OptimizedWavelet Filters and Modiﬁed Huffman Encoding ... · rate. Further the chaotic encryption algorithm has been eval-uated using suitable metrics, Experimental results show

International Journal of Applied Engineering Research, ISSN 0973-4562 Volume 12, Number 13 (2017) pp. 3961–3977© Research India Publications, http://www.ripublication.com

Optimized Wavelet Filters and Modified Huffman Encoding-basedCompression and Chaotic Encryption for Image Data

Renjith V Ravi and Kamalraj SubramaniamDepartment of Electronics and Communication Engineering, Faculty of Engineering,

Karpagam Academy of Higher Education,Karpagam University, Coimbatore, India.

ORCID : 0000-0001-9047-3220; ORCID : 0000-0002-6781-4282

Abstract: For the transmission of images through wirelesscommunication channels effectively, the two major con-cerns to be addressed are the bandwidth limitation andthe high probability of error. To overcome the bandwidthissue, compression is applied to the transmitted data. How-ever, compression increases bit dependency, which, in turn,introduces error extension effects. In this paper, a newtwo-level compression model is proposed namely, SPIHT-MHE algorithm. This model improves the compressionperformance of the original input data. Additionally, opti-mized discrete wavelet transform (DWT) is derived usinghybridization of genetic and gravitational search algorithmto improve the wavelet performance. The proposed systemof image compression and encryption system (ICES) con-sists of two modules:compression-Encryption module anddecompression-decryption . In the first phase, the input imageis transformed using hybrid GSA-GA algorithm-based DWT.In the second phase, the input image is firstly compressedusing SPIHT and subsequently, a second-level compressionscheme is proposed using merging-based Huffman encod-ing (MHE) algorithm. In the third phase, the compressed is,encrypted to have the secure transmission/storage. The per-formance of the proposed compression system is evaluatedby PSNR, MSE,SSIM, compression ratio, and compressionrate. Further the chaotic encryption algorithm has been eval-uated using suitable metrics, Experimental results show thatthe proposed system provides a greater compressing capacityand maintains the received image at a higher quality.

Keywords: image compression,optimized DWT, MHE,Hybrid GSA-GA, Gravitational Search Algorithm

INTRODUCTION

As of late, with the hasty development in transmitting imagesover public networks, the network bandwidth and securityhave gotten significant measures of consideration. The mosteffective method to compress images to spare bandwidth andencrypt images to ensure privacy has got to be the hotspot onwhich the researchers would investigate.

Extremely compelling and well known approaches toaccomplish compression of image data depends on the dis-crete cosine transform (DCT) and discrete wavelet transform(DWT). DCT gives a great energy compaction, and variousfast algorithms exist for computing the DCT. Recently, anawesome part of the research practices in image coding havebeen based on the DWT, which has turned into a standardtool in image compression applications on account of itsvarious advantages [1] over DCT. The most well-known dis-tortion in DWT based image compression framework is thequantization error [2]. In spite of the fact that quantizationgreatly enhances compression ratios; perfect reconstructionis unimaginable because of the loss of low-order bits [3]. Sothe performance of an image coder depends on the minimiza-tion of this loss at the desired compression ratio. This is solelydepends on the properties of filter banks used in DWT, used init. So, the introduction of optimized filter banks derived frommetaheuristic optimization algorithms will further increaseits performance [4],[5] in quality of reconstructed images. Animage compression system includes an encoder like SPIHTor Huffman that uses the redundancies to describe the imagedata in a compressed way, while the decoder is exploited torenovate the original image from the compressed data [6]. In


Huffman Encoding, the frequency of occurrence of a specificpixel value is employed to encode the image pixel informationby means of variable size bit-words [7][8]. This procedure isknown as entropy encoding.

However alone compression is not adequate as it has noconfirmation on security of the information, which is to betransmitted. The Security of data to keep up its confidentiality,proper access control, integrity and accessibility are somesignificant issues in information communication. There aresome conventional encryption methodologies, such as DES,3DES,AES and RSA and so forth.An account of images havea lot of data, high redundancy and solid correlation of pixelfeatures etc. These customary algorithms are not appropriate[9], [10], [11] for practical encryption of image data.

Chaos theory [12] is a branch of mathematics,which hasapplicability in various sciences such as non linear dynam-ics, cryptology, communications etc. Since Robert A. 1.Matthews exhibited the idea of chaotic cipher in 1989, chaoticencryption strategy has pulled in more consideration. Chaoticsequences’s great properties like pseudo-randomness, ergod-icity and their highly sensitive dependence on starting con-ditions and other system parameters fit the prerequisites ofciphers.

A secure image codec having compression and encryp-tion modules has been developed in this paper. Initially ahybridization of Gravitational search Algorithm (GSA) andGenetic Algorithm (GA) were carried out to produce a noveloptimized wavelet filter bank which is to be used for trans-formation of images from spatial domain to wavelet domain.Subsequently, an SPIHT algorithm modified Huffman encod-ing known as merging based Huffman encoding (MHE) hasbeen developed to achieve the compression of images.

Further an image encryption algorithm using chaoticcipher has been developed for assuring the securityof compressed images. The proposed codec comprisestwo modules, namely compression-encryption module, anddecompression-decryption module. In the compression mod-ule, the input image is decomposed to high frequency and lowfrequency components using optimized wavelet filters andcompressed using SPIHT with MHE. And the compressedimage is encrypted using Chaos based encryption. In thedecompression and decryption module, the decryption, andde-compression were carried out to get the estimated image.

DESIGN OF OPTIMIZED WAVELETCOEFFICIENTS

Discrete Wavelet Transform

In recent times, DWT has risen as a mainstream system forcompression of data [13] because of its high de-correlationand energy compaction proficiency. An image that is decom-posed by DWT method can be reconstructed with the desiredresolution. The most important feature of DWT is that it per-mits multi-resolution decomposition. This is because of thefilter bank, which has both a low-pass filter (LPF) (H1) anda high-pass filter (HPF) (H0), enabling it to exactly halvethe frequency range between the two filers. This filter pair iscalled the analysis filter pair and the filter pair used for thereconstruction process is called the synthesis filter pair, whichconsists of another LPF (G1) and an HPF (G0). Fig. 1 showsthe filter bank approach of DWT.

FIGURE 1. Filter bank approach of DWT

Most importantly, the LPF is applied for each row of datato obtain low frequency components of the row.

As the LPF is a half-band filter, the output informationconsists of frequencies just in the first half of the originalfrequency range. By Shannon’s Sampling Theorem, thesefrequencies can be sub-sampled into two, so that the out-put information contains only half the original number ofsamples. Similarly, the HPF is connected to the same lineof information; once the high-pass components are sepa-rated, put them by the side of the low-pass components. Thisprocedure is repeated for all the rows of the image [14].

Next, the filtering is done on every column and subse-quently we get four bands of data, each marked as LL (low-low), HL (high-low), LH (low-high), and HH (high-high).This process is depicted in Fig. 2.

The LL band can be decomposed till the end, in the sameway further for creating more sub-bands [15]. This shouldbe possible up to any level, along these lines bringing abouta pyramidal decomposition as appeared over the LL band at

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FIGURE 2. wavelet filter arrangement for Decomposition andreconstruction of an image

the highest level can be said as most imperative, and alter-nate bands are of lesser significance, the level of significanceabatements from the highest point of the pyramid to base. Forreconstructing the original image, the reverse of this processwould be done using the synthesis filter bank. Fig. 3 showsthe wavelet decomposition and reconstruction process.

FIGURE 3. Multi-level decomposition and reconstruction ofan image

Proposed Method for Optimization of Filter CoefficientsVia GSA-GA Hybridization

The high-pass and low-pass wavelet filter coefficients areoptimized using the hybrid GSA-GA optimization algo-rithm, which is basically the hybridization of GravitationalSearch (Algorithm 1) and Genetic (Algorithm 2) algorithms.

More clearly the hybrid GSA-GA is formed by incorporatingmutation and crossover operators into the GSA.

Randomized initialization The initial population israndomly generated with size X using the real coding rep-resentation. Each agent is encoded as a vector of floatingpoint numbers, with the same length as the vector of decisionvariables. Each agent contains two decision variables, one isthe Reconstruction filter (Rf) coefficients (b1 to bm) and theother is the decomposition filter (Df) coefficients (c1 to cm).

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Based on the wavelet coefficients, the ith solution of agent Pi

is encoded as follows

Pi = {(b1, b2, . . . , bm)(c1, c2, . . . , cn)} m = 10 & n = 10(1)

Fitness evaluation of agents Here, the fitness functionused is peak signal to noise ratio between the input and outputimages and is computed as follows:

PSNR = 10 log10Maxi

2

MSE(2)

Where, Maxi is the maximum possible pixel value of theimage. When the pixels are represented using 8 bits per sam-ple, this is 255. A high value of PSNR means less errorbetween the images. So this problem is a maximizationproblem.

Initialization of agents considering a system with Nagents(masses)

Updating Velocity and Position During the searchprocess, the agents are moved according to the followingEqns:

Vi(t + 1) = randi × Vi(t) + ai(t) (3)

Pi(t + 1) = Pi(t) + Vi(t + 1) (4)

Where, Pi(t) and Vi(t) represent the current position andvelocity of agent at iteration, respectively.

Updating G Gravitational constant G is computed atiteration t

G(t) = G0 exp( −αtT

) (5)

G0 and α are initialized at the beginning and will be reducedwith time to control the search accuracy. T is the total numberof iterations.

Updating Masses: Gravitational and inertia masses foreach agent are calculated at iteration t .

Mai = Mpi = Mii = Mi ∀i = 1, 2, . . . , N

m(t) = f iti(t) − worst (t)

best (t) − worst (t)(6)

Mi(t) = mi(t)∑Ni=1 mj(t)

(7)

Where, Mai and Mpi are the active and passive gravitationalmasses, respectively, Mii is the inertia mass of the ith agent,

f iti(t) represents the fitness value of the agent i at time t ,and, worst (t) and best (t) are

best (t) = maxj∈{1,...N}f itj (t) (8)

worst (t) = minj∈{1,...N}f itj (t) (9)

Calculating the Total Force The force [16] acting onmass i from mass j at a specific time t is as follows:

Fdij (t) = G(t)

Mi(t) × Mj(t)

||Pi(t), Pj (t)|| (bdi (t) − bd

j (t)) (10)

Where Mi and Mj are masses of agents. The randomlyweighted sum of the forces exerted from other agents towardsthe ith agent is Fd

i (t) given as follows

Fdi (t) =

∑j �=i

randjFdij (t) (11)

Updating Acceleration The acceleration related tomass in the time.Its dimension is given as follows:

adi = Fd

i (t)

Mii(t)(12)

Where, Mii(t) is the inertial mass of ith agent at time t .

Crossover: In this step, uniform crossover is appliedon the agents to improve the solution quality. It is the mostlikely the most dominant crossover [17], [18], [19] because itallows the offspring chromosomes to search all possibilitiesof re-combining those different genes in parents. In uniformcrossover a cross over operator Cr determines the number ofgenes to be considered for crossover.

Mutation: In this step, uniform mutation process isapplied. The mutation operator performs a small agent orsolution modification by selecting the genes with the lengthof population and by interchanging the gene order. Muta-tion is carried out on the basis of pre-determined mutatingprobability.

Termination criteria: The stopping criterion isachieved when the objective function does not change fora certain number of generations or when the number ofgenerations exceeds the specified maximum generations.

The best chosen parameters of hybrid GSA-GA algorithmis shown in Table 1

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

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Table 1. Parameters used in GSA-GA algorithm

Parameter ValuePopulation size 10Iteration Cycles 100α 0.01G0 0.1r Norm 2r Power 1Crossover Uniform CrossoverCrossover rate 0.5Mutation Uniform MutationMutation rate 0.5

from bat algorithm and the best solutions are selected. Thecomparison is made using the fitness function. Finally, afterall the iterations, the best solutions are found out, which givesthe optimized wavelet co-efficients, and making use of thesecoefficients, DWT is performed.The pseudo code of proposedGSA-GA algorithm is shown in algorithm 3.

DESIGN OF PROPOSED IMAGECOMPRESSION AND ENCRYPTION SYSTEM

The proposed image compression and encryption system(ICES) is depicted in Fig.4.In this, initially the input images

will be compressed using the optimized wavelet and twolevel encoding. The first level of two level encoding con-sists of Set Partitioning in Hierarchical Trees (SPIHT) [20]and modified form of basic Huffman encoding [21]. Further,this compressed image will be encrypted using chaos the-ory based image encryption algorithm. At the decompressionand decryption module, the coded image is decompressed anddecrypted.

FIGURE 4. Model of the proposed image compres-sion-encryption system

Optimized Wavelet and Two Level Encoding BasedCompression

In this module, the input images will compressed by transfor-mation using optimized DWT (discussed in section ) and twolevel encoding using SPIHT and modified Huffman encoding.

First-level Compression Via SPIHT Algorithm

Of late, the SPIHT [20] has surfaced as a dominant wavelet-based image compression technique. This technique encodesthe most vital wavelet transform coefficients and proceedsto communicate the bits in order that an incredibly refinedversion of the original image is gradually achieved. It glistens

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with the sparkling merits of superb image quality, adapted forprogressive image communication, colourfully emerges witha completely entrenched coded file, and is advantageouslyemployed for loss less compression.

Once the wavelet transform is applied to an image, theinnovative SPIHT technique segments the decayed waveletinto major and minor partitions in accordance with thefunction shown below.

γp(C) ={

1, maxm,n∈C

{|qm,n|}

� 2p

0, otherwise(13)

Here, γp(C) represents the importance of a set of co-ordinatesC and qm,n relates to the coefficient value at coordinate (i, j).This technique is home to two passes: the sorting pass andthe refinement pass. It effectively exploits three lists knownas the LIP (List of Insignificant Pixels), LIS (List of Insignif-icant Sets), and LSP (List of Significant Pixels). The LIP,in essence, comprises the individual coefficients with lowermagnitudes than those of the thresholds. On the other hand,the LIS is a set of wavelet coefficients defined by tree struc-tures with lower magnitudes than those of the threshold.Further, the LSP represents a list of pixels having biggermagnitudes than those of the threshold.

The sorting pass is executed on the three lists mentionedabove. The greatest number of bits needed to characterize theprincipal co-efficient in the spatial orientation tree is achievedand symbolized by pmax as per the following relation:

Pmax = [log2(maxm,n{|qm,n|})] (14)

In the case of sorting pass, the corresponding coordinatesof the pixels which stay in the LIP are evaluated for impor-tance with the help of the equation shown above. The outcomeis forwarded to the output and from this the important one willbe sent to the LSP along with their sign bit output. The Setsin the LIS will also be evaluated for their importance and ifthey are found important, they are segregated and segmentedinto subsets.

The subsets having a single coefficient, which are estab-lished as important, are segregated and segmented into sub-sets. Further, the subsets having a solitary coefficient, whichare proved to be important, are included in the LSP; in othercases, they are placed in the LIP. In the refinement pass, thepth MSB of the coefficients in the LSP represents the ultimateoutput. The value of p is decreased step by step and the sortingand refinement passes are executed again. These passes arerepeated till the preferred rate is obtained or all the nodes inthe LSP contain all their bits output. The latter case is approx-imately precise renovation as all the coefficients have been

effectively subjected to the total processing. It is also possibleto efficiently manage the bit rate in the SPIHT technique inview of the fact that the output generated is in solitary bitsand the technique can be completed at any time.

Second-level Compression Via Merging-based HuffmanEncoding (MHE)

Merging-based Huffman encoding (MHE) algorithm consistsof three significant steps: (i) Huffman code creation of orig-inal data (ii) code conversion-based conditioning, and (iii)encoding. The sub section below explains the detailed processof MHE algorithm.

Huffman code creation of original data Initially thecreation of huffman code for the original data would be doneby the technique used in algorithm 4.

Code conversion of condition-based sequence Thecode conversion of condition-based sequence is done aftergenerating Huffman code for each symbol or original data(unsigned 8-bit integer value). The process of code conver-sion of condition-based sequence is as follows: initially theoriginal data and its codeword are taken. Thereafter, the codeconversion process is done by merging the two symbols, i.e.,

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The number of times the selected combination of two sym-bols is repeated. Then, the merging process is based on thefollowing observations as below in Algorithm 5.

Encoding The encoding process is done based on thecombination of symbols used in the code conversion ofmerging-based sequence and the preceding symbol in theoriginal data. The encoding process is as follows: initiallythe combination of the symbols used for the code conversionprocess and the preceding symbol of the combination of thesymbols used for the code conversion process are checked todecide whether the code formed using the code conversionprocess is to be considered or not. Then the three conditionsexplained above are applied and checked if each symbol is inorder to encode the original data.After this verification, a codeis formed for the original data. The final code is the encodeddata based on merging-based Huffman encoding technique.

Example of the MHE algorithm: The complete pro-cess of MHE is explained by an example as follows: Let usassume ’(215) (145) (215) (145) (126) (215) (51) (45) (215)(126)’ is an original data and from this original data, the Huff-man code is formed for each symbol in the original data. Theformation of code is shown in Fig.5.

Fig. 5 is explained as follows: initially the repeated let-ters are considered once and the frequency of the letter ismarked in the original data, i.e., the numeric term 3 belowthe unsigned integer value ’215’ represents that the symbol

FIGURE 5. Formation of Huffman code

’215’ is repeated three times in the original data. Thereafter,two symbols with least frequency are taken and assigned zeroand one to them and then represent the total frequency of thetwo symbols below it. This process is repeated by taking thenext two symbols until the last step. The Huffman code isthen formed for each symbol by considering the correspond-ing branches of zeros and ones from the last step to the first.From Fig.5, the Huffman code formed for the symbol ’215’is 1; for the symbol ’145’ is 000; for the symbol ’126’ is01; for the symbol ’51’ is 0011; and the for the symbol ’45’is 0010. Eventually, the Huffman code for the original data’(215) (145) (215) (145) (126) (215) (51) (45) (215) (126)’is ’1000100001100110010101’. Fig.6 shows the direction ofHuffman code formed for each letter.

After generating the Huffman code for each letter, the codeconversion of condition-based sequence is done by arrangingthe least length letters first. The code conversion of merging-based sequence process is used to compress the data. InFig. 6, we obtained the frequency combination of two symbolsfirst and the merging process is applied only on the satisfiedcombination. Based on the merging conditions, at first, thecombination of symbols ’(215) (145)’ is repeated at least twotimes that only qualified for the merging process. Secondly,the pair that has the same combination of first digit of theselected pair ’(215) (145)’ that should not repeat. Thirdly, thebit length of the first position of pair (1) should be lesser than

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FIGURE 6. Direction of Huffman code formation

the bit length of the second position of pair (000). Now, thepair ’(215) (145)’ is qualified for the merging process. Thenthe merging process is done by step 4 in the code conversionsection. The new code (215) (215) is replaced by ahead for(215) (145). Similarly, the code conversion process is donefor all the original data. Finally, the MHE-based encoded datafor the original data ’(215) (145) (215) (145) (126) (215) (51)(45) (215) (126)’ is ’111101100110010101’. Table 2 showsthe symbols with its code after the code conversion process.

Chaos-based Encryption

Subsequently, the compressed image is encrypted by employ-ing the Chaos method [22]. This method proceeds throughtwo phases of processing: (a) shuffle and (b) diffusion. Thepositions of the pixels were relocated in the shuffle stage andin the subsequent phase of diffusion, the values of pixels aredispersed, which are described as position and values mask,correspondingly.

The function of shuffle is to conceal the original organi-zation of the pixels of the image. Particularly, it reshapes theentire pixels of the image without causing any alteration intheir values. With this end in view, a chaotic diagram is effec-tively used as shown by the following relation known aArnoldcat map: [

xm+1

ym+1

]=

[1 c

d cd + 1

] [xm

ym

]mod W (15)

Where, c and d signify two positive integers and W standsfor the width or height of the image. An image encryptiontechnique only contains the shuffle operation and its securityis fragile and the cat diagram is an invertible discrete diagramwithout integrating the pixels’ values. That is, the map doescause any variation in the statistical traits of the plain-text likeintensity distribution of the pixels.The task called diffusion[23],[24] using Quadratic map [25] shown in Eq. 16 has beenentrusted to overwhelm this deficiency.

xm+1 = 1 − 2x2m (16)

Where, x0 ∈ [−1, 1] and m = 0, 1, 2, . . . etc.

As the output xm is in the range of (0, 1),we need to convertit into the range of (0, 256) using the Eq. 17 before diffusionprocess.

ki = (mi × 105) mod 256 (17)

The diffusion using this key stream ki is as shown below inEqn 18

Ei = Ii ⊕ ki (18)

Where Ii is the value of corresponding pixel in the shuffledimage and Ei is the value in encrypted image.

Decryption,De-compression and IDWT

For retrieving the original data, de-encryption, two levelde-compression, and finally taken Inverse Discrete WaveletTransform (IDWT) will carryout.

The de-encryption is the inverse operation of the Choas-based technique. In this, the original pixel value Ii is obtainedby the Eq.19, provided that the secret initial value Ei−1 isknown. s

Pi = Ei ⊕ ki (19)

The first-level decompression is done by MHE algorithm.The de-compression based on the SPIHT process follows theinverse steps of compression exactly and is almost symmet-rical in terms of processing time. After de-compression, theimage is inverse transformed to time domain using IDWT.The IDWT reconstructs a signal from the approximation anddetail coefficients derived from decomposition. The IDWTrequires up-sampling and filtering.

RESULTS AND DISCUSSION

The performance of the proposed system has been tested forvarious standard test images from [26] shown in Fig. 7.

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Table 2. The symbols with its code after the code conversion process

Original 215 145 215 145 126 215 51 45 215 126

Modified 215 215 215 215 126 215 51 45 215 126

compressed 1 1 1 1 01 1 0011 0010 1 01

FIGURE 7. Test images

The proposed image compression and encryption tech-niques has been implemented in the working platform ofMATLAB (version7.12). This technique is performed on awindows machine having the following configuration: pro-cessor Dual-core CPU, RAM 1 GB, and Speed 2.70 GHz.The operating system is Microsoft Window 7 professional.

In this section,we analyses the performance of proposedGSA-GA algorithm, optimized wavelet filter bank and MHEhuffman algorithm, chaotic encryption algorithm.

Performance of the proposed GSA-GA algorithm

The performance of the proposed GSA-GA algorithm hasbeen evaluated using PSNR vs iteration graph shown in Fig. 8.

Even though PSNR can certainly measure the intensitydifference between two images, it is known that it may not

FIGURE 8. Performance of the proposed approach usingPSNR Vs Iteration

Table 3. Filter coefficients of the proposed GSA-GA-basedoptimized filter bank

Lo_D ( H1) Hi_D ( Ho) Lo_R ( G1) Hi_R ( G0)

0.0000 −0.0378 0.0378 0.0000

0.0378 −0.0238 −0.0238 −0.0378

−0.0238 0.1106 −0.1106 −0.0238

−0.1106 0.3774 0.3774 0.1106

0.3774 −0.8527 0.8527 0.3774

0.8527 0.3774 0.3774 −0.8527

0.3774 0.1106 −0.1106 0.3774

−0.1106 −0.0238 −0.0238 0.1106

−0.0238 −0.0378 0.0378 −0.0238

0.0378 0.0000 0.0000 −0.0378

identify the visual perceptual quality of the image. The idea ofour research is to compress unmanned vehicle images usingoptimized DWT and modified Huffman encoding. In Fig. 8,we obtain the maximum PSNR of 42.0577 db from the 5th to25th iteration, which is a very high value for the train image’Zelda(256×256). A high PSNR value means that the outputimage is of high quality.

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Performance Analysis of the Proposed GSA-GA-basedOptimized Filter

The optimized wavelet filters in the filter bank derived fromthe hybrid GSA-GA algorithm are stable digital filters ofeach of length 10. The order of low-pass decompositionH1 and high-pass reconstruction G0 are 9 and low-passreconstruction and high-pass decomposition filters are 8. Thecoefficients of the proposed GSA-GA-based filters are shownin Table 3 and its features are listed in Table 4.

Table 4. Properties of the proposed GSA-GA-based optimizedfilters

Sl. No. Information Lo_D Hi_D Lo_R Hi_R

1 Filter Length 10 10 10 10

2 Filter Order 9 8 8 9

3 Stable Yes Yes Yes Yes

The performance of the proposed decomposition filterbank is evaluated by taking the percentage of energy retainedin each of the four sub-bands after a single decomposition andadded these percentages of energies together to get the totalenergy in percentage. In all these test cases, the total percent-age energy in each sub-band is 100, which means there is noloss of energy in decomposition. These details are listed inTable 5. Here Ea, Eh, Ev, and Ed are the energy retained in theapproximation, horizontal, vertical, and diagonal sub-bands,respectively.

The decomposition and reconstruction of image camera-man.bmp of size 256 × 256 is shown below in Fig.9

FIGURE 9. Decomposition and reconstruction of an imageusing the proposed filter

Performance Evaluation of the Chaotic EncryptionAlgorithm

The plain and cipher images, and its corresponding his-tograms from the proposed chaotic encryption,algorithm is

shown in Fig. 10. In this, the shuffling using Arnold CatMap has been carried out for 12 rounds and diffusion usingquadratic map has been carried out for 1 round.

FIGURE 10. Results of chaotic Encryption

Histogram Analysis

It is attractive for a decent encryption algorithm that the grayvalues of pixels are to be scattered in the entire pixel valuespace [27]. From the Fig. ?? and Fig. ?? it is detected thatthe there is no alteration in the histogram, even after the shuf-fling process. But after the diffusion process, we can notice

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Table 5. Percentage of energy retained in each sub-bands

Sl.No Image Ea Eh Ev Ed Sum of Percentage of Energy

1 barbara 99.2538 0.1956 0.3397 0.2108 1002 bridge 98.5639 0.7522 0.4821 0.2017 1003 bird 99.9320 0.0183 0.0439 0.0059 1004 butterfly 96.8147 1.4804 1.2564 0.4485 100

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

Direction of adjacent pixels Plane image Encrypted Image [Proposed] Encrypted image [27] Encrypted image [28]

Horizontal 0.9335 0.0086 -0.0017 -0.0034

Vertical 0.9592 0.0013 -0.0162 0.0061

Diagonal 0.9087 0.0055 -0.0014 0.0089

in Fig. ?? that the gray values of pixels were scattered amongthe whole space. ie, after the diffusion, the statistical attackis not effective[27].

Correlation Analysis

It is attractive for an encryption algorithm to create theencrypted image, with less linear correlation (near to 0)between its pixels in the horizontal, vertical and diagonaldirections [27]. From the correlation results are delineatedin Fig. 11, it is monitored that the there is a high correlationbetween nearby pixels of the plain image and in the encryptedimage, it is less. This because; the linear correlation in the firstimage has been changed because of encryption process.

From the Table 6, it is observed that the correlation in allthe three directions, between pixels of original image is biggerthan the encryption image. This implies the nearest pixels oforiginal image have substantial correlation yet the encryptedimage has less correlation.Also contrasted with [28] and [11],the correlation coefficient in Horizontal,Vertical and diagonalpath is less for the encrypted image from the proposed chaoticencryption algorithm.

Comparison with the literature

The performance of the chaotic encryption algorithm hasbeen evaluated using the metrics such as entropy, Irregu-lar deviation(ID), NPCR, UCAI, Uniform Histogram Devi-ation(UHD), Histogram Deviation(HD) and Correlationbetween plain and cipher images etc. mentioned in [29], [28]and [11]. Further in Table 7, these results were compared withstandard results.

FIGURE 11. Correlation between adjacent pixels in plain andencrypted image in horizontal, vertical and diagonal direction.

Performance Evaluation of the Proposed ImageCompression System

The performance in maintaining image quality after decom-pression has been carried out using the metrics such as

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

Metric Proposed [28] [30] [31]Entropy 7.9963 7.9970 7.5717 7.9940Correlation −0.0018 − − 0.0024ID 0.5946 0.6034 − 0.5934HD 0.9971 − − −UHD 0.0728 0.0551 - −NPCR 99.63 98.8251 − 99.9985UCAI 31.46 33.1335 26.8856 −

MSE, PSNR [32] and SSIM [33] between the original imageand the decompressed image. Also, the metrics used forevaluating the performance of compression are, compres-sion ratio,compression rate, percentage of compression ratio(CR%) and relative data redundancy (RDR) [34] [35] betweenoriginal image and compressed image. The performanceachieved by the proposed filter in the case of reduction inMSE, improvement in image quality at bpp =1 is shown inTable 8.Also from the results shown in Table 10 and Fig-ures Fig. 12, 13, 14, 15, 16 and Fig. 17, it is observed thatthe proposed image compression algorithm achieves goodcompression result without highly affecting the quality ofdecompressed image at different bpp levels.

FIGURE 12. MSE Vs BPP for the test image ’Lena.bmp’

Further, we have compared our algorithm with other sys-tems in the literature and observed that our algorithm showsbetter performance all others. This comparison is shown inTable 9.

Table 8. Performance comparison of the proposed filter withother popular wavelet filters at bpp =1

Wavelet Filter bpp = 1

(lr)2-4 MSE PSNR SSIM

Barbara(256 × 256)bior5.5 + spiht 18.2532 35.5174 0.83349db4 + spiht 17.8421 35.6163 0.83939rbio4.4 21.0365 34.9011 0.82185optimized dwt+spiht+Humffman 16.1579 36.0470 0.85203optimized dwt+spiht+MHE 16.1579 36.0470 0.85203Cameraman(256 × 256)bior5.5 + spiht 21.4878 34.8089 0.53198db4 + spiht 20.3889 35.0369 0.54828rbio4.4 + spiht 23.5787 34.4056 0.53372optimized dwt+spiht+Humffman 18.2581 35.5163 0.5534optimized dwt+spiht+MHE 18.2581 35.5163 0.5534Einstein_orig(256 × 256)bior5.5 + spiht 1.2966 47.0026 0.55319db4 + spiht 1.2476 47.1702 0.57338rbio4.4 + spiht 1.3912 46.6968 0.56406optimized dwt+spiht+Humffman 1.1449 47.5432 0.58173optimized dwt+spiht+MHE 1.1449 47.5432 0.58173Lena(256 × 256)bior5.5 + spiht 11.2332 37.6258 0.7997db4 + spiht 10.9985 37.7175 0.81431rbio4.4 + spiht 13.4554 36.8418 0.79511optimized dwt+spiht+Humffman 9.428 38.3866 0.82473optimized dwt+spiht+MHE 9.428 38.3866 0.82473Pirate(256 × 256)bior5.5 + spiht 28.6055 33.5663 0.79127db4 + spiht 27.857 33.6815 0.80461rbio4.4 + spiht 35.7834 32.594 0.78289optimized dwt+spiht+Humffman 25.3173 34.0966 0.81556optimized dwt+spiht+MHE 457.0892 21.5308 0.25296woman_darkhair(256 × 256)bior5.5 + spiht 3.256 43.0039 0.83244db4 + spiht 3.1016 43.2149 0.84558rbio4.4 + spiht 3.78 42.3559 0.82869optimized dwt+spiht+Humffman 2.9758 43.3947 0.85224optimized dwt+spiht+MHE 2.9758 43.3947 0.85224Zelda(256 × 256)bior5.5 + spiht 4.3295 41.7664 0.91753db4 + spiht 4.2348 41.8625 0.91953rbio4.4 + spiht 5.4921 40.7335 0.90545optimized dwt+spiht+Humffman 3.9447 42.1707 0.92568optimized dwt+spiht+MHE 3.9476 42.1675 0.92568

CONCLUSION

This study has proposed a novel two-level compressionmodel, namely, SHIHT-MHE algorithm.It is to improve thecompression performance of the original input data. The opti-mized wavelet transform (DWT) is derived using hybridiza-tion of genetic and gravitational search algorithms to improvethe wavelet performance.The proposed system consists of

3972


Table 9. Comparison of Proposed Method With Existing Meth-ods using Lena(256 × 256)

Method PSNR BPP

SCPSOGA[36] 27.24 0.3931

SC-CPSO[37] 27.23 0.3934

SC-GA[38] 27.41 0.4000

SGA[39] 27.30 0.4000

GA with hybrid selection[40] 27.03 0.4000

FIC using DWT[41] 28.55 0.4000

Scalable Compression Through CSA[42] 27.90 0.4156

Proposed Work(Hybrid GSA-GA) 31.6382 0.3930

GA based method [43] 30.22 0.7600

DCT transform using difference 32.67 0.7400

lookup table [44]

Proposed Work(Hybrid GSA-GA) 36.1587 0.7600

FIGURE 13. PSNR Vs BPP for the test image ’Lena.bmp’

three phases, namely, the optimized transformation phase,the Encoding phase, and the decryption and decompression.The input image is first transformed using hybrid GSA-GAalgorithm-based DWT. Then the first-level compression usingSPIHT and Chaos-based encryption is carried out. Then, thesecond-level compression scheme is proposed using merging-based Huffman encoding (MHE) algorithm. In the receivermodule, the received signal from the AWGN channel isdemodulated, decrypted, and de-compressed to have the esti-mated image. The performance of the proposed system isevaluated using unmanned vehicle images in terms of PSNR,MSE, SSIM,compression ratio and compression rate. Theperformance of encryption algorithm has been verified using

FIGURE 14. SSIM Vs BPP for the test image ’Lena.bmp’

FIGURE 15. CR% Vs BPP for the test image ’Lena.bmp’

Deviation. The simulation results indicate that the proposedsystem provides a greater compressing capacity.

3973


Tabl

e10

Perf

orm

ance

com

pari

son

ofth

epr

opos

edfil

ter

with

othe

rpo

pula

rw

avel

etfil

ters

atdi

ffer

entb

ppva

lues

Wav

elet

Filte

rbp

p=

0.25

bpp

=0.

5bp

p=

0.75

MSE

PSN

RSS

IMC

RC

R%

MSE

PSN

RSS

IMC

RC

R%

MSE

PSN

RSS

IMC

RC

R%

Bar

bara

(256

×25

6)bi

or5.

5+

spih

t10

7.76

0727

.806

20.

5753

54.

0000

75.0

000

51.9

505

30.9

749

0.70

224

2.00

0150

.001

530

.076

433

.348

50.

7775

61.

3333

25db

4+

spih

t96

.312

728

.294

0.60

401

4.00

0275

.001

548

.985

31.2

302

0.71

979

250

29.7

637

33.3

939

0.78

892

1.33

3425

.001

5rb

io4.

4+

spih

t10

8.53

6827

.775

0.57

403

4.00

0275

.001

556

.270

730

.628

0.68

875

250

36.5

728

32.4

992

0.75

402

1.33

3425

.001

5op

timiz

eddw

t+sp

iht+

Hum

ffm

an89

.088

428

.632

60.

6154

84.

2151

76.2

756

45.9

047

31.5

122

0.73

22.

0844

52.0

248

25.8

609

34.0

044

0.80

539

1.37

8327

.447

5op

timiz

eddw

t+sp

iht+

MH

E89

.088

428

.632

60.

6154

84.

2189

76.2

9745

.904

731

.512

20.

732

2.08

5952

.059

941

.732

731

.926

0.75

321

1.37

9427

.502

4C

amer

aman

(256

×256

)bi

or5.

5+

spih

t14

4.59

1426

.529

40.

2957

64

7567

.973

229

.807

40.

4091

12.

0001

50.0

015

40.5

291

32.0

531

0.47

811

1.33

3325

db4

+sp

iht

140.

1821

26.6

639

0.31

491

475

64.6

907

30.0

224

0.42

661

250

37.0

615

32.4

416

0.49

458

1.33

3425

.001

5rb

io4.

4+

spih

t16

7.17

6325

.899

10.

3049

475

79.0

476

29.1

519

0.40

92

5041

.486

531

.951

70.

4814

91.

3333

25op

timiz

eddw

t+sp

iht+

Hum

ffm

an12

5.89

5727

.130

70.

3232

34.

2786

76.6

281

58.1

818

30.4

829

0.43

692

2.10

9952

.604

732

.637

332

.993

70.

5049

61.

3939

28.2

578

optim

ized

dwt+

spih

t+M

HE

125.

8957

27.1

307

0.32

323

4.28

5676

.666

358

.181

830

.482

90.

4369

22.

1118

52.6

474

32.6

373

32.9

937

0.50

496

1.39

4828

.306

6ei

nste

in_o

rig(

256×

256)

bior

5.5

+sp

iht

10.6

152

37.8

715

0.33

779

4.00

0275

.001

54.

1225

41.9

792

0.43

211

2.00

0150

.001

52.

3772

44.3

701

0.50

609

1.33

3425

.001

5db

4+

spih

t11

.197

937

.639

40.

3457

14.

0002

75.0

015

4.32

241

.774

0.44

833

250

2.17

0544

.765

20.

5266

21.

3333

25rb

io4.

4+

spih

t12

.700

537

.092

60.

3418

74.

0002

75.0

015

4.93

1441

.201

10.

4447

82.

0001

50.0

015

2.39

644

.335

90.

5170

21.

3334

25.0

015

optim

ized

dwt+

spih

t+H

umff

man

9.07

8238

.550

80.

3627

84.

2913

76.6

968

3.51

7142

.669

0.46

176

2.11

3752

.690

11.

8973

45.3

494

0.53

735

1.39

8328

.485

1op

timiz

eddw

t+sp

iht+

MH

E9.

0782

38.5

508

0.36

278

4.29

7476

.730

33.

5171

42.6

690.

4617

62.

1145

52.7

069

1.89

7345

.349

40.

5373

51.

3992

28.5

324

Len

a(25

6×25

6)bi

or5.

5+

spih

t94

.145

628

.392

80.

5557

34

7538

.304

332

.298

30.

6779

12.

0001

50.0

015

17.6

101

35.6

732

0.75

658

1.33

3325

db4

+sp

iht

88.4

708

28.6

628

0.57

774

475

37.8

343

32.3

519

0.69

865

250

18.8

5635

.376

30.

7612

11.

3334

25.0

015

rbio

4.4

+sp

iht

103.

3765

27.9

866

0.54

648

4.00

0275

.001

545

.191

31.5

803

0.67

103

2.00

0150

.001

525

.294

234

.100

60.

7308

81.

3333

25op

timiz

eddw

t+sp

iht+

Hum

ffm

an80

.112

129

.093

80.

6091

14.

2251

76.3

321

32.8

354

32.9

674

0.72

252.

094

52.2

446

16.1

433

36.0

509

0.78

221

1.38

9628

.035

optim

ized

dwt+

spih

t+M

HE

80.1

121

29.0

938

0.60

911

4.23

2576

.373

332

.835

432

.967

40.

7225

2.09

6152

.293

417

.480

535

.705

30.

7801

21.

3903

28.0

731

Pir

ate(

256×

256)

bior

5.5

+sp

iht

143.

7692

26.5

541

0.51

222

475

71.8

486

29.5

666

0.64

673

2.00

0150

.001

548

.707

31.2

549

0.72

645

1.33

3425

.001

5db

4+

spih

t13

1.56

1826

.939

50.

5305

74.

0002

75.0

015

70.1

093

29.6

730.

6679

42.

0001

50.0

015

43.7

778

31.7

183

0.75

396

1.33

3425

.001

5rb

io4.

4+

spih

t15

3.15

9826

.279

40.

4943

64.

0002

75.0

015

87.3

092

28.7

202

0.62

749

250

51.4

028

31.0

209

0.72

758

1.33

3425

.001

5op

timiz

eddw

t+sp

iht+

Hum

ffm

an12

6.69

7527

.103

10.

5410

54.

2265

76.3

397

64.7

744

30.0

168

0.67

733

2.09

9252

.363

640

.136

32.0

955

0.75

939

1.38

5527

.824

4op

timiz

eddw

t+sp

iht+

MH

E12

6.69

7527

.103

10.

5410

54.

2311

76.3

657

64.7

744

30.0

168

0.67

733

2.10

0752

.397

245

4.35

8921

.556

80.

2565

21.

3867

27.8

87w

oman

_dar

khai

r(25

6×25

6)bi

or5.

5+

spih

t24

.248

434

.284

0.62

709

475

9.28

9638

.450

80.

7368

52

504.

5859

41.5

165

0.80

114

1.33

3425

.001

5db

4+

spih

t24

.060

334

.317

80.

6323

4.00

0275

.001

59.

2045

38.4

908

0.75

235

250

4.87

8241

.248

20.

8056

61.

3334

25.0

015

rbio

4.4

+sp

iht

29.8

111

33.3

870.

5953

74.

0002

75.0

015

11.4

159

37.5

557

0.72

326

2.00

0150

.001

56.

5124

39.9

934

0.78

301

1.33

3325

optim

ized

dwt+

spih

t+H

umff

man

21.1

662

34.8

744

0.65

698

4.25

8976

.519

88.

3189

38.9

302

0.76

314

2.09

6652

.304

14.

4209

41.6

757

0.81

799

1.38

9628

.035

optim

ized

dwt+

spih

t+M

HE

21.1

662

34.8

744

0.65

698

4.26

3376

.544

28.

3189

38.9

302

0.76

314

2.09

7952

.333

116

6.13

0925

.926

30.

3406

81.

3903

28.0

746

Zel

da(2

56×2

56)

bior

5.5

+sp

iht

35.1

6132

.670

20.

7630

64.

0002

75.0

015

13.3

722

36.8

688

0.85

439

2.00

0150

.001

57.

0994

39.6

186

0.89

126

1.33

3425

.001

5db

4+

spih

t36

.113

932

.554

10.

7518

64.

0002

75.0

015

14.1

901

36.6

109

0.84

934

250

7.38

0939

.449

70.

8956

21.

3334

25.0

015

rbio

4.4

+sp

iht

47.5

699

31.3

575

0.71

737

475

19.0

518

35.3

314

0.82

059

2.00

0150

.001

59.

4029

38.3

982

0.87

635

1.33

3325

optim

ized

dwt+

spih

t+H

umff

man

31.4

928

33.1

487

0.77

976

4.23

1476

.367

212

.190

537

.270

60.

8654

12.

0865

52.0

721

6.51

5839

.991

10.

9012

71.

3827

27.6

764

optim

ized

dwt+

spih

t+M

HE

31.4

928

33.1

487

0.77

976

4.23

6976

.397

712

.190

537

.270

60.

8654

12.

0893

52.1

362

6.51

5839

.991

10.

9012

71.

3841

27.7

496

3974


FIGURE 16. Compression Rate Vs BPP for the test image’Lena.bmp’

FIGURE 17. RDR Vs BPP for the test image ’Lena.bmp’

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OptimizedWavelet Filters and Modiﬁed Huffman Encoding ... · rate. Further the chaotic encryption algorithm has been eval-uated using suitable metrics, Experimental results show