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.
[1] J.-L. Starck, and P. Querre, "Multispectral Data Restoration by the
Wavelet-Karhunen-Loève Transform," Preprint submitted to Elsevier
Preprint, 2000, pp. 1-29.
[2] D. L. Donoho, and I. M. Johnstone, "Adapting to unknown smoothness
via wavelet shrinkage," Journal of the American Statistical Assoc., vol.
90, no. 432, pp. 1200-1224., 1995.
[3] D. L. Donoho, and I. M. Johnstone, "Ideal spatial adaptation by wavelet
shrinkage," Biometrika, 81, 425-455, 1994.
[4] I. Daubechies. Ten Lectures on Wavelets, SIAM, Philadelphia, PA.
1992.
[5] I. Daubechies, "Different Perspectives on Wavelets," in Proceedings of
Symposia in Applied Mathematics, vol. 47, American Mathematical
Society, USA, 1993.
[6] S. Mallat, "A theory for multiresolution signal decomposition: The
wavelet representation," IEEE Trans. Pattern Anal. Machine Intell., vol.
11, pp. 674-693, July 1989.
[7] S. G. Mallat, "Multiresolution approximations and wavelet orthonormal
bases of L2 (R)," Transactions of the American Mathematical Society,
315(1), pp.69-87, 1989a.
[8] S. G. Chang, B. Yu, and M. Vetterli, "Adaptive wavelet thresholding for
image denoising and compression," IEEE Trans. Image Processing, vol.
9, pp. 1532-1546, Sept. 2000.
[9] M. Misiti, Y. Misiti, G. Oppenheim, and J.M. Poggi. (2001, June).
Wavelet Toolbox, for use with MATLAB®, User-s guide, version 2.1.
[10] C.S. Burrus, R.A. Gopinath, and H. Guo, Introduction to Wavelets and
Wavelet Transforms: A Primer, Prentice Hall, New Jersey, 1998.
[11] B.B. Hubbard, The World According to Wavelets: The Story of a
Mathematical Technique in the Making, A. K. Peter Wellesley,
Massachusetts, 1996.
[12] A. Grossman and J. Morlet, "Decomposition of Hardy Functions into
Square Integrable Wavelets of Constant Shape," SIAM J. App Math, 15:
pp.723-736, 1984.
[13] C. Valens. (2004). A really friendly guide to wavelets.
[14] G. Kaiser, A Friendly Guide To Wavelets, Boston: Birkhauser, 1994.
[15] J.S. Walker, A Primer on Wavelets and their Scientific Applications,
Chapman & Hall/CRC, New York, 1999.
[16] E. J. Stollnitz, T. D. DeRose, and D. H. Salesin, Wavelets for Computer
Graphics: Theory and Applications, Morgan Kaufmann Publishers, San
Francisco, 1996.
[17] J. Shen and G. Strang, "The zeros of the Daubechies polynomials," in
Proc. American Mathematical Society, 1996.
[18] H.Y. Gao, and A.G. Bruce, "WaveShrink with firm shrinkage,"
Statistica Sinica, 7, 855-874, 1997.
[19] V.S. Shingate, et al, "Still image compression using Embedded Zerotree
Wavelet Encoding," In International Conference on Cognitive Systems
New Delhi, December 14-15, pp.1-9, 2004.
[20] C. Valens, EZW encoding, 2004.
[21] Yuan-Yuan HU, et al, "Embedded Wavelet Image Compression
Algorithm Based on Full Zerotree," In IJCSES International Journal of
Computer Sciences and Engineering Systems, Vol.1, No.2, pp. 131-138,
April 2007.
[22] C.Wang, and K-L. Ma, "A Statistical Approach to Volume Data Quality
Assessment," IEEE Transactions on Visualization and Computer
Graphics, Vol.14, No. 3, May/June, 2008, pp. 590-602.
[23] R. Muller, A study of image compression techniques, with specific focus
on weighted finite automata, Thesis for Degree Master of Science at the
University of Stellenbosch, December 2005.
[24] S.S. Polisetty, Hardware acceleration of the embedded zerotree wavelet
algorithm, Thesis for Master of Science Degree at the University of
Tennessee, Knoxville, December 2004.
[25] V. Mahomed, and S.H. Mneney, "Wavelet based compression: the new
still image compression technique," In Sixteenth Annual Symposium of
the Pattern Recognition Association of South Africa, 23-25 November
2005, Langebaan, South Africa, pp.67-72.
[26] H.A. Kim Taavo, Scalable video using wavelets, Master of Science
Programme, Lulea University of Technology, May 14, 2002.
[27] D. Zhang, and S. Chen, "Fast image compression using matrix K-L
transform," Neurocomputing, Volume 68, pp.258-266, October 2005.
[28] R.C. Gonzalez, R.E. Woods, Digital Image Processing, 2nd Edition,
Prentice- Hall, Jan. 2002, pp.675-683.
[29] -, The transform and data compression handbook, Edited by K.R. Rao,
and P.C. Yip, CRC Press Inc., Boca Raton, FL, USA, 2001.
[30] B.R. Epstein, et al, "Multispectral KLT-wavelet data compression for
landsat thematic mapper images," In Data Compression Conference,
pp. 200-208, Snowbird, UT, March 1992.
[31] K. Konstantinides, et al, "Noise using block-based singular value
decomposition," IEEE Transactions on Image Processing, 6(3), pp.479-
483, 1997.
[32] J. Lee, "Optimized quadtree for Karhunen-Loève Transform in
multispectral image coding," IEEE Transactions on Image Processing,
8(4), pp.453-461, 1999.
[33] J.A. Saghri, et al, "Practical Transform coding of multispectral
imagery," IEEE Signal Processing Magazine, 12, pp.32-43, 1995.
[34] T-S. Kim, et al, "Multispectral image data compression using classified
prediction and KLT in wavelet transform domain," IEICE Transactions
on Fundam Electron Commun Comput Sci, Vol. E86-A; No.6, pp.1492-
1497, 2003.
[35] J.L. Semmlow, Biosignal and biomedical image processing: MATLABBased
applications, Marcel Dekker, Inc., New York, 2004.
[36] S. Borman, and R. Stevenson, "Image sequence processing,"
Department, Ed. Marcel Dekker, New York, 2003. pp.840-879.
[37] M. Wien, Variable Block-Size Transforms for Hybrid Video Coding,
Degree Thesis, Institut f├╝r Nachrichtentechnik der Rheinisch-
Westfälischen Technischen Hchschule Aachen, February 2004.
[38] E. Christophe, et al, "Hyperspectral image compression: adapting SPIHT
and EZW to anisotopic 3D wavelet coding," submitted to IEEE
Transactions on Image processing, pp.1-13, 2006.
[39] L.S. Rodríguez del Río, "Fast piecewise linear predictors for lossless
compression of hyperspectral imagery," Thesis for Degree in Master of
Science in Electrical Engineering, University of Puerto Rico, Mayaguez
Campus, 2003.
[40] Hyperspectral Data Compression, Edited by Giovanni Motta, Francesco
Rizzo and James A. Storer, Chapter 3, Springer, New York, 2006.
[41] B. Arnold, An Investigation into using Singular Value Decomposition as
a method of Image Compression, University of Canterbury Department
of Mathematics and Statistics, September 2000.
[42] S. Tjoa, et al, "Transform coder classification for digital image
forensics".
[43] M. Mastriani, and A. Giraldez, "Smoothing of coefficients in wavelet
domain for speckle reduction in Synthetic Aperture Radar images,"
ICGST International Journal on Graphics, Vision and Image Processing
(GVIP), Volume 6, pp. 1-8, 2005.
[44] M. Mastriani, and A. Giraldez, "Despeckling of SAR images in wavelet
domain," GIS Development Magazine, Sept. 2005, Vol. 9, Issue 9,
pp.38-40.
[45] M. Mastriani, and A. Giraldez, "Microarrays denoising via smoothing of
coefficients in wavelet domain," WSEAS Transactions on Biology and
Biomedicine, 2005.
[46] M. Mastriani, and A. Giraldez, "Fuzzy thresholding in wavelet domain for
speckle reduction in Synthetic Aperture Radar images," ICGST
International on Journal of Artificial Intelligence and Machine Learning,
Volume 5, 2005.
[47] M. Mastriani, "Denoising based on wavelets and deblurring via selforganizing
map for Synthetic Aperture Radar images," ICGST
International on Journal of Artificial Intelligence and Machine Learning,
Volume 5, 2005.
[48] M. Mastriani, "Systholic Boolean Orthonormalizer Network in Wavelet
Domain for Microarray Denoising," ICGST International Journal on
Bioinformatics and Medical Engineering, Volume 5, 2005.
[49] M. Mastriani, "Denoising based on wavelets and deblurring via selforganizing
map for Synthetic Aperture Radar images," International
Journal of Signal Processing, Volume 2, Number 4, pp.226-235, 2005.
[50] M. Mastriani, "Systholic Boolean Orthonormalizer Network in Wavelet
Domain for Microarray Denoising," International Journal of Signal
Processing, Volume 2, Number 4, pp.273-284, 2005.
[51] M. Mastriani, and A. Giraldez, "Microarrays denoising via smoothing of
coefficients in wavelet domain," International Journal of Biomedical
Sciences, Volume 1, Number 1, pp.7-14, 2006.
[52] M. Mastriani, and A. Giraldez, "Kalman- Shrinkage for Wavelet-Based
Despeckling of SAR Images," International Journal of Intelligent
Systems and Technologies, Volume 1, Number 3, pp.190-196, 2006.
[53] M. Mastriani, and A. Giraldez, "Neural Shrinkage for Wavelet-Based
SAR Despeckling," International Journal of Systems and Technologies,
Volume 1, Number 3, pp.211-222, 2006.
[54] M. Mastriani, "Fuzzy Thresholding in Wavelet Domain for Speckle
Reduction in Synthetic Aperture Radar Images," International Journal of
Systems and Technologies, Volume 1, Number 3, pp.252-265, 2006.
[55] M. Mastriani, "New Wavelet-Based Superresolution Algorithm for
Speckle Reduction in SAR Images ," International Journal of Computer
Science, Volume 1, Number 4, pp.291-298, 2006.
[56] M. Mastriani, "Denoising and compression in wavelet domain via
projection onto approximation coefficients," International Journal of
Signal Processing, Volume 5, Number 1, pp.20-30, 2008.
[57] H. Samet, The Design and Analysis of Spatial Data Structures, Addison-
Wesley, 1990.
[58] H. Samet, Applications of Spatial Data Structures - Computer Graphics,
Image Processing and GIS, Addison-Wesley, 1990.
[59] A.K. Jain, Fundamentals of Digital Image Processing, Englewood
Cliffs, New Jersey, 1989.
[60] MATLAB® R2008a (Mathworks, Natick, MA).
[61] A. Sharma, and K.K. Paliwal, "Fast principal component analysis using
fixed-point algorithm", Pattern Recognition Letters, Vol.28, pp.1151-
1155, 2007.
[62] E. Oja, "A Simplified Neuron Model as a Principal Component
Analyzer", Journal of Mathematical Biology, Vol.15, pp.267-273, 1982.
[63] T.D. Sanger, "Optimal Unsupervised Learning in a Single-Layer Linear
Feedforward Neural Networks," Vol.2, pp.459-473, 1989.
[1] J.-L. Starck, and P. Querre, "Multispectral Data Restoration by the
Wavelet-Karhunen-Loève Transform," Preprint submitted to Elsevier
Preprint, 2000, pp. 1-29.
[2] D. L. Donoho, and I. M. Johnstone, "Adapting to unknown smoothness
via wavelet shrinkage," Journal of the American Statistical Assoc., vol.
90, no. 432, pp. 1200-1224., 1995.
[3] D. L. Donoho, and I. M. Johnstone, "Ideal spatial adaptation by wavelet
shrinkage," Biometrika, 81, 425-455, 1994.
[4] I. Daubechies. Ten Lectures on Wavelets, SIAM, Philadelphia, PA.
1992.
[5] I. Daubechies, "Different Perspectives on Wavelets," in Proceedings of
Symposia in Applied Mathematics, vol. 47, American Mathematical
Society, USA, 1993.
[6] S. Mallat, "A theory for multiresolution signal decomposition: The
wavelet representation," IEEE Trans. Pattern Anal. Machine Intell., vol.
11, pp. 674-693, July 1989.
[7] S. G. Mallat, "Multiresolution approximations and wavelet orthonormal
bases of L2 (R)," Transactions of the American Mathematical Society,
315(1), pp.69-87, 1989a.
[8] S. G. Chang, B. Yu, and M. Vetterli, "Adaptive wavelet thresholding for
image denoising and compression," IEEE Trans. Image Processing, vol.
9, pp. 1532-1546, Sept. 2000.
[9] M. Misiti, Y. Misiti, G. Oppenheim, and J.M. Poggi. (2001, June).
Wavelet Toolbox, for use with MATLAB®, User-s guide, version 2.1.
[10] C.S. Burrus, R.A. Gopinath, and H. Guo, Introduction to Wavelets and
Wavelet Transforms: A Primer, Prentice Hall, New Jersey, 1998.
[11] B.B. Hubbard, The World According to Wavelets: The Story of a
Mathematical Technique in the Making, A. K. Peter Wellesley,
Massachusetts, 1996.
[12] A. Grossman and J. Morlet, "Decomposition of Hardy Functions into
Square Integrable Wavelets of Constant Shape," SIAM J. App Math, 15:
pp.723-736, 1984.
[13] C. Valens. (2004). A really friendly guide to wavelets.
[14] G. Kaiser, A Friendly Guide To Wavelets, Boston: Birkhauser, 1994.
[15] J.S. Walker, A Primer on Wavelets and their Scientific Applications,
Chapman & Hall/CRC, New York, 1999.
[16] E. J. Stollnitz, T. D. DeRose, and D. H. Salesin, Wavelets for Computer
Graphics: Theory and Applications, Morgan Kaufmann Publishers, San
Francisco, 1996.
[17] J. Shen and G. Strang, "The zeros of the Daubechies polynomials," in
Proc. American Mathematical Society, 1996.
[18] H.Y. Gao, and A.G. Bruce, "WaveShrink with firm shrinkage,"
Statistica Sinica, 7, 855-874, 1997.
[19] V.S. Shingate, et al, "Still image compression using Embedded Zerotree
Wavelet Encoding," In International Conference on Cognitive Systems
New Delhi, December 14-15, pp.1-9, 2004.
[20] C. Valens, EZW encoding, 2004.
[21] Yuan-Yuan HU, et al, "Embedded Wavelet Image Compression
Algorithm Based on Full Zerotree," In IJCSES International Journal of
Computer Sciences and Engineering Systems, Vol.1, No.2, pp. 131-138,
April 2007.
[22] C.Wang, and K-L. Ma, "A Statistical Approach to Volume Data Quality
Assessment," IEEE Transactions on Visualization and Computer
Graphics, Vol.14, No. 3, May/June, 2008, pp. 590-602.
[23] R. Muller, A study of image compression techniques, with specific focus
on weighted finite automata, Thesis for Degree Master of Science at the
University of Stellenbosch, December 2005.
[24] S.S. Polisetty, Hardware acceleration of the embedded zerotree wavelet
algorithm, Thesis for Master of Science Degree at the University of
Tennessee, Knoxville, December 2004.
[25] V. Mahomed, and S.H. Mneney, "Wavelet based compression: the new
still image compression technique," In Sixteenth Annual Symposium of
the Pattern Recognition Association of South Africa, 23-25 November
2005, Langebaan, South Africa, pp.67-72.
[26] H.A. Kim Taavo, Scalable video using wavelets, Master of Science
Programme, Lulea University of Technology, May 14, 2002.
[27] D. Zhang, and S. Chen, "Fast image compression using matrix K-L
transform," Neurocomputing, Volume 68, pp.258-266, October 2005.
[28] R.C. Gonzalez, R.E. Woods, Digital Image Processing, 2nd Edition,
Prentice- Hall, Jan. 2002, pp.675-683.
[29] -, The transform and data compression handbook, Edited by K.R. Rao,
and P.C. Yip, CRC Press Inc., Boca Raton, FL, USA, 2001.
[30] B.R. Epstein, et al, "Multispectral KLT-wavelet data compression for
landsat thematic mapper images," In Data Compression Conference,
pp. 200-208, Snowbird, UT, March 1992.
[31] K. Konstantinides, et al, "Noise using block-based singular value
decomposition," IEEE Transactions on Image Processing, 6(3), pp.479-
483, 1997.
[32] J. Lee, "Optimized quadtree for Karhunen-Loève Transform in
multispectral image coding," IEEE Transactions on Image Processing,
8(4), pp.453-461, 1999.
[33] J.A. Saghri, et al, "Practical Transform coding of multispectral
imagery," IEEE Signal Processing Magazine, 12, pp.32-43, 1995.
[34] T-S. Kim, et al, "Multispectral image data compression using classified
prediction and KLT in wavelet transform domain," IEICE Transactions
on Fundam Electron Commun Comput Sci, Vol. E86-A; No.6, pp.1492-
1497, 2003.
[35] J.L. Semmlow, Biosignal and biomedical image processing: MATLABBased
applications, Marcel Dekker, Inc., New York, 2004.
[36] S. Borman, and R. Stevenson, "Image sequence processing,"
Department, Ed. Marcel Dekker, New York, 2003. pp.840-879.
[37] M. Wien, Variable Block-Size Transforms for Hybrid Video Coding,
Degree Thesis, Institut f├╝r Nachrichtentechnik der Rheinisch-
Westfälischen Technischen Hchschule Aachen, February 2004.
[38] E. Christophe, et al, "Hyperspectral image compression: adapting SPIHT
and EZW to anisotopic 3D wavelet coding," submitted to IEEE
Transactions on Image processing, pp.1-13, 2006.
[39] L.S. Rodríguez del Río, "Fast piecewise linear predictors for lossless
compression of hyperspectral imagery," Thesis for Degree in Master of
Science in Electrical Engineering, University of Puerto Rico, Mayaguez
Campus, 2003.
[40] Hyperspectral Data Compression, Edited by Giovanni Motta, Francesco
Rizzo and James A. Storer, Chapter 3, Springer, New York, 2006.
[41] B. Arnold, An Investigation into using Singular Value Decomposition as
a method of Image Compression, University of Canterbury Department
of Mathematics and Statistics, September 2000.
[42] S. Tjoa, et al, "Transform coder classification for digital image
forensics".
[43] M. Mastriani, and A. Giraldez, "Smoothing of coefficients in wavelet
domain for speckle reduction in Synthetic Aperture Radar images,"
ICGST International Journal on Graphics, Vision and Image Processing
(GVIP), Volume 6, pp. 1-8, 2005.
[44] M. Mastriani, and A. Giraldez, "Despeckling of SAR images in wavelet
domain," GIS Development Magazine, Sept. 2005, Vol. 9, Issue 9,
pp.38-40.
[45] M. Mastriani, and A. Giraldez, "Microarrays denoising via smoothing of
coefficients in wavelet domain," WSEAS Transactions on Biology and
Biomedicine, 2005.
[46] M. Mastriani, and A. Giraldez, "Fuzzy thresholding in wavelet domain for
speckle reduction in Synthetic Aperture Radar images," ICGST
International on Journal of Artificial Intelligence and Machine Learning,
Volume 5, 2005.
[47] M. Mastriani, "Denoising based on wavelets and deblurring via selforganizing
map for Synthetic Aperture Radar images," ICGST
International on Journal of Artificial Intelligence and Machine Learning,
Volume 5, 2005.
[48] M. Mastriani, "Systholic Boolean Orthonormalizer Network in Wavelet
Domain for Microarray Denoising," ICGST International Journal on
Bioinformatics and Medical Engineering, Volume 5, 2005.
[49] M. Mastriani, "Denoising based on wavelets and deblurring via selforganizing
map for Synthetic Aperture Radar images," International
Journal of Signal Processing, Volume 2, Number 4, pp.226-235, 2005.
[50] M. Mastriani, "Systholic Boolean Orthonormalizer Network in Wavelet
Domain for Microarray Denoising," International Journal of Signal
Processing, Volume 2, Number 4, pp.273-284, 2005.
[51] M. Mastriani, and A. Giraldez, "Microarrays denoising via smoothing of
coefficients in wavelet domain," International Journal of Biomedical
Sciences, Volume 1, Number 1, pp.7-14, 2006.
[52] M. Mastriani, and A. Giraldez, "Kalman- Shrinkage for Wavelet-Based
Despeckling of SAR Images," International Journal of Intelligent
Systems and Technologies, Volume 1, Number 3, pp.190-196, 2006.
[53] M. Mastriani, and A. Giraldez, "Neural Shrinkage for Wavelet-Based
SAR Despeckling," International Journal of Systems and Technologies,
Volume 1, Number 3, pp.211-222, 2006.
[54] M. Mastriani, "Fuzzy Thresholding in Wavelet Domain for Speckle
Reduction in Synthetic Aperture Radar Images," International Journal of
Systems and Technologies, Volume 1, Number 3, pp.252-265, 2006.
[55] M. Mastriani, "New Wavelet-Based Superresolution Algorithm for
Speckle Reduction in SAR Images ," International Journal of Computer
Science, Volume 1, Number 4, pp.291-298, 2006.
[56] M. Mastriani, "Denoising and compression in wavelet domain via
projection onto approximation coefficients," International Journal of
Signal Processing, Volume 5, Number 1, pp.20-30, 2008.
[57] H. Samet, The Design and Analysis of Spatial Data Structures, Addison-
Wesley, 1990.
[58] H. Samet, Applications of Spatial Data Structures - Computer Graphics,
Image Processing and GIS, Addison-Wesley, 1990.
[59] A.K. Jain, Fundamentals of Digital Image Processing, Englewood
Cliffs, New Jersey, 1989.
[60] MATLAB® R2008a (Mathworks, Natick, MA).
[61] A. Sharma, and K.K. Paliwal, "Fast principal component analysis using
fixed-point algorithm", Pattern Recognition Letters, Vol.28, pp.1151-
1155, 2007.
[62] E. Oja, "A Simplified Neuron Model as a Principal Component
Analyzer", Journal of Mathematical Biology, Vol.15, pp.267-273, 1982.
[63] T.D. Sanger, "Optimal Unsupervised Learning in a Single-Layer Linear
Feedforward Neural Networks," Vol.2, pp.459-473, 1989.
@article{"International Journal of Information, Control and Computer Sciences:62775", author = "Mario Mastriani", title = "Union is Strength in Lossy Image Compression", abstract = "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.", keywords = "Haar's basis, Image compression, Karhunen-LoèveTransform, Morton's scan, row-rafter scan.", volume = "3", number = "11", pages = "2697-18", }
