Optimal Multiuser Spread-Spectrum Data Embedding in Video Streams

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1 Optimal Multiuser Spread-Spectrum Data Embedding in Video Streams Lili Wei, 1 Rose Qingyang Hu, 2 Dimitris A. Pados, 3 and Geng Wu 1 Abstract In this paper, we intend to hide multiuser data in a given host video stream with imperceptible spread-spectrum embedding. First, host video frames are picked in the original given video stream according to a frame selection pattern. We partition each host video frame into many small blocks. Based on a two-dimensional transformation of each small block and zigzag scanning, we construct the host video vectors. The embedded message for each user will be spread out with a signature and added to the host vectors. We present the orthonormal signature set of embedding carriers that achieves maximum sum signal-to-interference-plus-noise ratio (sum-sinr) at the linear filter output for any fixed embedding amplitudes. Then, for any given total embedding distortion constraint, we give the optimal multi-signature assignment and amplitude allocation pair that maximizes the sum capacity of the concealment procedure. Numerical results demonstrate the effectiveness of the proposed optimal data embedding methods in video streams. Index Terms Covert communications, code-division multiplexing, data concealment, data embedding, multiuser communications, video sequences, sum capacity. I. INTRODUCTION Secured information transmission is always of great concern in communication systems. In some scenarios, user data are hidden in digital hosts, such as images, audio or video streams, for authentication, annotation, or covert communications applications. Data embedding in images is investigated in [1]- [4]. For video communications [5]-[6], a tutorial on encoding and wireless transmission of compressively sampled videos is presented in [7]. Motion-aware decoding of compressedsensed video is considered in [8]. For the purpose of video sequence analysis, YUV video streams are often used. A testing database is available online in [9]. YUV video sequences consist of three separate signals: one for luminance (brightness) and two for chrominance (colors). This approach maintains better quality than the traditional composite video signal used in older televisions, video home system (VHS) recorders, etc. YUV provides essentially grayscale images from one channel (Y) and the color information is separated out into two channels: one for blue information minus the brightness, and one for red information minus the brightness. On the other hand, regarding the problem of signature design in spread-spectrum communications [10], adaptive binary signature design methods for code-division multiplexing 1 Lili Wei and Geng Wu are with the Mobile and Communications Group, Intel Corporation, USA ( {lili.wei, geng.wu}@intel.com). 2 Rose Qingyang Hu is with the Department of Electrical and Computer Engineering, Utah State University, USA ( rosehu@ieee.org). 3 D. A. Pados is with the Department of Electrical Engineering, S- tate University of New York at Buffalo, Buffalo, NY, USA ( pados@buffalo.edu). are investigated in [11]-[12]. For the general correlated or colored multiple-access vector channel, in [13] we derive algebraically the sum-sinr (signal-to-interference-plus-noise ratio) optimal orthonormal set of carriers for any given set of carrier amplitudes. In addition, if the correlated multipleaccess channel is assumed Gaussian, the sum-capacity optimal orthonormal carrier set design and the jointly sum-capacity optimal orthonormal carrier and power assignments, for a given power budget, are also obtained. In this work, we consider the problem of hiding multiuser data in a given host video stream with imperceptible spreadspectrum embedding. First, we present a procedure to generate host video vectors from the original video stream. According to a frame selection pattern, we pick host video frames in the original video sequence and each host video frame is partitioned into many small blocks. Based on a two-dimensional transformation of each small block and zig-zag scanning, we construct the host video vectors. The embedded message for each user will be spread out with a signature and added to the host vectors without causing noticeable distortion after embedding. In particular, based on the results of [13] we present the orthonormal signature set of video embedding carriers that achieves maximum sum-sinr at the linear filter output for any fixed embedding amplitudes. Then, for any given total embedding distortion constraint, we give the optimal multi-signature assignment and amplitude allocation pair that maximizes the sum capacity of the concealment procedure. Numerical results illustrate the optimality and demonstrate the effectiveness of the proposed data embedding methods in video streams. The notation used in this paper is as follows: { } T denotes the transpose operation; R n denotes the n dimensional real field; E{ } represents statistical expectation; I n is the identity matrix of size n n. We use boldface lowercase letters to denote column vectors and boldface uppercase letters to denote matrices. II. HOST VECTORS GENERATION Consider a general host YUV video stream with F all frames. We can choose F host frames for data hiding according to some frame selection pattern C, C {1,2,3,,F all }. (1) For example, picking one video frame every ten frames makes C = {1,11,21,, F all }. From each selected host video frame, we access the Y component H f M N1 N2, f = 1,2,,F, where M is the /14/$ IEEE 764

2 pixel alphabet andn 1 N 2 is the frame size in pixels for the Y channel. Each Y channel video frame H f is further partitioned inton n small blocks. There are in totalp = N 1 N 2 /n 2 small blocks for each host video frame f, H f 1, Hf 2,, Hf P. (2) With multiuser spread-spectrum embedding, each n n small block is about to carry K digital information bits, one for each different user potentially. In each n n small block H f p (p-th small block of the f-th host video frame of the Y channel, p = 1,2,,P, f = 1,2,,F ), we will perform data hiding in the real two-dimensional transform domain T, for example, the n n discrete cosine transform (DCT). In that direction, we calculate the n n transform-domain block T (H f p) and then vectorize the transform domain matrix by conventional zig-zag scanning to obtain the vector vp f R n2, vp f = Vec{T (H f p)} = T (H f p) 1,1 T (H f p) 2,1 T (H f p) 1,2 T (H f p) 1,3 T (H f p) 2,2 T (H f p) 3,1. T (H p ) n,n, (3) where T (H f p) i,j denotes the (i,j)-th element of the transform domain matrix T (H f p). The final host vector x f p obtained from p-th small block of the f-th host frame of the original video stream, f = 1,2,,F, p = 1,2,,P, is constructed by picking up some elements directly from v f p R n2 with length L n 2. For example, we can have host vector length L = n 2 1 by excluding only the dc coefficient T (H f p) 1,1, since modification of T (H p ) 1,1 will generally lead to visible distortion. We show the diagram of generating the host vectors from a given video stream (the Foreman YUV video stream is shown as an example) in Fig. 1. III. SPREAD SPECTRUM DATA HIDING For one host video frame f, multiuser data hiding will be carried out in the host vectors x f 1, xf 2,, xf P. Assume that there are K users of interest or signatures for spread-spectrum data embedding, where the embedded message for each user will be spread out with a given code/signature and added to a host vector. The multiuser embedded host vectors are of the forms yp f = A f k bf k,p sf k +xf p +n f p, (4) k=1 where b f k,p {±1}, k = 1,2,,K, p = 1,2,,P, f = 1,2,,F is the individual message bit of user k embedded in the the p-th small block of the f-th host video frame with Fig. 1: Host-vectors generation diagram. corresponding embedding amplitude A f k > 0 and normalized spread-spectrum signature s f k RL, s f k = 1, (5) k = 1,2,...,K. The additive vector n f p N (0,σ 2 I L ) accounts in the model for possible external white Gaussian noise of variance σ 2. Embedded bits, host vectors, and noise vectors are considered to be statistically independent from each other. The embedded bits themselves are considered as Bernoulli probability-1/2 random variables that are independent across time and users/messages. For independent embedded bits with orthogonal signatures, we can calculate the mean-square distortion over the f-th host video frame as D f = E k=1 A f k bf k,p sf k 2 K = k=1 ( A f k) 2. (6) 765

3 Fig. 2: Multiuser spread-spectrum data embedding and recovery procedure. The distortion caused by each individual embedded user k, k = 1,2,,K, for the f-th host video frame is D f k = E { A f k bf k,p sf k 2} = ( A f k) 2. (7) The autocorrelation matrix of the f-th video frame transform-domain host vectors is defined as R f x { = E x f x ft} = 1 P P x f px f pt. (8) p=1 To recover the embedded message of user j of interest at the receiver side, j {1,2,...,K}, the linear filter that operates on yp f and offers maximum SINR at its output can be calculated using the Cauchy-Schwarz inequality [14] as w f j = argmax w = E{ w T w ( ) T E{ } A f 2 j bf j,p sf j ( K ) } Af k b k,ps f k +xf p +n f 2 p ( ) 1s R f f /j j (9) where the matrix R f /j is defined as R f /j = E = R f x +σ 2 I L + A f k bf k,p sf k +xf p +n f p T A f k b k,ps f k +xf p +n f p A f f T k k sf k. (10) It can be easily observed that R f /j is a function of sf 1,, s f j 1, sf j+1,, sf K and independent of sf j. Then, the embedded message for user j in the f-th host video frame and the p-th small block can be recovered as ( ( ) ) T ˆbf j,p = sgn w f j y f p. (11) The multiuser spread-spectrum data embedding and recovery procedures are shown in Fig. 2. Fig. 3: Host-vector autocorrelation matrices of different host video frames. IV. SUM-SINR AND SUM-CAPACITY OPTIMAL SIGNATURE SET FOR DATA EMBEDDING For a general host video frame, the autocorrelation matrix R f x defined in (8) is far from constant-valued diagonal, i.e., R f x αi L, α > 0. In Fig. 3, we show several host vector autocorrelation matrices of different host video frames in the Foreman YUV video stream. It can be seen that the host vectors can be considered as colored noise to embedded data. Let {q f 1,qf 2,...,qf L } be the L eigenvectors of the f-th video frame host data autocorrelation matrix R f x with corresponding eigenvalues λ f 1 λf 2... λf L. We are going to derive and present the sum-sinr and sum-capacity optimal signature set for multiuser spread-spectrum data embedding. The output SINR value for the f-th host video frame and the j-th user of the maximum SINR filter w f j in (9) can be calculated as 766

4 SINR f j = A f ft j j R f x +σ 2 I L + = A f f k k sf k T 1 s f j (12) A f ft ( ) 1s j j R f f /j j. (13) We follow the sum-sinr and sum-capacity definitions in [13]. For the f-th host video frame, the sum-sinr is the summation of the K users output SINR values under maximum SINR filtering sumsinr f = SINR f j (14) where SINR f j is given by (12), (13). Let the signature set matrix of the f-th host video frame be S f = [s f 1,sf 2,...,sf K ], (15) which is an L K matrix formed by the spread-spectrum embedding signatures. Let A f = diag(a f 1,Af 2,...,Af K ) (16) be the K K diagonal matrix of the embedding amplitudes. Then, the sum capacity of the embedding process in the f-th host video frame is C f sum = 1 2 log 2det [ I L +(R f x +σ 2 I L ) 1 S f A f2 S ft]. (17) In [13], we have algebraically proved that, for K multipleaccess vector carriers with general correlated/colored Gaussian channels, the vector carriers (signatures) that maximize the sum-capacity are exactly and uniquely the K smallesteigenvalue eigenvectors of the noise autocorrelation matrix assigned inversely proportionally to the amplitude values. A prequel to the sum-capacity-optimal result is that the smallesteigenvalue amplitude-inverse eigenvector set assignment is also sum-sinr optimal under individual maximum-sinr linearfilter reception per signal [13]. Based on those results, we present the following lemmas and give the sum-sinr and sum-capacity optimal signature set for spread-spectrum data embedding in video streams. The proofs of the Lemma 1 and Lemma 2 are similar to Theorem 1 and 3 in [13] and omitted in this paper. Lemma 1 (Optimal Multiuser Spread-Spectrum Signatures for Data Embedding) For orthonormal signature sets in the f-th host video frame, {s f 1,sf 2,...,sf K }, K L, and corresponding fixed embedding amplitudes A f 1 Af 2... Af K > 0, the sum-sinr is maximized to sumsinrmax f (A f j = )2 λ f (18) L (j 1) +σ2 when s f 1, sf 2,..., sf K are assigned as the K smallest-eigenvalue eigenvectors of the f-th video frame host vectors autocorrelation matrix R f x in this order, i.e., s f j = qf L (j 1), j = 1,2,...,K. (19) If the transform-domain host data x f {x f 1,xf 2,,xf P } are Gaussian distributed, the same signature set assignment maximizes sum capacity to ) ( ) C f = 1 (A sum log max 2 (1+ f j )2 2 λ f (20) L (j 1) +σ2 bits per K-symbol embedding. Lemma 2 (Optimal Multiuser Spread Spectrum Signatures and Power Allocation for Data Embedding) For orthonormal signature sets in the f-th host video frame and a given total embedding distortion budget D f, the optimal (signature, amplitude) pairs to maximize the sum capacity for multiuser spread spectrum data embedding in transformdomain Gaussian hosts are ( [ ( s f j = qf L (j 1), (Af j )2 = λ f L (j 1) +σ2) +µ f] ) +, j = 1,2,...,K, where [x] + = max(x,0) and µ is the Kuhn-Tucker [15] coefficient chosen such that the distortion constraint is met with equality. D f = (A f j )2 (21) V. EXPERIMENTAL STUDIES In this section, we show first video frames before and after multiuser spread-spectrum data embedding using as an example the Stefan video sequence in database [9]. Stefan is a YUV video sequence of a total of F all = 90 frames in Common Intermediate Format (CIF) with Y channel video frame size , i.e., N 1 = 325, N 2 = 288. We pick host video frames according to the pattern C = {1,11,21, 81}, i.e., choose one host frame every ten frames which makes the total host video frame number F = 9. For each Y channel host video frame, we carry out partition into 8 8 small blocks, i.e.,n = 8. Then, there are in total P = N 1 N 2 /n 2 = 1584 small blocks for each host frame. After calculating the DCT transformation of each 8 8 small block, we remove the dc coefficient from the zig-zag scanned DCT-domain vectors and create 1584 vectors of length L = = 63. We hide K = 8 data messages via multiuser spread-spectrum embedding (8 bits in each small block, each embedding bit on a different signature) and include also additive white Gaussian noise of variance σ 2 = 3dB. In Fig. 4, the first column shows the first four host video frames before data embedding, i.e., the (1, 11, 21, 31) video frames in the overall video frames. The second column is the corresponding four host video frames after multiuser spreadspectrum data embedding with jointly optimal signature set and amplitudes by Lemma 1 and Lemma 2 of this paper at D f = 30dB total distortion per host video frame. There 767

5 35 30 optimal signatures 25 Sum SINR(dB) Fig. 5: Sum-SINR versus total distortion ( Stefan video stream, K = 8, σ 2 = 3dB). Fig. 4: Host video frames before and after data embedding. is no noticeable difference between the original clean host video frames and the embedded video frames, although in the second column, for each host video frame, there are 8 hidden messages of size 1584 bits each, i.e., = bits are secretly transmitted in one host frame. In Fig. 5, we present the overall sum-sinr for the Stefan host frame sequence when the embedding distortion in each host video frame is set to be the same with value varyimg from 12dB to 32dB. K = 8 multiuser spread-spectrum data embedding is carried out with either arbitrary signature assignment or sum-sinr optimal signatures according to Lemma 1 in this paper. As observed from Fig. 5, the gain in sum-sinr by the use of sum-sinr optimal signatures is significant and around 15dB. In Fig. 6, we show the overall sum-capacity of multiuser spread-spectrum data hiding in the Stefan video stream. Three different schemes are compared: (i) arbitrary signature set assignment; (ii) sum-sinr/sum-capacity optimal signature assignment alone according to Lemma 1; (iii) sum-capacity Sum Capacity (bits per 8 symbol embedding) optimal signatures (1db equal diff) optimal signatures and power allocation 0 Fig. 6: Sum-capacity versus total distortion ( Stefan video stream, K = 8, σ 2 = 3dB). optimal signature assignment and optimal power allocation according to Lemma 2. Note that the power allocation setting in scheme (ii) is not optimal, where the individual message amplitudes/distortions are fixed at D f 1, Df 2 = Df 1 1dB,, D f 8 = Df 7 1dB (1dB decrease for each successive user). At 20dB distortion in each host video frame, the optimal sum- SINR/sum-capacity signature assignment alone offers about 15 bits per embedding over arbitrary signature sets. About 40 more bits are added when the optimal sum-capacity signature is combined with optimal power allocation. Next, we present results for another video stream, Fore- 768

6 Sum SINR(dB) optimal signatures 10 Fig. 7: Sum-SINR versus total distortion ( Foreman video stream, K = 15, σ 2 = 3dB). Sum Capacity (bits per 15 symbol embedding) optimal signatures (1db equal diff) optimal signatures and power allocation 0 Fig. 8: Sum-capacity versus total distortion ( Foreman video stream, K = 15, σ 2 = 3dB). man, also obtained from the online video sequence database [9]. Foreman is F all = 300 frames long in Quarter Common Intermediate Format (QCIF) with Y channel video frame size , i.e., N 1 = 176, N 2 = 144. The host video frames are chosen according to the pattern C = {1,21,41, 281}, i.e., we choose one host frame every twenty frames, which makes the total host video frame number F = 15. For each Y channel host video frame, we carry out partition into 8 8 small blocks, i.e., n = 8. This way, there are in total P = N 1 N 2 /n 2 = 396 small blocks for each host frame. After calculating the DCT transform of each small block, we remove the dc coefficient from the zig-zag scanned DCT-domain vectors and create final host vectors with length L = 63. We hide K = 15 data messages via multiuser spreadspectrum embedding. We show the overall sum-sinr for the Foreman video stream in Fig. 7 and the overall sum-capacity in Fig. 8, both versus distortion per host video frame. The importance of sum-sinr signature set optimality and sumcapacity optimality of signature and power allocation is again demonstrated. VI. CONCLUSIONS In this work, we investigated the problem of carrying out multiuser spread-spectrum data embedding in arbitrary host video streams. Host-vector generation was based on video frame block partition, transform-domain calculation, and zigzag scanning. The embedded message symbols (bits herein) for each user were spread out with a signature and added to the host vectors. We presented (i) the orthonormal signature set of embedding carriers that achieves maximum sum-sinr at the receiver linear filter outputs for any fixed embedding amplitudes and (ii) the optimal sum-capacity multi-signature assignment and amplitude allocation pair for any given total embedding distortion constraint. REFERENCES [1] M. Kutter and S. Winkler, A vision-based masking model for spread spectrum image watermarking, IEEE Trans. Image Proc., vol. 11, pp , Jan [2] M. Wu and B. Liu, Data hiding in binary image for authentication and annotation, IEEE Trans. Multimedia, vol. 6, pp , Aug [3] M. Gkizeli, D. A. Pados, and M. J. Medley, Optimal signature design for spread-spectrum steganography, IEEE Trans. Image Proc., vol. 16, pp , Feb [4] L. Wei, D. A. Pados, S. N. Batalama, M. J. Medley, and R. Q. Hu, Advances in multiuser data embedding in digital media: Orthogonal sum-sinr-optimal carriers, in Proc. IEEE Inter. Conf. Commun. (ICC), Sydney, Australia, June 2014, pp [5] H. Wang, L. P. Kondi, A. Luthra and S. Ci, 4G Wireless Video Communications. Chichester, UK: John Wiley & Sons Ltd., [6] L. Zhou, M. Chen, Y. Qian and H. H. Chen, Fairness resource allocation in blind wireless multimedia communications, IEEE Trans. Multimedia, vol. 15, pp , June [7] S. Pudlewski and T. Melodia, A tutorial on encoding and wireless transmission of compressively sampled videos, IEEE Commun. Survey & Tutorials, vol. 15, no. 2, pp , [8] Y. Liu, M. Li and D. A. Pados, Motion-aware decoding of compressedsensed video, IEEE Trans. Circuits and Syst. for Video Tech., vol. 23, pp , March [9] ASU YUV Video Stream Database [Online]. Available: [10] A. J. Viterbi, CDMA: Principles of Spread Spectrum Communication. Upper Saddle River, NJ: Prentice Hall, [11] L. Wei, S. N. Batalama, D. A. Pados and B. W. Suter, Adaptive binary signature design for code-division multiplexing, IEEE Trans. Wireless Commun., vol. 7, no. 7, pp , July [12] L. Wei and W. Chen, Optimal binary/quaternary adaptive signature design for code-division multiplexing, IEEE Trans. Wireless Commun., vol. 12, pp , Feb [13] L. Wei and D. A. Pados, Optimal orthogonal carriers and sum- SINR/sum-capacity of the multiple-access vector channel, IEEE Trans. Commun., vol. 60, pp , May [14] D. G. Manolakis, V. K. Ingle and S. M. Kogon, Statistical and Adaptive Signal Processing. New York, NY: McGraw-Hill, [15] T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. New York, NY: Wiley,