Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30685
Denoising and Compression in Wavelet Domainvia Projection on to Approximation Coefficients

Authors: Mario Mastriani

Abstract:

We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only the approximation subband coefficients and three scalars are stored and/or transmitted to the channel. Besides, with the elimination of the details subbands coefficients, we obtain a bigger compression rate. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain.

Keywords: Compression, Wavelets, projections, denoising

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081477

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1309

References:


[1] D. L. Donoho, "De-noising by soft-thresholding," IEEE Trans. Inform. Theory, vol. 41, no. 3, pp. 613-627, 1995.
[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] X.-P. Zhang, and M. Desai, "Nonlinear adaptive noise suppression based on wavelet transform," Proceedings of the ICASSP98, vol. 3, pp. 1589- 1592, Seattle, 1998.
[9] X.-P. Zhang, "Thresholding Neural Network for Adaptive Noise reduction," IEEE Transactions on Neural Networks, vol.12, no. 3, pp.567-584, 2001.
[10] X.-P. Zhang, and M. Desai, "Adaptive Denoising Based On SURE Risk," IEEE Signal Proc. Letters, vol.5, no. 10, 1998.
[11] X.-P. Zhang and Z.Q. Luo, "A new time-scale adaptive denoising method based on wavelet shrinkage," in Proceedings of the ICASSP99, Phoenix, AZ., March 15-19, 1999.
[12] M. Lang, H. Guo, J. Odegard, C. Burrus, and R. Wells, "Noise reduction using an undecimated discrete wavelet transform," IEEE Signal Proc. Letters, vol. 3, no. 1, pp. 10-12, 1996.
[13] H. Chipman, E. Kolaczyk, and R. McCulloch, "Adaptive Bayesian wavelet shrinkage," J. Amer. Statist. Assoc., vol. 92, pp. 1413-1421, 1997.
[14] S. G. Chang, B. Yu, and M. Vetterli, "Spatially adaptive wavelet thresholding with context modeling for image denoising," IEEE Trans. Image Processing, vol. 9, pp. 1522-1531, Sept. 2000.
[15] 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.
[16] S. G. Chang and M. Vetterli, "Spatial adaptive wavelet thresholding for image denoising," in Proc. ICIP, vol. 1, 1997, pp. 374-377.
[17] M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, "Wavelet-based statistical signal processing using hidden Markov models," IEEE Trans.Signal Processing, vol. 46, pp. 886-902, Apr. 1998.
[18] M. Malfait and D. Roose, "Wavelet-based image denoising using a Markov random field a priori model," IEEE Trans. Image Processing, vol. 6, pp. 549-565, Apr. 1997.
[19] M. K. Mihcak, I. Kozintsev, K. Ramchandran, and P. Moulin, "Low complexity image denoising based on statistical modeling of wavelet coefficients," IEEE Trans. Signal Processing Lett., vol. 6, pp. 300-303, Dec. 1999.
[20] E. P. Simoncelli, "Bayesian denoising of visual images in the wavelet domain," in Bayesian Inference in Wavelet Based Models. New York: Springer-Verlag, 1999, pp. 291-308.
[21] E. Simoncelli and E. Adelson, "Noise removal via Bayesian wavelet coring," in Proc. ICIP, vol. 1, 1996, pp. 379-382.
[22] M. Belge, M. E. Kilmer, and E. L. Miller, "Wavelet domain image restoration with adaptive edge-preserving regularization," IEEE Trans. Image Processing, vol. 9, pp. 597-608, Apr. 2000.
[23] J. Liu and P. Moulin, "Information-theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients," IEEE Trans. Image Processing, vol. 10, pp. 1647-1658, Nov. 2000.
[24] H. Guo, J. E. Odegard, M. Lang, R. A. Gopinath, I. Selesnick, and C. S. Burrus, "Speckle reduction via wavelet shrinkage with application to SAR based ATD/R," Technical Report CML TR94-02, CML, Rice University, Houston, 1994.
[25] R.R. Coifman, and D.L. Donoho, Translation-invariant de-noising. A. Antoniadis & G. Oppenheim (eds), Lecture Notes in Statistics, vol. 103. Springer-Verlag, pp 125-150, 1995.
[26] M. Misiti, Y. Misiti, G. Oppenheim, and J.M. Poggi. (2001, June). Wavelet Toolbox, for use with MATLABĀ®, User-s guide, version 2.1. (Online). Available: http://www.rrz.unihamburg. de/RRZ/Software/Matlab/Dokumentation/help/pdf_doc/wavele t/wavelet_ug.pdf
[27] C.S. Burrus, R.A. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms: A Primer, Prentice Hall, New Jersey, 1998.
[28] B.B. Hubbard, The World According to Wavelets: The Story of a Mathematical Technique in the Making, A. K. Peter Wellesley, Massachusetts, 1996.
[29] 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.
[30] C. Valens. (2004). A really friendly guide to wavelets. (Online). Available: http://perso.wanadoo.fr/polyvalens/ clemens/wavelets/wavelets.html
[31] G. Kaiser, A Friendly Guide To Wavelets, Boston: Birkhauser, 1994.
[32] J.S. Walker, A Primer on Wavelets and their Scientific Applications, Chapman & Hall/CRC, New York, 1999.
[33] E. J. Stollnitz, T. D. DeRose, and D. H. Salesin, Wavelets for Computer Graphics: Theory and Applications, Morgan Kaufmann Publishers, San Francisco, 1996.
[34] J. Shen and G. Strang, "The zeros of the Daubechies polynomials," in Proc. American Mathematical Society, 1996.
[35] R. Yu, A.R. Allen, and J. Watson, An optimal wavelet thresholding for speckle noise reduction, in Summer School on Wavelets: Papers, Publisher: Silesian Technical University (Gliwice, Poland), pp77-81, 1996.
[36] H.Y. Gao, and A.G. Bruce, "WaveShrink with firm shrinkage," Statistica Sinica, 7, 855-874, 1997.
[37] L. Gagnon, and F.D. Smaili, "Speckle noise reduction of air-borne SAR images with Symmetric Daubechies Wavelets," in SPIE Proc. #2759, pp. 1424, 1996.
[38] M.S. Crouse, R. Nowak, and R. Baraniuk, "Wavelet-based statistical signal processing using hidden Markov models," IEEE Trans. Signal Processing, vol 46, no.4, pp.886-902, 1998.
[39] M. Mastriani y 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. (Online). Available: http://www.icgst.com/gvip/v6/P1150517003.pdf
[40] M. Mastriani y A. Giraldez, "Despeckling of SAR images in wavelet domain," GIS Development Magazine, Sept. 2005, Vol. 9, Issue 9, pp.38-40. (Online). Available: http://www.gisdevelopment.net/magazine/years/2005/sep/wavelet_1.htm
[41] M. Mastriani y A. Giraldez, "Microarrays denoising via smoothing of coefficients in wavelet domain," WSEAS Transactions on Biology and Biomedicine, 2005. (Online). Available: http://www.wseas.org/online
[42] M. Mastriani y 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. (Online). Available: http://www.icgst.com/aiml/v3/index.html
[43] 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. (Online). Available: http://www.icgst.com/aiml/v3/index.html
[44] M. Mastriani, "Systholic Boolean Orthonormalizer Network in Wavelet Domain for Microarray Denoising," ICGST International Journal on Bioinformatics and Medical Engineering, Volume 5, 2005. (Online). Available: http://www.icgst.com/bime/v1/bimev1.html
[45] 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. (Online). Available: http://www.waset.org/ijsp/v2/v2-4-33.pdf
[46] 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. (Online). Available: http://www.waset.org/ijsp/v2/v2-4-40.pdf
[47] M. Mastriani y A. Giraldez, "Microarrays denoising via smoothing of coefficients in wavelet domain," International Journal of Biomedical Sciences, Volume 1, Number 1, pp.7-14, 2006. (Online). Available: http://www.waset.org/ijbs/v1/v1-1-2.pdf
[48] M. Mastriani y A. Giraldez, "Kalman- Shrinkage for Wavelet-Based Despeckling of SAR Images," International Journal of Intelligent Technology, Volume 1, Number 3, pp.190-196, 2006. (Online). Available: http://www.waset.org/jit/v1/v1-3-21.pdf
[49] M. Mastriani y A. Giraldez, "Neural Shrinkage for Wavelet-Based SAR Despeckling," International Journal of Intelligent Technology, Volume 1, Number 3, pp.211-222, 2006. (Online). Available: http://www.waset.org/jit/v1/v1-3-24.pdf
[50] M. Mastriani, "Fuzzy Thresholding in Wavelet Domain for Speckle Reduction in Synthetic Aperture Radar Images," International Journal of Intelligent Technology, Volume 1, Number 3, pp.252-265, 2006. (Online). Available: http://www.waset.org/jit/v1/v1-3-30.pdf
[51] 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. (Online). Available: http://www.waset.org/ijcs/v1/v1-4-39.pdf
[52] S. Haykin. Adaptive Filter Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1986.
[53] Leon S. J., Linear Algebra with Applications, MacMillan, 1990, New York.
[54] A.K. Jain, Fundamentals of Digital Image Processing, Englewood Cliffs, New Jersey, 1989.