [19], and [23]are determined on the basis of some empirical rules, and theirCmpTimes are also negligibly small.

In our simulation, we test the CmpTime of the proposed GAscheme in the cross set of rhombus prediction with variousimage sizes for different payload, i.e., 0.2, 0.3, and 0.6 bitsper pixel. The simulation is implemented with MATLAB ona 3.2 GHz Intel Pentium Dual Core CPU with 4 GB memory.And the parameter setting for GA as shown in Table I is alsoadopted in our experiment. In the interest of fair comparison,we randomly select 100 grayscale images of 512 × 512 × 8bits from Bossbase ver.1.01 [27], which are then subsequentlyprocessed by converting to images of 1024 × 1024 × 8 bits

TABLE IVAVERAGE COMPUTATION TIME (CMPTIME) OF THE GA-BASED

OPTIMIZATION SCHEME

and 2048 × 2048 × 8 bits through interpolation. The averageCmpTimes over 100 images for different payloads and threeimage resolutions with the proposed GA-based scheme aresummarized in Table IV. It is observed that: 1) the averageCmpTime of the GA-based scheme for three image resolutionsis nearly the same, i.e., around 2.0 s, indicating that, withgiven initial histogram, the computational cost of our schemeis irrelevant to the cover image size and 2) our scheme couldbe implemented in a quite affordable computational cost.

VI. CONCLUSION

In this paper, an efficient GA based multiple embeddingscheme is proposed for HS-based reversible data hiding. Bydeveloping the rate and distortion model in terms of multiplepairs of peak and zero bins, the HS-based multiple embeddingis formulated as the problem of rate and distortion optimiza-tion. An evolutionary optimization algorithm, i.e., GA, is thenemployed to solve the optimization problem, which could notonly adaptively determine the proper pair number of the peakand zero bins but also their corresponding nearly optimalvalues for HS-based multiple embedding. Two main propo-sitions in distortion computation are also obtained to facilitatethe development of fast algorithm for distortion evaluationand the massive reduction of the solution space, which arepreferable for practical application of GA. By partitioningthe image into interleaved cross and round sets, the preciserhombus prediction and sorting are incorporated in the pro-cess of HS multiple embedding. Extensive simulations are



carried out, which demonstrates the superior rate and distortionperformance of the proposed scheme.

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewersand associate editor for their comments that greatly improvedthe paper.

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[25] D. E. Goldberg, Genetic Algorithms in Search, Optimization andMachine Learning. Reading, MA, USA: Addison-Wesley, 1989.

[26] SIPI Image Database, [Online]. Available: http://sipi.usc.edu/database/[27] P. Bas, T. Filler, and T. Pevny, “‘Break our steganographic sys-

tem’: The ins and outs of organizing BOSS,” in Information Hiding.Heidelberg, Germany: Springer, 2011, pp. 59–70. [Online]. Available:http://www.agents.cz/boss/

Junxiang Wang received the M.S. degree fromthe Harbin Institute of Technology, Harbin, China,and the Ph.D. degree from Sun Yat-sen University,Guangdong, China, in 2008 and 2012, respectively.

He is currently an Associate Professor with theSchool of Mechanical and Electronic Engineering,Jingdezhen Ceramic Institute, Jiangxi, China. Hiscurrent research interests include information secu-rity and image processing.

Jiangqun Ni (M’12) received the Ph.D. degreein electronic engineering from the University ofHong Kong, Hong Kong, in 1998.

From 1998 to 2000, he was a Post-DoctoralFellow for a joint program between Sun Yat-sen University, Guangdong, China, and GuangdongInstitute of Telecommunication Research. Since2001, he has been with the School of InformationScience and Technology, Sun Yat-sen University,where he is currently a Professor. His currentresearch interests include data hiding and digital

image forensics, image-based modeling and rendering, and image/videoprocessing. He has published over 50 papers in the above areas.

Xing Zhang received the B.S. degree in commu-nication engineering from Sun Yat-sen University,Guangzhou, China, in 2013, where he is cur-rently pursuing the M.S. degree with the School ofInformation Science and Technology.

His current research interests include digitalwatermarking and image processing.

Yun-Qing Shi (M’88–SM’92–F’05) received theM.S. degree from Shanghai Jiao Tong University,Shanghai, China, and the Ph.D. degree from theUniversity of Pittsburgh, Pittsburgh, PA, USA.

He has been with the New Jersey Institute ofTechnology, Newark, NJ, USA, since 1987. Hehas authored/co-authored 300 papers, one book,five book chapters, and an Editor of ten books.He holds 28 U.S. patents. His current researchinterests include digital data hiding, forensics andinformation assurance, visual signal processing, and

communications.He was a recipient of the Innovators Award 2010 by New Jersey Inventors

Hall of Fame for Innovations in Digital Forensics and Security and the2010 Thomas Alva Edison Patent Award by Research and DevelopmentCouncil of New Jersey for the U.S. patent 7 457 341 entitled “System andMethod for Robust Reversible Data Hiding and Data Recovery in the SpatialDomain.” He served as an Associate Editor of the IEEE TRANSACTIONS

ON SIGNAL PROCESSING and the IEEE TRANSACTIONS ON CIRCUITS AND

SYSTEMS (II), and a few other journals. He also served as a TechnicalProgram Chair of the IEEE ICME07, a Co-Technical Chair of IWDW06,07, 09, 10, 11, 12, 13, and the IEEE MMSP05, a Co-General Chair of theIEEE MMSP02, a Distinguished Lecturer of the IEEE CASS. He is a memberof a few IEEE technical committees.

http://sipi.usc.edu/database/

http://www.agents.cz/boss/

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