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EFFICIENT IMAGE COMPRESSION TECHNIQUE USING FULL, COLUMN AND ROW TRANSFORMS ON COLOUR IMAGE

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This paper presents image compression technique based on column transform, row transform and full transform of an image. Different transforms like, DFT, DCT, Walsh, Haar, DST, Kekre’s Transform and Slant transform are applied on colour images of size 256x256x8 by separating R, G, and B colour planes. These transforms are applied in three different ways namely: column, row and full transform. From each transformed image, specific number of low energy coefficients is eliminated and compressed images are reconstructed by applying inverse transform. Root Mean Square Error (RMSE) between original image and compressed image is calculated in each case. From the implementation of proposed technique it has been observed that, RMSE values and visual quality of images obtained by column transform are closer to RMSE values given by full transform of images. Row transform gives quite high RMSE values as compared to column and full transform at higher compression ratio. Aim of the proposed technique is to achieve compression with acceptable image quality and lesser computations by using column transform.

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EFFICIENT IMAGE COMPRESSION TECHNIQUE USING FULL, COLUMN AND ROW TRANSFORMS ON COLOUR IMAGE

  1. 1. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963EFFICIENT IMAGE COMPRESSION TECHNIQUE USING FULL, COLUMN AND ROW TRANSFORMS ON COLOUR IMAGE H. B. Kekre1, Tanuja Sarode2 and Prachi Natu3 1 Sr. Professor, MPSTME, Deptt. of Computer Engg., NMIMS University, Mumbai, India 2 Associate Professor Department of Computer Engg., TSEC, Mumbai University, India 3 Ph. D. Research Scholar, MPSTME, NMIMS University, Mumbai, IndiaABSTRACTThis paper presents image compression technique based on column transform, row transform and full transformof an image. Different transforms like, DFT, DCT, Walsh, Haar, DST, Kekre’s Transform and Slant transformare applied on colour images of size 256x256x8 by separating R, G, and B colour planes. These transforms areapplied in three different ways namely: column, row and full transform. From each transformed image, specificnumber of low energy coefficients is eliminated and compressed images are reconstructed by applying inversetransform. Root Mean Square Error (RMSE) between original image and compressed image is calculated ineach case. From the implementation of proposed technique it has been observed that, RMSE values and visualquality of images obtained by column transform are closer to RMSE values given by full transform of images.Row transform gives quite high RMSE values as compared to column and full transform at higher compressionratio. Aim of the proposed technique is to achieve compression with acceptable image quality and lessercomputations by using column transform.KEYWORDS: Image compression, Full transform, Column transform, Row transform. I. INTRODUCTIONRapid increase in multimedia applications has been observed since last few years. It leads to higheruse of images and videos as compared to text data. Use of these applications play important role incommunication, educational tools, gaming applications, entertainment industry and many other areas.When images and videos come into picture, issue of their storage, processing and transmission cannotbe neglected. Images contain considerable amount of redundancies. Hence storage and transmissionof compressed images instead of uncompressed images has been proved to be advantageous. Imagecompression has the added advantage of being tolerant to distortion due to peculiar characteristics ofhuman visual system [1]. Major aim of image compression is to reduce the storage space ortransmission bandwidth and maintain acceptable image quality simultaneously. Image compressiontechniques are broadly classified into two categories: lossless compression and lossy compression. Inlossless image compression exact replica of original image can be obtained from compressed image;however it gives low compression ratio, which is not the case in lossy image compression. Wideresearch has been done in this area and it includes compression using Discrete Fourier Transform(DFT) [11] and Discrete Cosine Transform (DCT) [2].Compression using warped DCT is proposed in[16]. Recent work includes wavelet based image compression using orthogonal wavelet transform[12]and hybrid wavelet transform[17].Fractal image compression is discussed by Veenadevi and Ananthin [18]. This paper presents transform based image compression that uses column transform, rowtransform and full transform of an image. 88 Vol. 6, Issue 1, pp. 88-100
  2. 2. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963II. TRANSFORM BASED IMAGE COMPRESSIONImage compression plays a vital role in several important and diverse applications including tele-video conferencing, remote sensing, medical imaging [2,3] and magnetic resonance imaging[4].Transform based coding is major component of image and video processing applications. It is basedon the fact that pixels in an image exhibit a certain level of correlation with their neighbouring pixels.A transformation is, therefore defined to map this spatial (correlated) data into transformed(uncorrelated) coefficients [5]. It means that the information content of an individual pixel isrelatively small and to a large extent visual contribution of a pixel can be predicted using itsneighbours [1, 6].Transform based compression techniques use a reversible linear mathematicaltransform to map the pixel values onto a set of coefficients which are then quantized and encoded. Itis lossy compression technique. Previously, Discrete Fourier Transform (DFT) is used to change thepixels in the original image into frequency domain coefficients. Discrete Cosine Transform (DCT) ismost widely used approach in image and video compression, as the performance approaches to that ofKarhunen-Loeve transform (KLT) for first order Morkov process[16].2.1. Discrete Cosine Transform (DCT)Discrete Cosine Transform (DCT) is widely used transformation technique for image compression.Other transforms like Haar, Walsh, Slant, Discrete sine transform (DST) can also be used for imagecompression. DCT converts the spatial image representation into frequency components. Lowfrequency components appear at the topmost left corner of the block that contains maximuminformation of the image.2.2. Walsh TransformWalsh transform is non-sinusoidal orthogonal transform that decomposes a signal into a set oforthogonal rectangular waveforms called Walsh functions. The transformation has no multipliers andis real because the amplitude of Walsh functions has only two values, +1 or -1. Walsh functions arerectangular or square waveforms with values of -1 or +1. An important characteristic of Walshfunctions is sequency which is determined from the number of zero-crossings per unit time interval.Every Walsh function has a unique sequency value. The Walsh-Hadamard transform involvesexpansion using a set of rectangular waveforms, so it is useful in applications involving discontinuoussignals that can be readily expressed in terms of Walsh functions.2.3. Haar TransformHaar transform was proposed in 1910 by a Hungarian mathematician Alfred HaarError! Referencesource not found.. The Haar transform is one of the earliest transform functions proposed.Attracting feature of Haar transform is its ability to analyse the local features. This property makes itapplicable in electrical and computer engineering applications. The Haar transform uses Haar functionfor its basis. The Haar function is an orthonormal, varies in both scale and position [8]. Haartransform matrix contains ones and zeros. Hence it requires no multiplications and less number ofadditions as compared to Walsh transform which makes it computationally efficient, fast and simple.2.4. Discrete Sine Transform (DST)Discrete Sine Transform (DST) is a complementary transform of DCT. DCT is an approximation ofKLT for large correlation coefficients whereas DST performs close to optimum KLT in terms ofenergy compaction for small correlation coefficients. DST is used as low-rate image and audio codingand in compression applications [9,10].2.5. Fourier TransformIn conventional Fourier transform, it is not easy to detect local properties of the signal. Hence ShortTerm Fourier Transform (STFT) was introduced. But it gives local properties at the cost of globalproperties [11]. 89 Vol. 6, Issue 1, pp. 88-100
  3. 3. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-19632.6. Kekre’s TransformMost of the transform matrices have to be in powers of two. This condition is not required in Kekretransform [12, 13] matrix. In Kekre transform matrix, all diagonal elements and the upper diagonalelements are one. Lower diagonal elements except the one exactly below the diagonal are zero.2.7. Slant TransformSlant transform matrix is orthogonal with a constant function for the first row. The elements in otherrows are defined by linear functions of the column index. Properties of Slant transform are: It hasorthonormal set of basis vectors. First basis vector is constant basis vector, one slant basis vector, thesequency property, variable size transformation, fast computational algorithm and high energycompaction. Definition of slant transform and its properties are given in [14, 15].III. PROPOSED TECHNIQUEIn proposed compression technique, seven different transforms namely DFT, DCT, DWT, DST, DHT,DKT and Slant transform are applied on each 256x256 size colour image to obtain transformed imagecontent. These transforms are applied in three different ways: column transform, row transform andfull transform. Let ‘T’ denotes the transformation matrix, ‘f’ denotes an image and ‘F’ indicatestransformed image. Then,Column transform of an image ‘f’ is [F] = [T]*[f]Row transform is written as: [F] = [f]*[T’]where, T’= Transpose of TAnd full transform is given by: [F] = [T]*[f]*[T’]In each of these three cases, low energy coefficients are eliminated from transformed image content.Then image is reconstructed by applying inverse transform on it. In column transform, number ofcoefficients is reduced by eliminating some rows of transformed image. In row transform, it is doneby eliminating some columns of transformed image whereas in full transform some rows as well assome columns are eliminated such that number of coefficients reduced is equal as that of column orrow transform. Image is then reconstructed by applying inverse transform on the image whichcontains reduced number of coefficients than original image. Root mean square error and compressionratio is calculated in each case till acceptable image quality is obtained. Average of these RMSEvalues and compression ratio is used for performance analysis.IV. EXPERIMENTAL RESULTSExperimentation is done on 12 sample colour images. Images of 256x256 sizes from different classesare selected. Experiments are performed in MATLAB 7.2 on a computer with dual core processor and4 GB RAM. Test images are shown in figure 1. 90 Vol. 6, Issue 1, pp. 88-100
  4. 4. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963Figure 1: Set of twelve test images of different classes used for experimental purpose namely (from left to right and top to bottom) Mandrill, Peppers, Lord Ganesha, Flower, Cartoon, dolphin, Birds, Waterlili, Bud, Bear, Leaves and LennaFor each transform, comparison of three cases i.e. RMSE in Full, column and row transform is shownin figure 2 to 8. Figure 2 shows this comparison for DFT. RMSE values for full and column transformare almost same in this case. But row transform gives slight high values of RMSE. Figure 2. Performance comparison of Average Figure 3. Performance comparison of Average RMSE for Full DFT, column DFT and Row DFT RMSE for Full Haar, column Haar and Row Haar against different Compression Ratios against different Compression RatiosFigure 3 shows comparison for Haar transform. Here, up to compression ratio 4, RMSE in full andcolumn transform are almost same. Afterwards RMSE in column transform is approximately same asthat of full transform. 91 Vol. 6, Issue 1, pp. 88-100
  5. 5. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963 Figure 4. Performance comparison of Average Figure 5. Performance comparison of Average RMSE for Full DCT, column DCT and Row DCT RMSE for Full Walsh, column Walsh and Row against different Compression Ratios Walsh against different Compression RatiosAs found in figure 4 and 5, RMSE values of column and full transform are closer. Row transformRMSE values are slightly higher in both DCT and Walsh transform. Figure 6. Performance comparison of Average Figure 7. Performance comparison of Average RMSE for Full Slant, column Slant and Row RMSE for Full Kekre transform, column Kekre Slant against different Compression Ratios and Row Kekre transform against different Compression RatiosGraph plotted in figure 6 and 7 shows RMSE values obtained by applying Slant transform and Kekretransform respectively. These values are higher than the values obtained in DFT, DCT, Haar andWalsh. But difference between Full transform values and column transform values is again verysmall. Comparison of RMSE values for DST is shown in figure 8. Here also there is slight differencein column transform RMSE values and the values in Full transform. Figure 8. Performance comparison of Average RMSE for Full DST, Column DST and Row DST against different compression ratios 92 Vol. 6, Issue 1, pp. 88-100
  6. 6. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963 Figure 9.Performance comparison of Average RMSE for Full DFT, Haar, DCT, Walsh, Slant, Kekre Transform, and DST against compression ratio 1 to 5Graph plotted in figure 9 shows comparison of RMSE values for seven different full transformsnamely DFT, Haar, DCT, Walsh, Slant, Kekre Transform and DST. From the graph it can beobserved that, full DFT gives least RMSE value among all other full transforms. Figure 10.Performance comparison of Average RMSE for Column DFT, Haar, DCT, Walsh, Slant, Kekre Transform, and DST against compression ratio 1 to 5.By observing and comparing Figure 10 with Figure 9, it is found that RMSE values of columntransform for compression ratio 1 to 5 are close to the values obtained by full transform. Since incolumn transform we use [F] = [T]x[f] and not [F] = [T]x[f]x [T’] like in full transform, it saves halfnumber of computations. Figure 11. Performance comparison of Average RMSE for Row DFT, Haar, DCT, Walsh, Slant, Kekre Transform, DST against compression ratio 1 to 5.It can be seen from Figure 11 that RMSE values for row transform are slight higher than column andfull transforms. 93 Vol. 6, Issue 1, pp. 88-100
  7. 7. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963Table 1 presents the summary of Average RMSE and PSNR for full transforms. It can be observedthat, good PSNR upto32 dB is obtained by DFT, DCT and DST at compression ratio 2. Table 1. Summary of Average RMSE and PSNR for various ‘Full Transforms’ Compression Ratio Full 2 4 8 Transform AVG AVG AVG PSNR PSNR PSNR RMSE RMSE RMSE DFT 6.325 32.21 10.47 27.73 14.71 24.77 Haar 10.828 27.44 14.932 24.64 18.843 22.62 DCT 6.012 32.55 10.241 27.92 14.665 24.8 Walsh 9.273 28.78 13.195 25.72 16.950 23.54 Slant 33.628 17.59 40.301 16.02 42.536 15.55 Kekre 28.666 18.98 39.332 16.23 44.867 15.09 Transform DST 6.229 32.24 10.661 27.57 15.135 24.53Table 2 gives average RMSE and PSNR summary for column transform. Average RMSE in columntransform is closer to that of full transform. Better PSNR is obtained for DFT. Table 2. Summary of Average RMSE and PSNR for various ‘Column Transforms’ Compression Ratio Column 2 4 8 Transform AVG AVG AVG PSNR PSNR PSNR RMSE RMSE RMSE DFT 2.541 40.03 4.4072 35.24 6.288 32.16 Haar 9.728 28.37 15.440 24.35 20.886 21.73 DCT 7.386 30.76 12.915 25.91 18.343 22.86 Walsh 9.728 28.37 15.440 24.35 20.886 21.73 Slant 35.900 17.02 42.512 15.56 44.686 15.12 Kekre 31.232 18.23 43.213 15.41 47.717 14.55 Transform DST 8.046 30.01 14.770 24.74 21.893 21.32Table 3 shows performance of different row transforms in terms of RMSE and PSNR. DFT, DCT andDST show good average RMSE. Better PSNR is obtained for DFT. Table 3. Summary of Average RMSE and PSNR for various ‘Row Transforms’ Row Compression Ratio Transform 2 4 8 AVG AVG AVG PSNR PSNR PSNR RMSE RMSE RMSE DFT 2.559 39.96 4.458 35.14 6.410 31.99 Haar 9.910 28.2 15.869 24.12 21.705 21.4 DCT 7.530 30.59 13.168 25.74 18.874 22.61 Walsh 9.910 28.2 15.869 24.12 21.705 21.4 Slant 36.765 16.82 43.484 15.36 45.761 14.92 Kekre 32.164 17.98 42.313 15.6 46.788 14.72 Transform DST 8.260 29.79 15.124 24.53 22.458 21.1From twelve different query images with different colour and texture combination, ‘Mandrill’ imageis selected as representative image for perceptual comparison. It contains different colour 94 Vol. 6, Issue 1, pp. 88-100
  8. 8. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963combinations and edges. Compressed images obtained by applying full, column and row transformsare shown below with corresponding compression ratio and RMSE value for each image. Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE= 2.685373 RMSE=4.641359 RMSE=6.248745 Figure 12: Compressed ‘Mandrill’ images by applying full DFT Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE=3.615713 RMSE=5.167002 RMSE=6.27264 Figure 13: Compressed ‘Mandrill’ images by applying column DFT Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE=8.59163 RMSE=13.5814 RMSE=17.0931 Figure 14: Compressed ‘Mandrill’ images by applying Row DFTFigures 12, 13, 14shows compressed ‘Mandrill’ image using full, column and row DFT respectively.In each of the three cases compression ratio 2, 4 and 8 is considered. It is observed that RMSE valueof column DFT at compression ratio 8 is very closer to one obtained by total DFT at samecompression ratio. Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE=9.224652 RMSE=14.47318 RMSE=18.31172 Figure 15: Compressed ‘Mandrill’ images by applying full DCT 95 Vol. 6, Issue 1, pp. 88-100
  9. 9. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963 Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE= 11.8693776 RMSE= 17.16473991 RMSE= 20.90614907 Figure 16: Compressed ‘Mandrill’ images by applying column DCT Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE= 9.88663 RMSE= 16.16006 RMSE= 21.11612 Figure 17: Compressed ‘Mandrill’ images by applying row DCTFigures 15,16,17 show compressed ‘Mandrill’ image using full, column and row DCT forcompression ratio 2,4 and 8. Again it is observed that RMSE value of column DCT at compressionratio 8 is very closer to one obtained by total DCT at same compression ratio. Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE= 11.5486 RMSE= 16.14666 RMSE= 19.64522 Figure 18: Compressed ‘Mandrill’ images by applying full Haar Transform Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE=12.93917685 RMSE= 18.34300842 RMSE= 22.14955424 Figure 19: Compressed ‘Mandrill’ images by applying column Haar Transform Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE=11.84323 RMSE= 18.0668 RMSE= 22.9688 Figure 20: Compressed ‘Mandrill’ images by applying row Haar Transform 96 Vol. 6, Issue 1, pp. 88-100
  10. 10. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963Similarly, figures 18, 19, 20 present compressed images for full, column and row Haar transformrespectively. At compression ratio 8, it gives acceptable compressed image but RMSE is higher thanDFT and DCT. Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE= 11.38372 RMSE= 16.26495 RMSE= 19.62808 Figure 21: Compressed ‘Mandrill’ images by applying full Walsh Transform Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE= 12.93918 RMSE= 18.34301 RMSE= 22.14955 Figure 22: Compressed ‘Mandrill’ images by applying column Walsh Transform Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE=11.8432 RMSE= 18.0668 RMSE= 22.9688 Figure 23: Compressed ‘Mandrill’ images by applying row Walsh TransformSame results regarding RMSE values are observed for Walsh transform in figure 21, 22 and 23. Forfull, column and row Walsh transforms, image quality is acceptable but at the cost of higher RMSEvalues. Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE= 9.331971 RMSE= 14.69161 RMSE= 18.56635 Figure 24: Compressed ‘Mandrill’ images by applying full DST 97 Vol. 6, Issue 1, pp. 88-100
  11. 11. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963 Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE= 12.2453 RMSE= 18.74562 RMSE= 24.4524 Figure 25: Compressed ‘Mandrill’ images by applying column DST Compression Ratio= 2 Compression Ratio= 4 Compression Ratio= 8 RMSE=10.29123 RMSE= 17.4362 RMSE= 23.74187 Figure 26: Compressed ‘Mandrill’ images by applying row DSTAs shown in figures 24, 25 and 26 DST also gives good image quality with less error in three differentcases i.e. full column and row DST. Slant and Kekre’s transform show poor performance in terms ofRMSE for comp ratio greater than two. As compressed image quality is not perceptible, thesetransforms are not recommended. V. CONCLUSIONSHere performance of column transform, row transform and full transform is compared using RootMean Square Error (RMSE) as a performance measure with respect to compression ratio. RMSEvalues are calculated for compression ratio 1 to 5. Experimental results prove that RMSE valuesobtained for various compression ratios in column transform are closer to those obtained in fulltransform of an image. Hence instead of full transform of an image, column transform can be used forimage compression, saving half number of computations. RMSE obtained in row transform is quitehigher than column and full transform at higher values of compression ratio. Hence it is notrecommended. Good PSNR is obtained using column transform. Among all the seven transformsused, DFT, DCT and DST give better results in terms of RMSE and reconstructed image quality thanother transforms. Walsh and Haar transforms also give acceptable results with an advantage of lesscomputation whereas Slant and Kekre transform do not give good results. Hence they are notrecommended.VI. FUTURE WORKFuture work includes application of orthogonal wavelet transforms on colour images. Change in theRMSE values if any, can be compared. Also PSNR values and quality of reconstructed image can bestudied to compare their performance against the one in this paper.REFERENCES [1]. Dipti Bhatnagar, Sumit Budhiraja, “Image Compression using DCT based Compressive Sensing and Vector Quantization”, IJCA, Vol50 (20), pp. 34-38, July 2012. [2]. Ahmed, N., Natarajan T., Rao K. R.: Discrete cosine transform. In: IEEE Transactions on Computers, Vol. 23, 90-93, 1974. [3]. Menegaz, G., L. Grewe and J.P. Thiran, “Multirate Coding of 3D Medical Data”, in proc. of International Conference on Image Processing, IEEE, 3: 656-659, 2000. [4]. Wang, J. and H.K. Huang, “Medical Image Compression by using Three-Dimensional Wavelet Transform”, IEEE Transactions on Medical Imaging, 15(4): 547-554, 1996. 98 Vol. 6, Issue 1, pp. 88-100
  12. 12. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963 [5]. Bullmore, E., J. Fadili, V. Maxim, L. Sendur, J. Suckling, B. Whitcher, M. Brammer and M. Breakspear, “Wavelets and Functional Magnetic Resonance Imaging of the Human Brain NeuroImage”, 23(1): 234-249, 2004. [6]. R. D. Dony and S. Haykins, “Optimally adaptive transform coding”, IEEE Trans. Image Process., 4, 1358-1370, 1995. [7]. Prabhakar.Telagarapu, V.Jagan Naveen, A.Lakshmi Prasanthi, G.Vijaya Santhi, “Image compression using DCT and wavelet transformation”, IJSPIPPR, vol 4, issue 3, pp. 61-74, Sept 2011. [8]. R.S. Stanković and B.J. Falkowski. “The Haar wavelet transform: its status and achievements”. Computers and Electrical Engineering, Vol.29, No.1, pp.25-44, January 2003. [9]. P. M. Fanelle and A. K. Jain, “Recursive block coding: A new approach to transform coding”, IEEE Trans. Comm., C-34,161-179, 1986. [10]. M. Bosi and G. Davidson, “High quality low bit-rate audio transform coding for transmission and Multimedia applications”, J. Audio Eng. Soc.32, pp. 43-50, 1992 [11]. Strang G. "Wavelet Transforms versus Fourier Transforms." Bull. Amer. Math. Soc. 28 pp. 288- 305, 1993. [12]. H.B.Kekre, Tanuja Sarode, Sudeep Thepade, “Inception of hybrid wavelet Transform using Two orthogonal Transforms and It’s use for Image compression”, IJCSIS, vol 9, no. 6, 2011. [13]. H. B. Kekre, Sudeep Thepade, “Image retrieval using Non – Involutional Orthogonal Kekre’s Transform”, International Journal of Multidisciplinary Research and Advances in Engineering (IJMRAE), Ascent Publication House, 2009, Volume 1, No. I, 2009. Abstract available online at www.Ascent-journals.com [14]. Mourence M. Anguh and Ralph R. Martin, “A truncation method for computing slant transforms with applications to image processing”, IEEE Trans. on Communications, vol. 43, no. 6, pp. 2103-2110, 1995. [15]. W. K. Pratt, W.H.Cheng and L. R. Welch, “Slant Transform Image Coding”, IEEE Trans. commn. Vol. Comm. 22, pp. 1075-1093, Aug. 1974. [16]. Nam IK Cho, Sanjit K. Mitra, “Warped Discrete Cosine Transform and Its Applications in Image Compression”, IEEE Trans. On Circuits and Systems on Video Technology, vol. 10, no. 8, pp. 1364-1373, Dec 2000. [17]. H.B.Kekre, Tanuja Sarode, sudeep Thepade, Sonal Shroff, “ Instigation of Orthogonal Wavelet Transforms using Walsh, Cosine, Hartley, Kekre Transforms and their use in Image Compression”, International Journal of Computer Science and Information Security (IJCSIS), Vol 9, No. 6, pp. 125-133, 2011. [18]. Veensdevi S.V., A. G. Ananth, “Fractal Image compression using Quadtree Decomposition and Huffman Coding”, Signal and Image Processing: An International Journal (SIPIJ), Vol. 3, No.2, pp. 207-212, April 2012.AUTHORSH. B. Kekre has received B.E. (Hons.) in Telecomm. Engg. from Jabalpur University in1958, M.Tech (Industrial Electronics) from IIT Bombay in 1960, M.S.Engg. (ElectricalEngg.) from University of Ottawa in 1965 and Ph.D. (System Identification) from IITBombay in 1970. He has worked Over 35 years as Faculty of Electrical Engineering andthen HOD Computer Science and Engg. at IIT Bombay. After serving IIT for 35 years, heretired in 1995. After retirement from IIT, for 13 years he was working as a professor andhead in the department of computer engineering and Vice principal at Thadomal ShahaniEngg. College, Mumbai. Now he is senior professor at MPSTME, SVKM’s NMIMS University. He has guided17 Ph.Ds., more than 100 M.E./M.Tech and several B.E. / B.Tech projects, while in IIT and TSEC. His areas ofinterest are Digital Signal processing, Image Processing and Computer Networking. He has more than 450papers in National / International Journals and Conferences to his credit. He was Senior Member of IEEE.Presently He is Fellow of IETE, Life Member of ISTE and Senior Member of International Association ofComputer Science and Information Technology (IACSIT). Recently fifteen students working under his guidancehave received best paper awards. Currently eight research scholars working under his guidance have beenawarded Ph. D. by NMIMS (Deemed to be University). At present seven research scholars are pursuing Ph.D.program under his guidance.Tanuja K. Sarode has received M.E. (Computer Engineering) degree from MumbaiUniversity in 2004, Ph.D. from Mukesh Patel School of Technology, Management andEngg. SVKM’s NMIMS University, Vile-Parle (W), Mumbai, INDIA. She has more than11 years of experience in teaching. Currently working as Assistant Professor in Dept. ofComputer Engineering at Thadomal Shahani Engineering College, Mumbai. She is member 99 Vol. 6, Issue 1, pp. 88-100
  13. 13. International Journal of Advances in Engineering & Technology, Mar. 2013.©IJAET ISSN: 2231-1963of International Association of Engineers (IAENG) and International Association of Computer Science andInformation Technology (IACSIT). Her areas of interest are Image Processing, Signal Processing and ComputerGraphics. She has 137 papers in National /International Conferences/journal to her credit.Prachi Natu has received B.E. (Electronics and Telecommunication) degree from MumbaiUniversity in 2004. Currently pursuing Ph.D. from NMIMS University. She has 08 years ofexperience in teaching. Currently working as Assistant Professor in Department of ComputerEngineering at G. V. Acharya Institute of Engineering and Technology, Shelu (Karjat). Herareas of interest are Image Processing, Database Management Systems and OperatingSystems. She has 12 papers in International Conferences/journal to her credit. 100 Vol. 6, Issue 1, pp. 88-100

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