Data smoothing using Gaussian scale-space and discrete wavelet transform

InECCE 2011 - International Conference on Electrical, Control and Computer Engineering

Volumn , Issue , 2011, Pages 344-348

  Karim, Samsul Ariffin Abdul ^a   Pang, Kong Voon ^b  

^a DEPARTMENT OF CHEMICAL ENGINEERING   (Malaysia)

^b SCHOOL OF PHYSICS   (Malaysia)

Author keywords

data smoothing; DWT; financial data; Gaussian function; Gaussian scale space

Indexed keywords

DATA SMOOTHING; DWT; FINANCIAL DATA; GAUSSIAN FUNCTIONS; GAUSSIANS;

DISCRETE WAVELET TRANSFORMS; ELECTROENCEPHALOGRAPHY; GAUSSIAN DISTRIBUTION;

METADATA;

EID: 80051639844     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/INECCE.2011.5953904     Document Type: Conference Paper

References (30)

1. Al Wadi, S., Ismail, M.T., and Karim, S.A.A. (2010). Volatility Computational in Financial Time Series Data Based on Wavelet Transforms. International Journal of Mathematics and Computation. Vol. 7 Number 10: 102-113.
2. Blanco, S., Kochen, S., Quiroga R.Q., Riquelme, L, Rosso, O. and Salgado, P. (1997). Characterization of Epileptic EEG Time Series (I): Gabor Transform and Nonlinear Dynamics Methods. In Wavelet Theory and Harmonic Analysis in Applied Sciences, D'Attellis, C.E. and Berdaguer-F, E.M. (eds.), Birkhauser-Boston, pp. 179-226.
3. Chui, C.K. 1992. An Introduction to wavelets. Academic Press, Boston, MA.
4. Daubechies, "Ten Lectures on Wavelets," CBMS-NSF Reg. Con. Ser. Appl. Math., Society for Industrial Applied Maths (SIAM), Philadelphia, PA, vol. 61, 1992.
5. Gao, X., S. L. Lee and Q. Sun. 2001. Stochastic multiscale operators and Appell sequences, Proc. Second International Congress of Chinese Mathematicians, Chang-Shou Lin, Lo Yang, Shing Tung Yau (eds.) , International Press, pp. 569-573.
6. Georgeson, M.A, May, K.A, Freeman, T.C & Hesse, G.S. 2007. From filters to features: Scale-space analysis of edge and blur coding in human vision. Journal of Vision 13(7): 1-21.
7. Goh, S.S, Goodman, T.N.T & Lee, S.L. 2007. Causality properties of refinable functions and sequences. Adv. Comput. Math. 26(1-3): 231-250.
8. Goh, S.S, Goodman, T.N.T & Lee, S.L. 2010. Scale-space Meets wavelets. Preprint.
9. Goodman, T.N.T & Lee, S.L. 2004. Asymptotic optimality in time-frequency localization of scaling functions and wavelets. In Frontiers in Interpolation and Approximation, 145-171. Chapman & Hall/CRC, Boca Raton, FL.
10. S. A. A. Karim, M. T. Ismail and B. A. Karim (2008). "Denoising non-stationary time series using Daubechies wavelets," Proceedings of Seminar Kebangsaan Matematik & Masyarakat (SKMM), UMT Terengganu 13-14 February 2008, Grand Continental Hotel, Kuala Terengganu (In CD), 2008.
11. S. A. A. Karim and M. T. Ismail. (2008). "Wavelet method in statistics," Proceedings of the Sixteenth National Symposium on Mathematical Sciences, 3-5 Jun 2008 at Hotel Renaissance, Kota Bharu, Malaysia, 2008.
12. S. A. A. Karim, B. A. Karim, M. T. Ismail, M. K. Hasan, and J. Sulaiman Applications of Wavelet Method in Stock Exchange Problem. Proceedings of International Conference on Fundamental and Applied Sciences (ICFAS 2010), 15-17 June 2010, Kuala Lumpur Convention Centre, 2010, 2010a.
13. th August 2010, Kuching, Sarawak, Malaysia Conference on Engineering and Technology Education. In CD, 2010b, pp. 321-326.
14. Karim, S.A.A and Kong, V.P. B-Spline Scale-Space in CAGD. In Proceedings of International Conference on Mathematical Sciences (ICMS2 2010), 30 November - 3 December 2010, PWTC Lumpur , 2010a, pp. 658-666.
15. Karim, S.A.A and Kong, V.P. Data Smoothing using Gaussian Scale-Space, 2010b. Preprint.
16. Lee, S.L. 2009. Approximation of Gaussian by Scaling Functions and Biorthogonal Scaling Polynomials. Bulletin of the Malaysian Mathematical Sciences Society (2) 32(3): 261-282.
17. Lee, S.L. 2010. B-Splines Scale-Space and Continuous Wavelet Transform (CWT). Presented at International Conference on Fundamental and Applied Sciences (ICFAS 2010), 15-17 June 2010, Kuala Lumpur Convention Centre, 2010.
18. Lin, Hsin-Chih, Wang, Ling-Ling and Yang, Shi-Nine, Automatic determination of the spread parameter in Gaussian smoothing, Pattern Recognition Letters 17: 1247-1252, 1996.
19. rd edition. San Diego: Academic Press.
20. Romeny, B. H. ter Haar. (Ed.), Geometry-driven diffusion in computer vision. Kluwer Dordrecht, the Netherlands, 1994.
21. Romeny, B. H. ter Haar. Front-End Vision and Multi-Scale Image Analysis, Multi-Scale Computer Vision Theory and Applications, written in Mathematica, Springer Sciences, 2003.
22. Wang, Y.P and Lee, S.L. 1998. Scale-spaced Derived from B-spline. IEEE Trans. On Pattern Analysis and Machine Intelligent 10(20): 1040-1055.
23. P. Thévenaz, T. Blu, M. Unser, "Interpolation Revisited," IEEE Transactions on Medical Imaging, vol. 19, no. 7, pp. 739-758, July 2000.
24. Unser, M., A. Aldroubi and M. Eden, "On the asymptotic convergence of B-spline wavelets to Gabor functions," IEEE Trans. Information Theory, vol. 38, no. 2, pp. 864-872, 1992.
25. Unser M., A. Aldroubi and M. Eden, "B-spline signal processing: Part I - theory," IEEE Trans. Signal Processing, vol. 41, no. 2, pp. 821-833, 1993a.
26. Unser, M., A. Aldroubi and M. Eden, "B-spline signal processing: Part II - efficient design and applications," IEEE Trans. Signal Processing, vol. 41, no. 2, pp. 834-848, 1993b.
27. Unser, M., A. Aldroubi and M. Eden, "A family of polynomial spline wavelet transforms," Signal Processing, vol. 30, no. 2, pp. 141-162, 1993c.
28. M. Unser, T. Blu, "Self-Similarity: Part I - Splines and Operators," IEEE Transactions on Signal Processing, vol. 55, no. 4, pp. 1352- 1363, April 2007.
29. M. Unser, "Sampling-50 Years After Shannon," Proceedings of the IEEE, vol. 88, no. 4, pp. 569-587, April 2000.
30. R.A. Young, "The Gaussian Derivative Model for Machine Vision:Visual Cortex Simulation," J. Optical Soc. Am., July 1987.