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  1. 1. R.Srinivasa Rao, M.Vijay Karthik, Saraswathi Nagla / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 6, November- December 2012, pp.1509-1514 Wavelet Transform Based Image Compression R.Srinivasa Rao1, M.Vijay Karthik2,Saraswathi Nagla3 Department of Electronics & Communications Engineering1, Department of Electrical & Electronics Engineering2,3, Aurora‟s Scientific & Technological Institute, Ranga Reddy Dist, Andhra Pradesh-501301, INDIAABSTRACT Image require substantial storage and The paper is organized as follows: Integer wavelettransmission resources, thus image compression Transform described in section II. Section IIIis advantages to reduce these requirements. A represents Histogram adjustment for thegood strategy of image compression should preprocessing and post processing of the imageassure a good compromise between a high compression, section IV gives detailed compressioncompression rate and a low distortion of the technique, and section V provides thepicture. In this paper a lossless digital image implementation of the proposed technique withcompression technique based on Integer Wavelet results.Transform is proposed. The small deviations indata values are not allowed in certain images for II INTEGER WAVELET TRANSFORMobvious reasons and a potential risk of a person The Wavelet Transform produces floatingmisinterpreting an image. A preprocessing and point coefficients even when applied to integerpost processing histogram adjustment is used to values. The original integer data can beprevent overflow/underflow. In proposed reconstructed perfectly in theory by using thesetechnique wavelet transform is applied to entire coefficients. However in practice, we usually useimage, so it produces no blocking artifacts. The the fixed point format for data values because theresults show improved high performances in fixed point systems are easier to implement[3] [4].terms of compression ratio and reconstruction The reduced precession arithmetic used in suchquality. systems can introduce round off errors in the computations. In practice traditional waveletIndex Terms; Digital compression, Integer transform have some drawbacks such as it is awavelet transform, Histogram modification. floating point algorithm, computer finite word length will bring in rounding error and signals can‟tINTRODUCTION be reconstructed exactly, the computation is very The fast development of computer complicated, computation cost is very high, itapplications came with an enormous increase of the requires more storage space and it is not appropriateuse of digital images, mainly in the domain of to hardware implementation. In order to overcomemultimedia, games, satellite transmissions and above drawbacks, this paper uses lifting schememedical imagery. This implies more the research on wavelet - integer wavelet transform[5]. It doesn‟teffective compression algorithms, the basic idea of depend on Fourier transform, but it still inherits ,the image compression is to reduce the middle multi resolution properties of traditional waveletnumber of bits by pixel necessary for image transform and transforming coefficient, calculationrepresentation. The image compression approaches speed is more fast, and it doesn‟t need extra storagecan be divided in two methods: lossless and loss. cost so it is called second generation waveletDifferent compression approaches have been studied transform. Hence in applications where we needin the literature[1]. lossless reconstruction, we need transforms which A lossless high-capacity data for have reversibility properties even when reducedimage compression based on integer wavelet is precision is used. It was shown by calderbank et al.,proposed. After extracting data embedded, the that we can build wavelet transforms that maporiginal image should be reversible from compressed integers to integers by using lifting structure. Theimage[2]. The wavelets are excellent approximates reversibility property is obtained by rounding of theand signal analyzers. Their time-frequency analysis predict filter or update filter output before adding ormakes them an effective and innovative tool. subtracting in each lifting step. Wavelet filters are In this paper, we investigate integer decomposed into basic modules by integer waveletwavelet transform technique for transforming the transform, that is, wavelet transform is completedimage. The basic idea behind this technique is to through splitting, predicting and updating, as figureuse integer wavelet to transform the data into the 1 displays.different basis. A pre and post histogram is used forA preprocessing and post processing histogramadjustment is used to prevent overflow/underflow. 1509 | P a g e
  2. 2. R.Srinivasa Rao, M.Vijay Karthik, Saraswathi Nagla / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 6, November- December 2012, pp.1509-1514 + J i-1 - 0.018 0.016 0.014 SPLIT P U U P MERGE Ji 0.012Ji Density 0.01 0.008 0.006 K i-1 0.004 - + 0.002 0 50 100 150 200 250 Fig 1. Integer wavelets transform decomposition and Data Reconstruction diagram Fig 2(b). Gray scale histogram modification modified histogram After integer wavelet transform, it has four sub-bands. We will embed the information into three high frequency sub bands. Except that it has 0.018 advantages of traditional wavelet transform, integer 0.016 wavelet transform which is applied to digital 0.014 compression technology has following 0.012 advantages[6]: Density 0.01 (1) It avoids rounding error of floating point in 0.008 mathematical transformation; 0.006 (2) Its transforming speed is fast and it doesn‟t 0.004 need extra storage cost. 0.002 0 III HISTOGRAM ADJUSTMENT 40 60 80 100 120 140 Data 160 180 200 220 240 For a given image, after data embedding in some IWT coefficients, it is possible to cause Fig 2(c). Gray scale histogram modification overflow/underflow, which means that after inverse histogram after data embedding. wavelet transform the gray scale values of some pixels in the compressed image may exceed the IV PROPOSED COMPRESSION SCHEME upper bound (255 for an eight-bit grayscale image) 1. Data Embedding Process: and/or the lower bound (0 for an eight-bit grayscale The main steps of the embedding procedure image). In order to prevent the overflow/underflow, developed are presented here and summarized. we adopt histogram modification, which narrows a. Histogram modification is applied on the histogram from both sides as shown in. Fig.2. original image that prevents possible Please refer to [7],[8] for the detailed algorithm. overflow and underflow. The bookkeeping information will be embedded b. We first apply integer wavelet into the cover media together with the information decomposition to the original image. In our data. experiments, CDF (2, 2) wavelet filters are used to decompose the original gray scale image into one level. After integer wavelet 0.018 transform, it has four sub-bands. 0.016 c. In order to have the compressed image 0.014 perceptually the same as the original image, 0.012 we choose to hide data in one (or more than one) “middle” bit-plane(s) in the IDWT Density 0.01 0.008 domain. To further enhance the visual 0.006 quality of the compressed image, we embed 0.004 data only in the middle and high frequency 0.002 sub bands, specifically in the LH1, HL1 and 0 40 60 80 100 120 140 160 180 200 220 HH1 sub bands. Data d. Construct binary images from 5th bit of Fig 2(a). Gray scale histogram modification of LH1, HL1 and HH1 wavelet coefficients. Original histogram For constructing binary image using LH1, the each integer wavelet coefficients in LH1 is converted into 8 bit binary sequence, if 5th bit of each binary sequence 1510 | P a g e
  3. 3. R.Srinivasa Rao, M.Vijay Karthik, Saraswathi Nagla / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 6, November- December 2012, pp.1509-1514 is 1 then assign 2 to binary image otherwise 2. Extraction Process assign 1. For constructing binary image Extraction of compressed image and inverting of using HL1 and HH1 is same as above. compressed image into original one is reverse e. Compress data in binary image obtained process of embedding. from LH1, HL1 and HH1 by using arithmetic coding because of its high a. Perform histogram modification on coding efficiency. compressed image. f. Insert the header information and b. Perform one level integer wavelet compressed data together, the embed signal decomposition on compressed image. consists of these three. If embedded bit is c. Extract the embed signal from 5th bit of 1or (0) then convert first integer wavelet LH1, HL1 and HH1 wavelet coefficients. coefficient in LH1 sub band into 8 bit binary sequence and replace 1or (0) to the For extracting embed signal with using LH1, the 5th bit plane of that binary sequence and each integer wavelet coefficient in LH1 is converted convert back to integer. In this way all the into 8 bit binary sequence and if 5th bit of each embedded bits hide in “5th” bit-plane in the binary sequence is 1, then embed bit is 1 otherwise LH1, HL1 and HH1 coefficients. embed bit is 0. g. The way of accessing each wavelet The sample code given below: coefficient for embedding depends on secret key. Index=1 h. A secret key function that keeps the hidden for i=1: size (LH1, 1) data secret even after the algorithm is for j=1:size(LH1,2) known to public. binSeq = dec2bin (abs (LH1(i, j)),8); i. Take the Inverse integer wavelet transform if binSeq (5) == 1 to reconstruct the compressed image. embed Signal (index, 1) = 1; j. Perform histogram modification on else compressed image. embed Signal(index,1) = 0; k. The invisibility of the compressed image. end We use the formula (1) to compare the difference index = index + 1; between the original image and the compressed end image, Figure 5 demonstrates that the compressed end image embedded with the proposed algorithm is invisible, where (a) is the original image, and (b) For extracting embedded signal with using HL1 is the compressed image with compression ratio and HH1 same as above. =91.25. (a) Based on header information extract binary compressed image from embed ٢ = (1- Tc / To) X 100 (1) signal. (b) Extract the respective binary images of Where Tc Is Size of Original cover image LH1, HL1 and HH1 from embed signal To Is Size of Compressed cover image based on header information. (c) Decompress to get the original sequence. (d) Insert the uncompressed 5th bit data back into LH1, HL1 and HH1. (e) Take the Inverse integer wavelet transform to reconstruct the original image. (f) Perform histogram adjustment on original image.Fig.3 Embedding Method 1511 | P a g e
  4. 4. R.Srinivasa Rao, M.Vijay Karthik, Saraswathi Nagla / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 6, November- December 2012, pp.1509-1514 (a) (b)Fig.4 Extraction methodV IMPLEMENTATION The program code is written in (c) (d)„MATLAB‟. Test images of „Airplane‟, „Lena‟, Fig.6 Compressed images (a) Compressed„Baboon‟, „Gold hill‟, and „Barbara‟ are used as Goldhill image (b) Compressed Baboon image (c)input images for validation of developed Compressed Barbara image (d) Compressed Lenaalgorithms. The wavelet decomposition of image imageis done by using CDF (2,2) wavelet filter.The compressed logo is binary image created and Table I The Compression Ratio(%)embedded as per algorithm discussed. The Valueembedding is done for the visible compressedlogo. The resultant coefficients were inverse Host Compressiontransformed to obtain the compressed image. Image Ratio value(%)Several test gray scale images of size 512×512 are 512×512used in experiments. The original and compressed Lena 81.36Airplane images are shown in fig.5. Compression Baboon 89.13ratio value of Airplane image after compressedembedding is measured as 91.25%. It is observed Goldhill 78.57that imperceptibility requirement is met. The Airplane 79.23same experiment is conducted on other four Barbara 84.56images. Fig.6 contains other four compressedimages. Table I shows some experimental results. Table I show that Airplane image has a better embedding capacity than the other images in the experiment. It also shows it has a better visual quality as far as peak signal to noise ratio is concerned. Table II shows image quality tested for different payloads on the same image using different wavelets. Among various wavelet filters, CDF(2,2) performs better than others for the same payloads. Image quality quickly changes when different wavelets are used. 2 (a) (b) PSNR  255 M N  (H (i, j) W (i, j)) 1 2Fig.5 Airplane image : (a) Original Airplane M N i 1 j 1 (2)image (b) Compressed image (91.25%) Where H (i, j) Is Original cover image W (i, j) Is Compressed image 1512 | P a g e
  5. 5. R.Srinivasa Rao, M.Vijay Karthik, Saraswathi Nagla / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 6, November- December 2012, pp.1509-1514 Table II Comparison of performance of various wavelet families on Airplane image for 250000 different payload size 196152 200000Payloa cdf(2,2) db2 Sym4 bior3.3 bior6.8 rbio3.3 150000d PSNR PSNR PSNR PSNR PSNR PSNRbits (db) (db) (db) (db) (db) (db) 94000 Number of Bits 10000010000 37.78 35.84 36.37 36.31 36.31 36.2415129 37.73 35.78 36.25 36.28 36.23 36.29 50000 2400020164 37.67 35.73 36.26 36.24 36.26 36.1625281 37.60 35.69 36.11 36.16 36.00 35.99 050176 37.11 35.708 35.89 35.76 35.85 35.58 Goljan,s Gurong Proposed75076 36.84 35.67 35.90 35.71 36.00 34.6710048936.74 ** 35.86 35.51 35.05 33.86 Fig.8 Comparison between proposed and existing methods Image Quality Tested on different wavelets 38 CONCLUSION 37.5 Simulation experiments on the digital compression of images have been performed usingImage Quality (PSNR db) 37 two standard images: Lena and Airplane. In 36.5 proposed method we verify the compromise that exists between the compression ratio and the quality 36 of the rebuilt image. The proposed image 35.5 compression algorithm based on integer wavelet transform is able to embed up to 81.36% and 35 cdf2.2 91.25% compression ratio value and into image of db2 Sym4 512 by 512 imperceptibly and extracts the embedded 34.5 bior3.3 data and original image from compressed image 34 bior6.8 without loss of information. The performance of rbio3.3 proposed lossless compression algorithm verified by 33.5 various wavelet filters. Among various wavelet 1 2 3 4 5 6 7 8 9 10 Payload Bits 4 x 10 filters, CDF (2,2) performs better than others for the same payloads. Fig.7 Image Quality Tested on Different Wavelets REFERENCES Table III shows the comparison between existing [1] W. Sweden‟s, “The lifting scheme: A methods in literature and proposed method. The custom-design construction of biorthogonal proposed method is able to embed up to 196k bits wavelets,” Appl. Comput. Harmon. Anal., into image of 512 by 512 imperceptibly. vol. 3, no. 2, pp. 186–200, 1996. [2] Fridrich, J.,Goljan, M., Du, R., "Invertible Table III Comparison between existing methods Authentication", In: Proc. SPIE, Security and proposed method and Compression of Multimedia Contents, San Jose, California January 2001 Methods The amount of data [3] Jiang Zhu. M., Guorong Xuan., Jidong embedded in a 512 × Chen., "Distortion less data hiding based on 512 image integer wavelet transform ", Vol.38, No.25, Electronics Letters 5th December 2002. Goljan‟s 3,000-24,000 bits [4] I. Daubechies and W. Sweldens, Guorong 15,000-94,000 bits “Factoring wavelet Transforms into lifting steps,” J. Fourier Anal. Appl.,vol. 4, no. 3, Proposed 10000-1,96152 bits pp. 245–267, 1998. [5] M. D. Adams and F. Kossentini, “Performance evaluation of reversible integer-to-integer wavelet transforms for image compression,” in IEEE Data Compression Conference, now bird, UT, USA, March 1999, pp. 514–524, IEEE. 1513 | P a g e
  6. 6. R.Srinivasa Rao, M.Vijay Karthik, Saraswathi Nagla / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 6, November- December 2012, pp.1509-1514 [6] A. R. Calderbank, I. Daubechies, W. Sweldens and B. Yeo, “Wavelet transforms that map integers to integers,” Applied and Computational Harmonic Analysis, vol.5, no.3, pp.332-369, 1998. [7] G. Xuan, C. Yang, Y. Q. Shi and Z. Ni: High Capacity Lossless Data Hiding Saraswathi Nagla was born in Nizamabad, India in Algorithms. IEEE International Symposium 1986. At present she is working as Assistant on Circuits and Systems (ISCAS04), Professor in the Department of Electrical & Vancouver, Canada, May 2004. Electronics Engineering, Aurora‟s Scientific and [8] D. Kundur, D.Hatzinakos, "Digital Technological Institute, Ranga Reddy Dist -501301, compression using multi resolution wavelet Andhra Pradesh, India. She obtained her M.E decomposition", Proceedings of the IEEE Degree from Chaitanya Bharathhi Institute of international conference on acoustics, Technology (CBIT) Gandipet, Osmania University, speech and signal processing, Seattle, 1998. Hyderabad, and Andhra Pradesh, India. She Obtained B-Tech Degree from Srinivasa Reddy Institute of Technology, Munipally, JNTU R. Srinivasa Rao was born in Hyderabad, Andhra Pradesh. Her research area West Godavari, India in 1977. includes Image Processing, Wavelets, Power At present he is working as Quality, Power System, and Power Semiconductor Associate Professor in the Drives. Department of Electronics and Communications Engineering,Aurora‟s Scientific and Technological Institute,Ranga Reddy Dist -501301, Andhra Pradesh, India.He obtained his M.Tech degree JNTU College ofEngineering, JNTU Hyderabad, and AndhraPradesh, India. He completed Graduation inEngineering, AMIE, The Institution of Engineers(INDIA), Kolkata. His research area includesSignals and Systems, Digital Image Processing andcommunication systems.Mamidala Vijay Karthik was born inHyderabad, India in 1985. At present he is workingas Senior Assistant Professor in the Department ofElectrical & Electronics Engineering, Aurora‟sScientific and Technological Institute, Ranga ReddyDist -501301, Andhra Pradesh, India. He obtainedhis M.E degree from Chaitanya Bharathi Institute ofTechnology (CBIT) Gandipet, Osmania University,Hyderabad, and Andhra Pradesh, India. He obtainedB.Tech degree from Church Institute of Technology,Gagillapur, JNTU Hyderabad, and Andhra Pradesh.His research area includes Wavelets, Power Quality,Power System, and Power Semiconductor Drives. 1514 | P a g e