image compression and encryption using optimized wavelet ... · image compression and encryption...

International Journal of Applied Engineering Research, ISSN 0973-4562 Volume 12, Number 21 (2017) pp. 10595–10610© Research India Publications, http://www.ripublication.com

Image Compression and Encryption using OptimizedWavelet Filter Bank and Chaotic Algorithm

Renjith V RaviResearch Scholar, Department of Electronics and Communication Engineering,

Faculty of Engineering, Karpagam University, Coimbatore, India.

Kamalraj SubramaniamAssociate Professor, Department of Electronics and Communication Engineering,

Faculty of Engineering, Karpagam University, Coimbatore, IndiaORCID: 0000-0001-9047-3220; ORCID: 0000-0002-6781-4282

Abstract: Over the past two decades, many developmentshas been made in the area of image processing. Growingdemand for storage and transmission of visual informationwas the real catalyst. Here, a novel image processing systememploying compression and encryption has been proposed.The system consists of optimized transformation module,compression and encryption module. A hybrid optimiza-tion algorithm has been developed initially, by combiningthe techniques of Bat and Genetic algorithms together andthe hybrid algorithm is used for developing an optimizedwavelet filter bank. This filter bank has been used withSPIHT algorithm for wavelet based image compression.Further a chaotic map based algorithm has been devel-oped for encryption of the compressed image data.Thequality of decompressed image has been assessed throughthe performance analysis of PSNR, MSE and SSIM. Theperformance of compression has been validated based oncompression ratio and compression rate. The results showthat the proposed filter performs better than other popularwavelet filters in terms of quality of decompression withoutaffecting the compression performance. Also, the perfor-mance of chaotic encryption algorithm has been verifiedusing different quality metrics and observed that, it resistsvarious cryptanalytic attacks.

Keywords: Optimized wavelet coefficients, HybridGenetic Bat algorithm, Chaotic Encryption, image Com-pression.

INTRODUCTION

In communication engineering, the rapid increase inrange and use of electronic imaging justifies attention forsystematic design of an image compression system withthe image quality needed in different applications [1]. Thechallenge however is that while high compression ratesare desired, the usability of reconstructed images dependson certain significant characteristics of the original imageswhich need to be preserved after the compression processhas been finished [2].

Several reputed image coders utilizes the transformDWT to accomplish improved compression performance[3], [1], [4], [5], [6]. A DWT based image compressionsystem consists of a quantizer and an encoder that exploitsthe redundancies to represent the image data in a com-pressed manner, whereas the decoder is used to reconstructthe original image from the compressed data. Despite thefact that the quantization incredibly enhances compressionratios, perfect reconstruction is unimaginable because ofthe quantization error[2].

A study in [7] on metaheuristic optimization for imagecompression demonstrates that it can be utilized to optimizewavelet coefficients and give enhanced image reconstruc-tion over the DWT when subject to quantization error.Theworks presented in the literature demonstrates the opti-mized transforms and its superior performance over stan-dard wavelets for satellite images[8], [9], [10], [11], [12],Military images [13], [14], [15], fractal images [16], space

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images [8], [17], [18], [19], Finger print images [20], [21]and medical images [22], [23] and [24].

When increasing access to the Internet and informa-tion resources like, image and video has a great impact inour everyday life and is making humans more dependenton computer systems and networks. This dependency hasbrought many threats to information security. As a result,reliably secure mechanisms are required to protect theimportant information which is presented as video or imageagainst vulnerabilities. One of the best known techniquesto protect data is cryptography. In this, the Encryptionand decryption are accomplished by using mathematicalalgorithms in such a way that no one but the intendedrecipient can decrypt and read the message.Among thecryptographic algorithms, the chaotic algorithms are bestsuitable for image encryption [25], [26], [27].

This paper deals with an optimized wavelet based imagecompression has been proposed and a chaotic transformbased image encryption algorithm has been developed. Thetechnique comprises of two modules, namely compressionmodule and chaotic encryption [28] module. In compres-sion module, the input image is transformed to waveletdomain with the use of hybrid bat-genetic algorithm basedoptimized wavelet filter bank and compressed using SPIHT[29]. Afterwards, in the encryption module, the encryptionusing chaos based encryption is carried out. For getting theoriginal image from the compressed and encrypted data, adecryption and decompression modules are also presented.

PROPOSED METHOD FOROPTIMIZATION OF WAVELET FILTERCOEFFICIENTS

Bat-Genetic hybridization

The hybrid Bat-Genetic hybridization is formed by incor-porating mutation [30] and cross-over operators [31] intothe bat algorithm [32] [33]. Bats are the only mammalsendowed with wings having the capability of echo loca-tion. The echolocation characteristics of bats assist in thedevelopment of several bat-inspired algorithms or bat algo-rithms. The vital features connected with the bat algorithmare the velocity of bats, the location of bats, and theirloudness. The technique derived in the bat algorithm isfor exploration and exploitation of issues based on these

features. Motivated by the characteristics of bats, the pro-posed approach adopts the bat algorithm for optimizing thefeatures listed in the feature list.

In the proposed technique, the wavelet filter banks areconsidered as the virtual bats. Based on the definition ofbat algorithm, each virtual bat is assigned a velocity vej aposition poj and loudness loj .

It is presumed that all bats invariably use echolocationto sense distance, in addition to guessing the distinctionbetween food/prey and background barriers in a certainamazing manner. Bats x‚y with velocity vej at positionpoj with a fixed frequency f remin, varying wavelength λ

and loudness loj to search for prey. They can automaticallyadjust the wavelength of their emitted pulses and adjustthe rate of pulse emission pe ∈ [0, 1], depending on theproximity of their target.

Bat algorithm [32] consists of diverse steps such as ini-tialization, creation of new solutions, local search, andgeneration of a new solution by randomly and finallyascertaining the current best solution. In the initializationprocess, all the elements are assigned arbitrary values in aspecific range demanded by the problem definition. Onceall the bats are initialized, their fitness levels are estimatedby means of a fitness function, which represents a ratiolinking the velocity, position, and the loudness. As it ispresumed that virtual bats are moving over the space, it iscertain that their velocity and position also will undergochange.

So the velocity and position should be updated forthe existing virtual bats. The new updated solutions canbe defined as based on equations (1a), (1b) and (1c)respectively.

f rej = f remin + (f remax − f remin)β (1a)

vetj = vet−1

j + (potj − pogb)f rej (1b)

potj = pot−1

j + potj (1c)

where t , is the time (iteration) in consideration, β ∈ [0, 1]isa random vector drawn from a uniform distribution, andpogb is the current global best location (solution) after com-paring all the solutions among all the bats. Subsequently,the initial best solutions are found out. For the local searchpart, once a solution is selected among the current bestsolutions, a new solution for each bat is generated locallyusing a local random walk:

ponew = poold + �Lot (2)

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where, � ∈ [−1, 1] is a random number, while Lot isthe average loudness of all the bats at the current time step.Accordingly, the velocity and position of all the virtual batsare updated till an end criterion.

The fitness function employed is the PSNR (Peak Sig-nal to Noise Ratio) value. The best solutions obtained afterthe bat algorithm is then modified using GA operators ofcross-over and mutation. GAs are adaptive heuristic searchalgorithms premised on the evolutionary concept of naturalselection and genetics, which have been extensively stud-ied, experimented and applied in several fields, includingengineering. GAs belong to the bigger class of evolutionaryalgorithms (EA), which generate solutions to optimizationissues using techniques enthused by natural evolution, likeinheritance, mutation, selection, and crossover. In a GA, apopulation of strings (chromosomes), which encode can-didate solutions to an optimization problem, is evolvedtowards superlative solutions.

Crossover characterizes the procedure of integratingtraits of two different individuals to generate solutions thatcan be of superior fitness than that of each of the parents.In our case, the wavelet filter bank constitutes the parents.Two parent individuals are chosen from the current popu-lation of the set to generate a new offspring. The numberof offspring chromosomes is evaluated using the crossoverprobability. In this connection, the modified Ranking par-ent selection, a modified version of ranking parent selection[34], is employed for choosing the parent individuals.Thealgorithm for modified ranking parent selection is shownin algorithm 1.

In this type of parent selection, the best solutions frombat algorithm will be arranged in the descending orderaccording to their fitness and selects the first and best fivesolutions. A uniform crossover [35] shown in algorithm 2is habitually used for performing this operation.

Mutations are perturbed probabilistically to usher in achange in the individuals. Crossover is incapable of bring-ing in any new features because it merely combines theexisting features with a new generation. The use of a muta-tion operator is likely to affect/remove certain new featuresdue to modifications in the chromosome. Uniform muta-tion [35] shown in algorithm 3 is effectively employed tomutate the individuals.

Mutation, on the other hand, is carried on the basis ofpre-determined mutating probability. The best chosen con-trol parameters for hybrid Bat-Genetic algorithm is listedin Table 1.

After performing the crossover and mutation, theobtained solutions are compared with the earlier solutions

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Table 1. Parameters of hybrid Bat-Genetic algorithm

Parameter ValuePopulation size 25Loudness 0.9Pulse rate 0.1Minimum frequency 0Maximum frequency 2No. of iterations 100Crossover Uniform crossoverCrossover rate 0.1Mutation Uniform MutationMutation rate 0.1Parent selection Modified Ranking

from bat algorithm and the best solutions are selected. Thecomparison is made by the use of fitness function. Finally,after all the iterations, the best solutions that emerge givethe optimized wavelet coefficients. Making use of thesecoefficients, decomposition and reconstruction are per-formed. The pseudo code of the proposed Bat-Geneticalgorithm hybridization is given in algorithm 4.

PROPOSED MODEL FOR SECURE IMAGECOMPRESSION AND ENCRYPTION

In this paper, an optimized wavelet filter-based image com-pression is proposed and shown in Fig. 1. The techniqueemploys hybrid bat-genetic algorithm based optimizedDWT and Chaos theory-based encryption. It comprisestwo modules, compression and encryption. In compressionmodule, the input image is transformed to wavelet domainusing optimized wavelet coefficients-based DWT. The opti-mality is brought about by the use of hybrid bat-geneticalgorithm. Subsequently, the compression is carried outusing SPIHT and encryption using Chaos-based algo-rithm.On the other side, a decryption and decompressionmodules were presented to do the reverse process.

FIGURE 1. Block diagram of the proposed technique

Image Compression Module

In this module, the input images are decomposed into subbands using optimized wavelet high-pass and low-passfilters.

After decomposition of an image, there will be four fre-quency bands, in particular the Low-Low(LL), Low–High(LH), High–Low (HL), and High–High (HH). The follow-ing level decomposition is simply connected to the LL

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FIGURE 2. Image decomposition. Each sub band has anatural orientation

band of the current decomposition stage, which structuresa recursive decomposition technique as shown in Fig. 2.Hence, an N-level decomposition will at long last have3n+1 diverse frequency bands, which incorporate 3n highfrequency bands and only one LL frequency band.

After applying wavelet transform to an image, theSPIHT [36],[5] algorithm has been used to encode thewavelet coefficients for achieving image compression.

Chaos-based encryption

The compressed image has been encrypted using permu-tation diffusion based Chaos technique [37].The techniquecomprises two processing stages: permutation (shuffle) anddiffusion. The shuffling processes the positions of pixelsand the diffusion diffuses the values of the pixels, whichare mentioned as position and values mask, respectively.

Specifically, the shuffle permutes the original organiza-tion pixels in the image, without changing their values. Forthis purpose, chaotic map named Arnold cat map is used,which is defined by equation (3).

[xm+1

ym+1

]=

[1 c

d cd + 1

] [xm

ym

]mod W (3)

Where c and d are two positive integers and W is the widthor height of the image. The terms xm and ym represents thecurrent position of pixels and xm+1 and ym+1 representsthe position of shuffled pixels. An image encryption algo-rithm only has the shuffle; its security is weak because thecat map is an invertible discrete map without mixing thepixelsâŁ™ values. In other words, it does not change thestatistical properties of the plain image such as the inten-sity distribution of the pixels.So another process known asdiffusion using Gaussian map[38] is done for overcomingthis drawback.In this process,initially a key stream has beengenerated using the Equation (4) with α = 20, β = −0.9

and m1 = 0.1.

G(mi) = mi+1 = e(−α×m2i ) + β (4)

Usually, the output stream from a chaotic system is in therange of 0 to 1. So we will convert it into the range of 0 to256 using the Equation (5), before the diffusion process.

ki = (mi × 105) mod 256 (5)

The diffusion using this key stream ki is as shown belowin Equation (6)

Ei = Pi ⊕ ki (6)

Where Pi is the value of corresponding pixel in the shuffledimage and Ei is the value in encrypted image.The wholeencryption process has been described in Algorithm 5.

Decryption and Decompression

In order to obtain the original image from the compressedand encrypted data, the decryption and decompositionprocesses are to be carried out.The decryption is inverseoperation of the Chaos based encryption technique.In this,the original pixel value Pi is obtained by the Equation (7),provided that the secret key value Ei is known.

Pi = Ei ⊕ ki (7)

After that the inverse shuffling process will be carried outusing the Arnold Cat Map for getting the decrypted data.

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FIGURE 3. Test images

The decoding based on SPIHT process follows theinverse steps of compression exactly and is almost sym-metrical in terms of processing time. After decoding, theimage is inverse transformed to time domain using InverseDiscrete Wavelet Transform (IDWT). IDWT reconstructsa signal from the approximation and detail coefficientsderived from decomposition.

RESULTS AND DISCUSSION

The techniques are implemented in MATLAB on a systemhaving 8 GB RAM and 3.2 GHz Intel i-5 processor.The testimages [39] used for evaluation are shown in Fig. 3.

This section deals with the performance analysis ofproposed compression and encryption systems where eval-uated.The metrics used to evaluate the performance of theimage compression and decompression system includesthe PSNR, MSE [40], Compression ratio(CR) and thepercentage of compression ratio(CR%) [41], [42].

Performance of the Proposed Hybrid Bat-GeneticAlgorithm

Figure 4 shows the PSNR vs Iteration curve for theproposed hybrid Bat-Genetic algorithm.

Here, the use of this algorithm reveals that PSNR valueincreases with each iteration and reaches nearly saturation

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FIGURE 4. PSNR Vs Iteration of Proposed HybridBat-Genetic Algorithm

when the iteration count reaches more than 41. The max-imum PSNR value reached is around 42.3 for the trainedimage of ‘zelda’ of size (256 × 256) shown in Fig. 3(e).

Proposed Optimized Filter

After successful iteration of the hybrid Bat–Genetic algo-rithm, the coefficients of four optimized wavelet filterssuch as low pass decomposition filter (Lo_D), high passdecomposition filter (Hi_D), low pass reconstruction fil-ter (Lo_R), high pass reconstruction filter (Hi_R) wereobtained are shown in Table 2 and some of its propertiesare shown in Table 3.These filters performs their role in thecompression as like in [6].

Table 2. Filter coefficients of the proposed optimized filterbank

Lo_D Hi_D Lo_R Hi_R

−0.00038752 2.6966e−05 −2.6966e−05 −0.00038752

0.037922 −0.064251 −0.064251 −0.037922

−0.023092 0.039956 −0.039956 −0.023092

−0.11357 0.41771 0.41771 0.11357

0.38049 −0.78683 0.78683 0.38049

0.85321 0.41839 0.41839 −0.85321

0.37635 0.040143 −0.040143 0.37635

−0.10997 −0.06485 −0.06485 0.10997

−0.023781 −0.0004287 0.0004287 −0.023781

0.037046 7.9518e−05 7.9518e−05 −0.037046

Table 3. Properties of the proposed optimized filters

Sl.No. Characteristic Lo_D Hi_D Lo_R Hi_R

1 Filter Length 10 10 10 10

2 Filter Order 9 9 9 9

3 Stable Yes Yes Yes Yes

The single level decomposition and reconstruction ofimage in Fig. 3(a) using the proposed optimized waveletfilter is shown in Fig. 5.

Table 4 shows the performance analysis of the novel fil-ter based on energy and correlation coefficient. Ea, Eh, Ev,and Ed are the percentages of energy retained in the approx-imation, horizontal, vertical, and diagonal components,respectively.

The sum of energy is 100 in all cases; it means that thereis no loss of energy due to decomposition. Also the correla-tion coefficient between original image and reconstructedimage is unity; it means that there is no difference betweenthese two.

Performance Analysis of the Proposed Optimized FilterBased image compression

The results obtained from proposed optimized wavelet fil-ter and other existing wavelet filters with SPIHT basedcompression techniques are given in this section. Figure 6shows the corresponding decompressed output for the testimage ‘Lena.bmp’ obtained from our proposed techniqueand other wavelet filters such as haar, db4, Bior 5.5 andRbior 4.4 with SPIHT encoding at 1.0 bpp.

The evaluation metrics PSNR, MSE [40] and SSIM [43]are taken between the original image and decompressedimage and, compression ratio and the percentage of com-pression ratio (CR%) [41], [42] between original image andcompressed image. The comparison has been made withrespect to other popular wavelet filters such as Bior 5.5,RBior 4.4, Db4, haar at different bpp values and the resultsare shown in Table 5 and Table 9. The figures Fig. 7, 8, 9 and10 shows the performance comparison of the proposed filterwith other filters for the test image ‘Lena(256×256)’. Alsothe Table 8 shows the comparison of our results with somestandard results from literature.In all these cases the pro-posed optimized wavelet filter achieved better performancein image reconstruction compared to all other filters.

These results demonstrates the superiority of proposedoptimized wavelet filter over other wavelet filters. Note

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FIGURE 5. Decomposition and Reconstruction of test image ’Barbara.bmp(256 × 256)’ using proposed optimized filter

Table 4. Performance of Proposed optimized wavelet filter

Sl.No Image Ea Eh Ev Ed Sum of Percentage of Energy Correlation Coefficient1 Barbara 99.4275 0.1351 0.2756 0.1618 100 1.002 Cameraman 99.3776 0.1917 0.3671 0.0636 100 1.003 Bridge 98.8672 0.5932 0.3947 0.1449 100 1.004 Butterfly 97.6677 1.0761 0.9347 0.3215 100 1.005 Circuit 99.9031 0.0371 0.0544 0.0054 100 1.00

that Compression ratio is nearly same in all cases, thisclearly indicates that the use of proposed wavelet filter pre-serves the performance of image compression. In most ofthe cases, the use of proposed wavelet filter shows min-imum value of MSE and maximum value of PSNR andSSIM as compared to other standard wavelet filters. Thisindicates that there is less error between the original imageand decompressed image while using the proposed filter.

Performance Analysis of the Chaotic Image EncryptionAlgorithm

The results of chaotic encryption and decryption algorithmsare shown in Fig. 11. Here the shuffling process usingArnold Cat Map has been carried out for 12 rounds anddiffusion using Gauss Map has been carried out for onlyone round.

Histogram Analysis

It is desirable for a good encryption algorithm that the greyvalues of pixels are to be dispersed in the whole pixel valuespace [44]. From the Fig. 11(b) and 11(d) it is observedthat there is no change in the histogram, even after theshuffling process. But after the diffusion process,we can seein Fig. 11(f) that the gray values of pixels were scatteredamong the entire space. i.e., after encryption process thestatistical attack is not effective [44].

Correlation of Adjacent Pixels

It is desirable for an encryption algorithm to producethe encrypted image with less linear correlation (near to0) among its pixels in horizontal, vertical and diagonaldirection [44]. Here the correlation results are depictedin Fig. 12. It is observed that the there is high correla-tion between adjacent pixels in the plain image and in theencrypted image,it is less.Otherwise the linear correlationin the original image has been changed due to encryptionprocess.

From the Table 6, it is observed that the correlation inall the three directions, between pixels of original imageis larger than the encryption image. This means that theclosest pixels of original image have very large correlationbut the encrypted image has less correlation.Also comparedto [45] and [46], the correlation coefficient in Horizontal,Vertical and diagonal direction is less for the encryptedimage from proposed chaotic encryption algorithm.

Comparison with the literature

The performance analysis of chaotic image encryptionalgorithm has been done by using the evaluation metricssuch as Correlation between plain and encrypted images,entropy, Irregular Deviation(ID), Histogram Deviation(HD),Uniform Histogram Deviation(UHD), NPCR and

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Table 6. Correlation coefficient of two adjacent pixels for the test image Lena (256 × 256)

Direction of Plane Encrypted Image Encrypted Encryptedadjacent pixels image [Proposed Algorithm] image [45] image [46]Horizontal 0.9456 -0.0042 -0.0254 -0.0034Vertical 0.9727 -0.0018 0.0034 0.0061Diagonal 0.9213 0.0014 0.0315 0.0089

FIGURE 6. Decompressed image obtained from proposedtechnique and other wavelet filters such as for haar, db4, Bior4.4, Rbior 4.4, coif 4, and sym4 based techniques

UCAI mentioned in [47], [46] and [45]. The comparisonwith standard results are shown in Table 6 and 7.

From the Table 7, it is observed that entropy values ofthe encrypted image is near to 8 and thus the proposed

Table 5. Performance comparison of the proposed filter withother popular wavelet filters at bpp =1

Wavelet Filter bpp = 1.0

MSE PSNR SSIM

Barbara(256 × 256)bior5.5 18.2532 35.5174 0.83349db4 17.8421 35.6163 0.83939haar 31.1669 33.1939 0.76557rbio4.4 21.0365 34.9011 0.82185proposed 16.0459 36.0772 0.85299Lena(256x256)bior5.5 11.2332 37.6258 0.7997db4 10.9985 37.7175 0.81431haar 20.1757 35.0825 0.72155rbio4.4 13.4554 36.8418 0.79511proposed 9.3076 38.4424 0.82535Pepper(256x256)bior5.5 11.3805 37.5692 0.82167db4 10.3009 38.0021 0.84136haar 20.759 34.9587 0.75323rbio4.4 12.5261 37.1526 0.82455proposed 8.7879 38.692 0.85009Pirate(256x256)bior5.5 28.6055 33.5663 0.79127db4 27.857 33.6815 0.80461haar 41.5773 31.9422 0.73834rbio4.4 35.7834 32.594 0.78289proposed 25.208 34.1154 0.81721Zelda(256x256)bior5.5 4.3295 41.7664 0.91753db4 4.2348 41.8625 0.91953haar 12.2847 37.2372 0.84497rbio4.4 5.4921 40.7335 0.90545proposed 3.8306 42.2981 0.92611

Table 7. Evaluation of Chaotic Encryption Algorithm usingTest image Cameraman(256 × 256)

Metric Proposed [46] [48] [49]

Entropy 7.9970 7.9970 7.5717 7.9940

Correlation -0.0018 - - 0.0024

ID 0.5966 0.6034 - 0.5934

HD 0.9807 - - -

UHD 0.0680 0.0551 - -

NPCR 99.63 98.8251 - 99.9985

UCAI 31.33 33.1335 26.8856 -

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FIGURE 7. MSE Vs BPP for the test image ‘Lena.bmp’

FIGURE 8. PSNR Vs BPP for the test image ‘Lena.bmp’

FIGURE 9. SSIM Vs BPP for the test image ‘Lena.bmp’

chaotic encryption algorithm is able to resist the entropyattacks [45]. In the case of ID, a lower value indicates goodaccuracy in encryption[50]. Here the value of ID is lesscompared to [46] and near to [49].In the case of HD, ahigher value indicates good accuracy[50] and here it is

FIGURE 10. CR% Vs BPP for the test image ‘Lena.bmp’

FIGURE 11. Results of chaotic Encryption

0.9807. As a larger value of NPCR and UCAI is showsbetter accuracy of image encryption, the proposed algo-rithm had obtained nearly good values compared to [46]and [48].

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FIGURE 12. Correlation between adjacent pixels in plainand encrypted image in horizontal, vertical and diagonaldirection.

Table 8. Comparison of Proposed Method With ExistingMethods using Lena (256 × 256)

Method PSNR BPP

SCPSOGA[51] 27.24 0.3931

SC-CPSO[52] 27.23 0.3934

SC-GA[53] 27.41 0.4

SGA[54] 27.30 0.4

GA with hybrid selection[55] 27.03 0.4

FIC using DWT[16] 28.55 0.4

Proposed Hybrid BA-GA 31.6579 0.393

GA based method[56] 30.22 0.76

Proposed WorkHybrid BA-GA 36.1953 0.76

CONCLUSION

Optimized wavelet filter based image processing sys-tem makes use of hybrid BAT-Genetic algorithm basedoptimized DWT based compression and Chaos theory-based encryption. The proposed technique was comparedwith haar, Daubechies 4, biorthogonal 5.5, and ReverseBiorthogonal 4.4. The simulation results shows that theproposed technique has obtained better evaluation metric

compared to all the other existing wavelet-based imagecompression systems in terms of PSNR, MSE and SSIMvalues without affecting the compression performance.Further, the performance in decomposition and reconstruc-tion using the proposed filter, in terms of energy retainedin sub-bands and coefficient of correlation is analyzed.The sum of percentage of energy retained in all sub-bandsin all cases is 100%, which means that there is no lossin decomposition. Similarly, the coefficient of correlationbetween the reconstructed images is unity in all cases. Thisshows the proposed filter gives perfect decomposition andreconstruction. From all these results, we can infer that theproposed technique shows better performance in terms ofimage quality after decompression without affecting thecompression, compared to other existing filters.Also theperformance of encryption algorithm has been comparedusing various evaluation metrics and observed that it is alsoshowing optimized performance. The performance of com-pression can be improved by making proper modificationsin the encoding technique.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this article.

REFERENCES

[1] Sonja Grgic, Mislav Grgic, and Branka Zovko-Cihlar.Performance analysis of image compression usingwavelets. Industrial Electronics, IEEE Transactions on,48 (3): 682–695, 2001.

[2] Bryan E Usevitch. A tutorial on modern lossy waveletimage compression: foundations of jpeg 2000. IEEEsignal processing magazine, 18 (5): 22–35, 2001.

[3] Sonja Grgic, Krešimir Kerš, and Mislav Grgic. Imagecompression using wavelets. In Industrial Electronics,1999. ISIE’99. Proceedings of the IEEE InternationalSymposium on, volume 1, pages 99–104. IEEE, 1999.

[4] R Loganathan and YS Kumaraswamy. Medical imagecompression using biorthogonal spline wavelet with dif-ferent decomposition. IJCSE International Journal onComputer Science and Engineering, 2 (9): 3003–3006,2010.

[5] Bhawna Rani, RK Bansal, and Savina Bansal. Compar-ison of jpeg and spiht image compression algorithmsusing objective quality measures. In Multimedia, Sig-nal Processing and Communication Technologies, 2009.

10605


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10607


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[9] Michael R Peterson, Toby Horner, and Frank Moore.Evolving matched filter transform pairs for satelliteimage processing. In SPIE Defense, Security, and Sens-ing, pages 80590L–80590L. International Society forOptics and Photonics, 2011.

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