Scalable Coding of Encrypted Images.bak

3108 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 21, NO. 6, JUNE 2012

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base/

Scalable Coding of Encrypted Images

Xinpeng Zhang, Member, IEEE, Guorui Feng, Yanli Ren, andZhenxing Qian

Abstract—This paper proposes a novel scheme of scalable coding forencrypted images. In the encryption phase, the original pixel values aremasked by a modulo-256 addition with pseudorandom numbers that arederived from a secret key. After decomposing the encrypted data into adownsampled subimage and several data sets with a multiple-resolutionconstruction, an encoder quantizes the subimage and the Hadamardcoefficients of each data set to reduce the data amount. Then, the data ofquantized subimage and coefficients are regarded as a set of bitstreams.At the receiver side, while a subimage is decrypted to provide the roughinformation of the original content, the quantized coefficients can be usedto reconstruct the detailed content with an iteratively updating procedure.Because of the hierarchical coding mechanism, the principal originalcontent with higher resolution can be reconstructed when more bitstreamsare received.

Index Terms—Hadamard transform, image compression, image encryp-tion, scalable coding.

I. INTRODUCTION

In recent years, encrypted signal processing has attracted con-siderable research interests [1]. The discrete Fourier transform andadaptive filtering can be implemented in the encrypted domain basedon the homomorphic properties of a cryptosystem [2], [3], and acomposite signal representation method can be used to reduce the sizeof encrypted data and computation complexity [4]. In joint encryptionand data hiding, a part of significant data of a plain signal is encryptedfor content protection, and the remaining data are used to carrythe additional message for copyright protection [5], [6]. With some

Manuscript received July 26, 2011; revised October 29, 2011 and December15, 2011; accepted January 26, 2012. Date of publication February 13, 2012;date of current version May 11, 2012. This work was supported in part by theNational Natural Science Foundation of China under Grant 61073190, Grant61103181, and Grant 60832010, and in part by the Alexander von HumboldtFoundation. The associate editor coordinating the review of this manuscript andapproving it for publication was Dr. Anthony Vetro.

The authors are with School of Communication and Information Engineering,Shanghai University, Shanghai 200072, China (e-mail: [email protected]).

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

Digital Object Identifier 10.1109/TIP.2012.2187671

1057-7149/$31.00 © 2012 IEEE

http://ieeexploreprojects.blogspot.com

IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 21, NO. 6, JUNE 2012 3109

buyer–seller protocols [7], [8], the fingerprint data are embedded intoan encrypted version of digital multimedia to ensure that the sellercannot know the buyer’s watermarked version while the buyer cannotobtain the original product.

A number of works on compressing encrypted images have been alsopresented. When a sender encrypts an original image for privacy pro-tection, a channel provider without the knowledge of a cryptographickey and original content may tend to reduce the data amount due to thelimited channel resource. In [9], the compression of encrypted data isinvestigated with the theory of source coding with side information atthe decoder, and it is pointed out that the performance of compressingencrypted data may be as good as that of compressing nonencrypteddata in theory. Two practical approaches are also given in [9]. In thefirst one, the original binary image is encrypted by adding a pseudo-random string, and the encrypted data are compressed by finding thesyndromes of low-density parity-check (LDPC) channel code. In thesecond one, the original Gaussian sequence is encrypted by addingan independent identically distributed Gaussian sequence, and the en-crypted data are quantized and compressed as the syndromes of trelliscode. While Schonberg et al. [10] study the compression of encrypteddata for memoryless and hidden Markov sources using LDPC codes,Lazzeretti and Barni [11] present several lossless compression methodsfor encrypted gray and color images by employing LDPC codes intovarious bit planes. In [12], the encrypted image is decomposed in aprogressive manner, and the data in most significant planes are com-pressed using rate-compatible punctured turbo codes. Based on localstatistics of a low-resolution version of the image, the original contentcan be perfectly reconstructed. By extending the statistical models tovideo, some algorithms for compressing encrypted video are presentedin [13]. In most of aforementioned schemes, the syndrome of channelcode is exploited to generate the compressed data in a lossless manner.

Furthermore, several methods for lossy compressing encrypted im-ages have been developed. In [14], a compressive sensing mechanismis introduced to achieve the lossy compression of encrypted images,and a basis pursuit algorithm is used to enable joint decompressionand decryption. In [15], the original gray image is encrypted by pixelpermutation; then, the encrypted data are compressed by discarding theexcessively rough and fine information of coefficients generated fromorthogonal transform. When having the compressed data and the per-mutation way, a receiver can reconstruct the principal content of theoriginal image by retrieving the values of coefficients. However, therate–distortion performance in [14] is low, and there is a leakage ofstatistical information in [15] since only the pixel positions are shuf-fled and the pixel values are not masked in the encryption phase.

This paper proposes a novel scheme of scalable coding for encryptedgray images. Although there have been a lot of works on scalablecoding of unencrypted images/videos [16], [17], the scalable codingof encrypted data has not been reported. In the encryption phase ofthe proposed scheme, the pixel values are completely concealed sothat an attacker cannot obtain any statistical information of an originalimage. Then, the encrypted data are decomposed into several parts,and each part is compressed as a bitstream. At the receiver side withthe cryptographic key, the principal content with higher resolution canbe reconstructed when more bitstreams are received.

II. PROPOSED SCALABLE CODING SCHEME

In the proposed scheme, a series of pseudorandom numbers derivedfrom a secret key are used to encrypt the original pixel values. Afterdecomposing the encrypted data into a subimage and several datasets with a multiple-resolution construction, an encoder quantizesthe subimage and the Hadamard coefficients of each data set toeffectively reduce the data amount. Then, the quantized subimage

and coefficients are regarded as a set of bitstreams. When having theencoded bitstreams and the secret key, a decoder can first obtain anapproximate image by decrypting the quantized subimage and thenreconstructing the detailed content using the quantized coefficientswith the aid of spatial correlation in natural images. Because of thehierarchical coding mechanism, the principal original content withhigher resolution can be reconstructed when more bitstreams arereceived.

A. Image Encryption

Assume that the original image is in an uncompressed format andthat the pixel values are within [0, 255], and denote the numbers ofrows and columns as �� and �� and the pixel number as �� . Therefore, the bit amount of the original image is �� . Thecontent owner generates a pseudorandom bit sequence with a lengthof �� . Here, we assume the content owner and the decoder has thesame pseudorandom number generator (PRNG) and a shared secret keyused as the seed of the PRNG. Then, the content owner divides thepseudorandom bit sequence into � pieces, each of which containing 8bits, and converts each piece as an integer number within [0, 255]. Anencrypted image is produced by a one-by-one addition modulo 256 asfollows:

��

� � � � �� (1)

where �� represents the gray values of pixels at positions �� ,�� represents the pseudorandom numbers within [0, 255] gener-ated by the PRNG, and �� represents the encrypted pixel values.Fig. 1 gives an original image Lena and its encrypted version.

Clearly, the encrypted pixel values �� are pseudorandomnumbers since �� values are pseudorandom numbers. It is wellknown that there is no probability polynomial time (PPT) algorithm todistinguish a pseudorandom number sequence and a random numbersequence until now. Therefore, any PPT adversary cannot distinguishan encrypted pixel sequence and a random number sequence. Thatis to say, the image encryption algorithm that we have proposed issemantically secure against any PPT adversary.

B. Encrypted Image Encoding

Although an encoder does not know the secret key and the originalcontent, he can still compress the encrypted data as a set of bitstreams.The detailed encoding procedure is as follows.

First, the encoder decomposes the encrypted image into a series ofsubimages and data sets with a multiple-resolution construction. Thesubimage at the �� th level�� is generated by downsamplingthe subimage at the �th level as follows:

��

�� (2)

where�� is just the encrypted image and is the number of decom-position levels. In addition, the encrypted pixels that belong to�� butdo not belong to�� form data set�� as follows:

��

��

� � �� (3)

That means each �� is decomposed into �� and ��, andthe data amount of �� is three times of that of ��. After themultiple-level decomposition, the encrypted image is reorganized as�� , and ��.



Fig. 1. (a) Original image Lena and (b) its encrypted version.

For the subimage �� , the encoder quantizes each value using astep � as follows:

��

�(4)

where the operator �� takes an integer toward minus infinity and

� � �� (5)

Here, � is an integer shared by the encoder and the decoder, and itsvalue will be discussed later. Clearly

� � �� (6)

Then, the data of �� are converted into a bitstream, which is denotedas BG. The bit amount of BG is

��

�� (7)

For each data set�� , the encoder permutes anddivides encrypted pixels in it into �� groups, each of which con-taining �� pixels �� . In this way, the ��

pixels in the same group scatter in the entire image. The permutationway is shared by the encoder and the decoder, and the values of ��

will be discussed later. Denote the encrypted pixels of the �th groupas ��

��

��

�� , and perform the

Hadamard transform in each group as follows:

��

��

...��

��

� � �

��

��...

��

��

(8)

where� is a �� Hadamard matrix made up of �1 or�1. Thatimplies the matrix � meets

�� (9)

where�� is a transpose of�, � is an �� identity matrix, and �� must be a multiple of 4. For each coefficient ��

��, calculate

��

��

�� (10)

where

� �� round �� (11)

and round�� finds the nearest integer. In (10), the remainder of ��

modulo 256 is quantized as integer ��, and the quantization steps

are approximately proportional to square roots of ��. Then, ��

at different levels are converted into bitstreams, which are denoted asBS��. Since

� � �� (12)

and the number of �� at the th level is ��, the bit amount of

BS�� is

��

�� (13)

The encoder transmits the bitstreams with an order of�BG�BS�� BS�� BS��. If the channel bandwidth islimited, the latter bitstreams may be abandoned. A higher resolutionimage can be reconstructed when more bitstreams are obtained at thereceiver side. Here, the total compression ratio �� , which is a ratiobetween the amount of the encoded data and the encrypted imagedata, is

��

��

�

�

��

��

� � � ��

��

��

��

�� (14)

C. Image Reconstruction

With the bitstreams and the secret key, a receiver can reconstruct theprincipal content of the original image, and the resolution of the re-constructed image is dependent on the number of received bitstreams.While BG provides the rough information of the original content, BS��

can be used to reconstruct the detailed content with an iteratively up-dating procedure. The image reconstruction procedure is as follows.



When having the bitstream BG, the decoder may obtain the valuesof �� and decrypts them as a subimage, i.e.,

��

��

� � � ��

��

��

��(15)

where �� are derived from the secret key.If the bitstreams BS�� are also received, an image

with a size of ��

� �� will be reconstructed. First,

upsample the subimage �� by factor �� to yield an��

��

�� image as follows:

��

� � � ��

��

��

��(16)

and estimate the values of other pixels according to the pixel values in(16) using a bilinear interpolation method. Then, the interpolated pixelsare reorganized as data sets with multiple-resolution construction, andthe data in each set are permuted and divided into a series of groups.Denote the interpolated pixel values of the th group at the th level as��

��

�� and their

corresponding original pixel values as ��

��

��.

The errors of interpolated values are

��

��

��

� � � � �� (17)

Define the encrypted values of �� as

��

��

��

� � � � �� (18)

where �� are pseudorandom numbers derived from the secret key

and corresponding to ��. Then

��

��

�� (19)

We also define

��

��

��

��...

��

��

� � �

��

��

...��

��

��

(20)

where � is a �� Hadamard matrix made up of �1 or �1.

Since only the addition and subtraction are involved in the Hadamardtransform

��

��

��

��...

��

��

��

��

��...

��

��

��

��

��...

��

��

�� (21)

That means the transform of errors in the plain domain is equivalentto the transform of errors in the encrypted domain with the modulararithmetic. Denoting

��

��

��...

��

��

� � �

��

��...

��

��

(22)

we have

��

��

��

�� (23)

With the bitstreams BS�� , the values of �� can

be retrieved, which provide the information of ��

��. Therefore, thereceiver may use an iterative procedure to progressively improve thequality of the reconstructed image by updating the pixel values ac-cording to �

��. The detailed procedure is as follows.

1) For each group ��

��

��, calculate ��

��

and ��

�� using (18) and (22).2) Calculate

��

��

��

�� (24)

��

�� if ��

�� if �� (25)

�� are the differences between the values consistent with the

corresponding �� and ��

��

��. Then, considering �� as

an estimate of ��

��, modify the pixel values of each group asfollows:

��

��...

��

�

��

��...

��

��

�

��

��

��

...��

��

(26)

and enforce the modified pixel values into [0, 255] as follows:

��

� � if ��

�� if � � ��

��

� � if ��

(27)

3) Calculate the average energy of difference due to the modificationas follows:

� �

�

��

�

��

�

��

��

��

�

�

��

��(28)

If � is not less than a given threshold of 0.10, for each pixel ��,

after putting it back to the position in the image and regarding the av-erage value of its four neighbor pixels as its new value �

��, go to

Step 1. Otherwise, terminate the iteration, and output the image as afinal reconstructed result.

In the iterative procedure, while the decrypted pixels �� areused to give an initial estimation of other pixels, the values of ��

�� in

bitstreams BS�� provide more detailed information to produce the finalreconstructed result with satisfactory quality. In Step 2, by estimating��

��

�� according to ��, the pixel values are modified to lower

the reconstruction errors. If the image is uneven and �� is big, theabsolute value of actual ��

��

�� may be more than 128 due to the



Fig. 2. Reconstructed Lena using �BS �, �BS �BS �, �BS �BS �BS �, and �BS �BS �BS �BS �. The values of PSNR in (a), (b), (c), and(d) when regarding the corresponding downsampled versions of original Lena as references are 38.4, 34, 37.1, and 38.4 dB.

TABLE ICOMPRESSION RATIOS, PSNR IN RECONSTRUCTED RESULTS AND ITERATION NUMBERS WITH DIFFERENT �

WHEN � � �, � � �, � � �, AND � � �� WERE USED FOR LENA AND MAN

error accumulation in a group, so that �� in (25) may be not close

to ��. To avoid this case, we let �� decrease with a increasing

� since the spatial correlation in a subimage with lower resolution isweaker. For instance, �� , �� , and �� for � � .Furthermore, in Step 3, the value of each pixel is assigned as the averageof its four neighbors to further approach its original value. Althoughthe estimate of a certain pixel may be very different from its originalvalue, the updating operation in Step 3 can effectively lower the erroron the pixel since its neighbors are probably modified well. At last,we terminate the iterative procedure when the reconstruction qualityis not improved further. Here, the small threshold of 0.10 ensures theconvergence of iterative procedure.

III. EXPERIMENTAL RESULTS AND DISCUSSION

Two test images Lena and Man that are sized 512 � 512 were usedas the original images in the experiment. We let � � and encodedthe encrypted images using � � ��, �� , �� , and�� to produce the bitstreams BG, BS��, BS��, and BS��. Inthis case, the total compression ratio �� . Fig. 2 gives thereconstructed Lena using �BG�, �BGBS��, �BGBS��BS��and �BGBS��BS��BS��, respectively. Reconstructed resultswith higher resolution were obtained when more bitstreams were used.When regarding the corresponding downsampled versions of originalimages as reference, the values of PSNR in reconstructed results are

denoted as PSNR�, PSNR�, PSNR�, and PSNR�. While the PSNRvalues of Lena are 38.4, 34, 37.1, and 38.4 dB, those of Man are 38.4,31.9, 33.9, and 37.1 dB. In addition, the iterative updating proceduresignificantly improved the reconstruction quality. For example, whilePSNR in an interpolated 512 � 512, Lena is 23.9 dB; this value in thefinal reconstructed image is 38.4 dB with a gain of 14.5 dB.

Table I lists the compression ratios; the PSNR in reconstructed re-sults and the numbers of iterations with respect to different � when� � , �� , �� , and �� were used for im-ages Lena and Man. All the encryption, encoding and reconstructionprocedures were finished in several seconds by a personal computer.When the value of � is larger, the compression ratio is higher, and thereconstruction quality are better since ��

�� provide more detailed in-

formation. As there is less texture/edge content in Lena than Man, thequality of reconstructed Lena is better than that of Man. In addition,the larger �� corresponds to the lower compression ratio and moredetailed �

��. When we changed �� from (4, 8, 12)

to (4, 12, 32), the compression ratio decreased from 0.318 to 0.283,and the value of PSNR� in reconstructed Lena and Man were 37.8and 35.2 dB, respectively. Compared with the results in Table I, thenew ��-PSNR� performance of Lena is better, whereas that of Manis worse. The reason is that Lena is smoother than Man. For Lena, thelarger �� was helpful to uniformly distribute the errors on pixels intothe Hadamard coefficients, and most of ��

�� still fell into [�128,



Fig. 3. Performance of the proposed scheme with different � .

Fig. 4. Performance comparison of several compression methods.

128], so that the quality of reconstructed result was better. For Man,the excessively large �� caused more ��

�� with absolute values

bigger than 128, leading to a lower reconstruction quality. Fig. 3 givesthe ��-PSNR� curves with different values of � . When an encryptedimage is decomposed within more levels, more data are involved inquantization and compression; therefore, the ��-PSNR� performanceis better, and more iterations for image reconstruction are required. It isalso shown that the performance improvement is not significant whenusing a higher � more than 3.

We also compare the proposed scheme with the previous methodsand unencrypted JPEG compression in Fig. 4. Because it is difficultto completely remove the spatial data redundancy by the operations inthe encrypted domain, the rate–distortion performance of the proposedscheme is significantly lower than that of JPEG compression. On theother hand, the proposed scheme outperforms the method in [15]. Withthe method in [15], the original image is encrypted by pixel permu-tation, which implies an attacker without the knowledge of the secretkey can know the original histogram from an encrypted image. In thisproposed scheme, the original values of all pixels are encrypted by amodulo-256 addition with pseudorandom numbers, leading to semanticsecurity. That means the attacker cannot obtain the original histogramfrom an encrypted image. In addition, the method in [15] does not sup-port the function of scalable coding. Liu et al. [12] proposed a losslesscompression method for encrypted images in a bit-plane based fashion.

By discarding the encrypted data in the lowest bit planes, the method in[12] can be extended to achieve lossy compression. The performanceof the extended method, which is also given in Fig. 4, is better thanthat of the proposed scheme. However, a decoder with higher compu-tation complexity and the decoder’s feedback for sending rate of eachbit plane are required in the method extended from [12]. That meansthe proposed scheme is more suitable for real-time decompression andsome scenarios without feedback channel.

IV. CONCLUSION

This paper has proposed a novel scheme of scalable coding forencrypted images. The original image is encrypted by a modulo-256addition with pseudorandom numbers, and the encoded bitstreamsare made up of a quantized encrypted subimage and the quantizedremainders of Hadamard coefficients. At the receiver side, while thesubimage is decrypted to produce an approximate image, the quantizeddata of Hadamard coefficients can provide more detailed informationfor image reconstruction. Since the bitstreams are generated with amultiple-resolution construction, the principal content with higherresolution can be obtained when more bitstreams are received. Thelossy compression and scalable coding for encrypted image with betterperformance deserves further investigation in the future.

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewers for theirvaluable comments.

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Onboard Low-Complexity Compression ofSolar Stereo Images

Shuang Wang, Lijuan Cui, Samuel Cheng, Lina Stankovic, andVladimir Stankovic

Abstract—We propose an adaptive distributed compression solutionusing particle filtering that tracks correlation, as well as performingdisparity estimation, at the decoder side. The proposed algorithm istested on the stereo solar images captured by the twin satellites systemof NASA’s Solar TErrestrial RElations Observatory (STEREO) project.Our experimental results show improved compression performance w.r.t.to a benchmark compression scheme, accurate correlation estimation byour proposed particle-based belief propagation algorithm, and significantpeak signal-to-noise ratio improvement over traditional separate bit-planedecoding without dynamic correlation and disparity estimation.

Index Terms—Distributed source coding, image compression, multiviewimaging, remote sensing.

I. INTRODUCTION

Onboard data processing has been a challenging task in remotesensing applications due to severe computational limitations ofonboard equipment. This is especially the case in deep-space ap-plications where mission spacecraft are collecting a vast amount ofimages. In such emerging applications, efficient low-complexity imagecompression is a must. While conventional solutions such as JPEGhave been used in many prior missions, the demand for increasingimage volume and resolution, as well as increased space resolution

Manuscript received July 17, 2011; revised November 28, 2011; acceptedJanuary 17, 2012. Date of publication February 13, 2012; date of current ver-sion May 11, 2012. This work was supported in part by the National ScienceFoundation under Grant CCF 1117886. This paper was presented in part at IEEEInternational Conference on Image Processing (ICIP-2011), Brussels, Belgium,September 2011. The associate editor coordinating the review of this manuscriptand approving it for publication was Prof. Brian D. Rigling.

S. Wang, L. Cui, and S. Cheng are with School of Electrical and ComputerEngineering, The University of Oklahoma at Tulsa, Tulsa, OK 74135-2512 USA(e-mail: [email protected]; [email protected]; [email protected]).

L. Stankovic and V. Stankovic are with Department of Electronic and Elec-trical Engineering, University of Strathclyde, Glasgow G1 1XW, U.K. (e-mail:[email protected]; [email protected]).

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

Digital Object Identifier 10.1109/TIP.2012.2187669

and wide-swath imaging, calls for larger coding efficiency at reducedencoding complexity.

NASA’s Solar TErrestrial RElations Observatory (STEREO) is pro-viding groundbreaking images of the Sun using two space-based obser-vatories.1 These images aim to reveal the processes in the solar surface(photosphere) through the transition region into the corona and providethe 3-D structure of coronal mass ejections (CMEs).

A variety of image compression tools are currently used in deep-space missions, ranging from Rice and lossy wavelet-based compres-sion tools (used in PICARD mission by CNES 2009), discrete cosinetransform (DCT) + scalar quantization + Huffman coding (Clementine,NASA 1994), and ICER (a low-complexity wavelet-based progressivecompression algorithm used in Mars mission, NASA 2003) to (12-bit)JPEG-baseline (Trace NASA1998, Solar-B JAXA2006) [1]. The keycharacteristics of these algorithms are relatively low encoding powerconsumption, coding efficiency, and error resilience features. Note thatall current missions, including STEREO, use 2-D monoview imagecompression trading off computational cost and compression perfor-mance. Since STEREO images are essentially multiview images, withhigh interview correlation, current compression tools do not provide anoptimum approach. In this paper, we propose a distributed multiviewimage compression (DMIC) scheme for such emerging remote sensingsetups.

When an encoder can access images from multiple views, a jointcoding scheme [2] achieves higher compression performance thanschemes with separate coding. However, due to the limited computingand communication power of space imaging systems, it is not feasibleto perform high-complexity power-hungry onboard joint encoding ofcaptured solar images. Although, intuitively, this restriction of separateencoding seems to compromise the compression performance, dis-tributed source coding (DSC) theory [3], [4] proves that independentencoding can be designed as efficiently as joint encoding as long asjoint decoding is allowed.

The proposed DMIC image codec is characterized by low-com-plexity image encoding and relatively more complex decoding meant tobe performed on the ground. The proposed scheme extends our previouswork [5], where a joint bit-plane decoder is described, which integratesparticle filtering with standard belief propagation (BP) decoding toperform inference on a single joint 2-D factor graph. In [5], the pro-posed decoding method is used in the context of monoview coding ofnatural video based on DCT-based distributed video coding (DVC) [6].In this paper, we extend the scheme to multiview image compressionto further reduce the complexity we work in the pixel domain. The keycontributions of this paper can be summarized as follows.

• An adaptive distributed multiview image decoding scheme, whichcan estimate the blockwise correlation and disparity change be-tween two correlated images.

• A BP decoder with integrated particle filtering to estimate block-wise correlation changes in the pixel domain. This extends ourprevious work [5], [7] from 1-D correlation estimation to 2-D andfrom time-varying correlation estimation to spatially varying cor-relation estimation.

• A joint bit-plane decoder (as compared with the traditional sep-arate bit-plane decoder [8]), which allows the estimation of thecorrelation and the disparity between two pixels directly ratherthan just the correlation between a corresponding pair of bits ofthe pixels as in [5].

We test our lossy DMIC setup with grayscale stereo solar images ob-tained from NASA’s STEREO mission to demonstrate high compres-

1[Online.] Available: http://www.nasa.gov/mission_pages/stereo/mis-sion/index.html

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