{"references": ["J.-L. Starck, and P. Querre, \"Multispectral Data Restoration by the\nWavelet-Karhunen-Lo\u00e8ve Transform,\" Preprint submitted to Elsevier\nPreprint, 2000, pp. 1-29.", "D. L. Donoho, and I. M. Johnstone, \"Adapting to unknown smoothness\nvia wavelet shrinkage,\" Journal of the American Statistical Assoc., vol.\n90, no. 432, pp. 1200-1224., 1995.", "D. L. Donoho, and I. M. Johnstone, \"Ideal spatial adaptation by wavelet\nshrinkage,\" Biometrika, 81, 425-455, 1994.", "I. Daubechies. Ten Lectures on Wavelets, SIAM, Philadelphia, PA.\n1992.", "I. Daubechies, \"Different Perspectives on Wavelets,\" in Proceedings of\nSymposia in Applied Mathematics, vol. 47, American Mathematical\nSociety, USA, 1993.", "S. Mallat, \"A theory for multiresolution signal decomposition: The\nwavelet representation,\" IEEE Trans. Pattern Anal. Machine Intell., vol.\n11, pp. 674-693, July 1989.", "S. G. Mallat, \"Multiresolution approximations and wavelet orthonormal\nbases of L2 (R),\" Transactions of the American Mathematical Society,\n315(1), pp.69-87, 1989a.", "S. G. Chang, B. Yu, and M. Vetterli, \"Adaptive wavelet thresholding for\nimage denoising and compression,\" IEEE Trans. Image Processing, vol.\n9, pp. 1532-1546, Sept. 2000.", "M. Misiti, Y. Misiti, G. Oppenheim, and J.M. Poggi. (2001, June).\nWavelet Toolbox, for use with MATLAB\u00ae, User-s guide, version 2.1.\n[10] C.S. Burrus, R.A. Gopinath, and H. Guo, Introduction to Wavelets and\nWavelet Transforms: A Primer, Prentice Hall, New Jersey, 1998.\n[11] B.B. Hubbard, The World According to Wavelets: The Story of a\nMathematical Technique in the Making, A. K. Peter Wellesley,\nMassachusetts, 1996.\n[12] A. Grossman and J. Morlet, \"Decomposition of Hardy Functions into\nSquare Integrable Wavelets of Constant Shape,\" SIAM J. App Math, 15:\npp.723-736, 1984.\n[13] C. Valens. (2004). A really friendly guide to wavelets.\n[14] G. Kaiser, A Friendly Guide To Wavelets, Boston: Birkhauser, 1994.\n[15] J.S. Walker, A Primer on Wavelets and their Scientific Applications,\nChapman & Hall/CRC, New York, 1999.\n[16] E. J. Stollnitz, T. D. DeRose, and D. H. Salesin, Wavelets for Computer\nGraphics: Theory and Applications, Morgan Kaufmann Publishers, San\nFrancisco, 1996.\n[17] J. Shen and G. Strang, \"The zeros of the Daubechies polynomials,\" in\nProc. American Mathematical Society, 1996.\n[18] H.Y. Gao, and A.G. Bruce, \"WaveShrink with firm shrinkage,\"\nStatistica Sinica, 7, 855-874, 1997.\n[19] V.S. Shingate, et al, \"Still image compression using Embedded Zerotree\nWavelet Encoding,\" In International Conference on Cognitive Systems\nNew Delhi, December 14-15, pp.1-9, 2004.\n[20] C. Valens, EZW encoding, 2004.\n[21] Yuan-Yuan HU, et al, \"Embedded Wavelet Image Compression\nAlgorithm Based on Full Zerotree,\" In IJCSES International Journal of\nComputer Sciences and Engineering Systems, Vol.1, No.2, pp. 131-138,\nApril 2007.\n[22] C.Wang, and K-L. Ma, \"A Statistical Approach to Volume Data Quality\nAssessment,\" IEEE Transactions on Visualization and Computer\nGraphics, Vol.14, No. 3, May/June, 2008, pp. 590-602.\n[23] R. Muller, A study of image compression techniques, with specific focus\non weighted finite automata, Thesis for Degree Master of Science at the\nUniversity of Stellenbosch, December 2005.\n[24] S.S. Polisetty, Hardware acceleration of the embedded zerotree wavelet\nalgorithm, Thesis for Master of Science Degree at the University of\nTennessee, Knoxville, December 2004.\n[25] V. Mahomed, and S.H. Mneney, \"Wavelet based compression: the new\nstill image compression technique,\" In Sixteenth Annual Symposium of\nthe Pattern Recognition Association of South Africa, 23-25 November\n2005, Langebaan, South Africa, pp.67-72.\n[26] H.A. Kim Taavo, Scalable video using wavelets, Master of Science\nProgramme, Lulea University of Technology, May 14, 2002.\n[27] D. Zhang, and S. Chen, \"Fast image compression using matrix K-L\ntransform,\" Neurocomputing, Volume 68, pp.258-266, October 2005.\n[28] R.C. Gonzalez, R.E. Woods, Digital Image Processing, 2nd Edition,\nPrentice- Hall, Jan. 2002, pp.675-683.\n[29] -, The transform and data compression handbook, Edited by K.R. Rao,\nand P.C. Yip, CRC Press Inc., Boca Raton, FL, USA, 2001.\n[30] B.R. Epstein, et al, \"Multispectral KLT-wavelet data compression for\nlandsat thematic mapper images,\" In Data Compression Conference,\npp. 200-208, Snowbird, UT, March 1992.\n[31] K. Konstantinides, et al, \"Noise using block-based singular value\ndecomposition,\" IEEE Transactions on Image Processing, 6(3), pp.479-\n483, 1997.\n[32] J. Lee, \"Optimized quadtree for Karhunen-Lo\u00e8ve Transform in\nmultispectral image coding,\" IEEE Transactions on Image Processing,\n8(4), pp.453-461, 1999.\n[33] J.A. Saghri, et al, \"Practical Transform coding of multispectral\nimagery,\" IEEE Signal Processing Magazine, 12, pp.32-43, 1995.\n[34] T-S. Kim, et al, \"Multispectral image data compression using classified\nprediction and KLT in wavelet transform domain,\" IEICE Transactions\non Fundam Electron Commun Comput Sci, Vol. E86-A; No.6, pp.1492-\n1497, 2003.\n[35] J.L. Semmlow, Biosignal and biomedical image processing: MATLABBased\napplications, Marcel Dekker, Inc., New York, 2004.\n[36] S. Borman, and R. Stevenson, \"Image sequence processing,\"\nDepartment, Ed. Marcel Dekker, New York, 2003. pp.840-879.\n[37] M. Wien, Variable Block-Size Transforms for Hybrid Video Coding,\nDegree Thesis, Institut f\u251c\u255dr Nachrichtentechnik der Rheinisch-\nWestf\u251c\u00f1lischen Technischen Hchschule Aachen, February 2004.\n[38] E. Christophe, et al, \"Hyperspectral image compression: adapting SPIHT\nand EZW to anisotopic 3D wavelet coding,\" submitted to IEEE\nTransactions on Image processing, pp.1-13, 2006.\n[39] L.S. Rodr\u251c\u00a1guez del R\u251c\u00a1o, \"Fast piecewise linear predictors for lossless\ncompression of hyperspectral imagery,\" Thesis for Degree in Master of\nScience in Electrical Engineering, University of Puerto Rico, Mayaguez\nCampus, 2003.\n[40] Hyperspectral Data Compression, Edited by Giovanni Motta, Francesco\nRizzo and James A. Storer, Chapter 3, Springer, New York, 2006.\n[41] B. Arnold, An Investigation into using Singular Value Decomposition as\na method of Image Compression, University of Canterbury Department\nof Mathematics and Statistics, September 2000.\n[42] S. Tjoa, et al, \"Transform coder classification for digital image\nforensics\".\n[43] M. Mastriani, and A. Giraldez, \"Smoothing of coefficients in wavelet\ndomain for speckle reduction in Synthetic Aperture Radar images,\"\nICGST International Journal on Graphics, Vision and Image Processing\n(GVIP), Volume 6, pp. 1-8, 2005.\n[44] M. Mastriani, and A. Giraldez, \"Despeckling of SAR images in wavelet\ndomain,\" GIS Development Magazine, Sept. 2005, Vol. 9, Issue 9,\npp.38-40.\n[45] M. Mastriani, and A. Giraldez, \"Microarrays denoising via smoothing of\ncoefficients in wavelet domain,\" WSEAS Transactions on Biology and\nBiomedicine, 2005.\n[46] M. Mastriani, and A. Giraldez, \"Fuzzy thresholding in wavelet domain for\nspeckle reduction in Synthetic Aperture Radar images,\" ICGST\nInternational on Journal of Artificial Intelligence and Machine Learning,\nVolume 5, 2005.\n[47] M. Mastriani, \"Denoising based on wavelets and deblurring via selforganizing\nmap for Synthetic Aperture Radar images,\" ICGST\nInternational on Journal of Artificial Intelligence and Machine Learning,\nVolume 5, 2005.\n[48] M. Mastriani, \"Systholic Boolean Orthonormalizer Network in Wavelet\nDomain for Microarray Denoising,\" ICGST International Journal on\nBioinformatics and Medical Engineering, Volume 5, 2005.\n[49] M. Mastriani, \"Denoising based on wavelets and deblurring via selforganizing\nmap for Synthetic Aperture Radar images,\" International\nJournal of Signal Processing, Volume 2, Number 4, pp.226-235, 2005.\n[50] M. Mastriani, \"Systholic Boolean Orthonormalizer Network in Wavelet\nDomain for Microarray Denoising,\" International Journal of Signal\nProcessing, Volume 2, Number 4, pp.273-284, 2005.\n[51] M. Mastriani, and A. Giraldez, \"Microarrays denoising via smoothing of\ncoefficients in wavelet domain,\" International Journal of Biomedical\nSciences, Volume 1, Number 1, pp.7-14, 2006.\n[52] M. Mastriani, and A. Giraldez, \"Kalman- Shrinkage for Wavelet-Based\nDespeckling of SAR Images,\" International Journal of Intelligent\nSystems and Technologies, Volume 1, Number 3, pp.190-196, 2006.\n[53] M. Mastriani, and A. Giraldez, \"Neural Shrinkage for Wavelet-Based\nSAR Despeckling,\" International Journal of Systems and Technologies,\nVolume 1, Number 3, pp.211-222, 2006.\n[54] M. Mastriani, \"Fuzzy Thresholding in Wavelet Domain for Speckle\nReduction in Synthetic Aperture Radar Images,\" International Journal of\nSystems and Technologies, Volume 1, Number 3, pp.252-265, 2006.\n[55] M. Mastriani, \"New Wavelet-Based Superresolution Algorithm for\nSpeckle Reduction in SAR Images ,\" International Journal of Computer\nScience, Volume 1, Number 4, pp.291-298, 2006.\n[56] M. Mastriani, \"Denoising and compression in wavelet domain via\nprojection onto approximation coefficients,\" International Journal of\nSignal Processing, Volume 5, Number 1, pp.20-30, 2008.\n[57] H. Samet, The Design and Analysis of Spatial Data Structures, Addison-\nWesley, 1990.\n[58] H. Samet, Applications of Spatial Data Structures - Computer Graphics,\nImage Processing and GIS, Addison-Wesley, 1990.\n[59] A.K. Jain, Fundamentals of Digital Image Processing, Englewood\nCliffs, New Jersey, 1989.\n[60] MATLAB\u00ae R2008a (Mathworks, Natick, MA).\n[61] A. Sharma, and K.K. Paliwal, \"Fast principal component analysis using\nfixed-point algorithm\", Pattern Recognition Letters, Vol.28, pp.1151-\n1155, 2007.\n[62] E. Oja, \"A Simplified Neuron Model as a Principal Component\nAnalyzer\", Journal of Mathematical Biology, Vol.15, pp.267-273, 1982.\n[63] T.D. Sanger, \"Optimal Unsupervised Learning in a Single-Layer Linear\nFeedforward Neural Networks,\" Vol.2, pp.459-473, 1989."]}

In this work, we present a comparison between different techniques of image compression. First, the image is divided in blocks which are organized according to a certain scan. Later, several compression techniques are applied, combined or alone. Such techniques are: wavelets (Haar's basis), Karhunen-Loève Transform, etc. Simulations show that the combined versions are the best, with minor Mean Squared Error (MSE), and higher Peak Signal to Noise Ratio (PSNR) and better image quality, even in the presence of noise.