4-Tap Wavelet Filters Using Algebraic Integers

  IJETT-book-cover  International Journal of Engineering Trends and Technology (IJETT)          
© 2015 by IJETT Journal
Volume-25 Number-2
Year of Publication : 2015
Authors : Sravya.K, V.Santhosh Kumar
DOI :  10.14445/22315381/IJETT-V25P215


Sravya.K, V.Santhosh Kumar"4-Tap Wavelet Filters Using Algebraic Integers", International Journal of Engineering Trends and Technology (IJETT), V25(2),82-88 July 2015. ISSN:2231-5381. www.ijettjournal.org. published by seventh sense research group

An Image is often corrupted by noise in its acquisition or transmission. The goal of denoising is to remove the noise while retaining as much as possible the important signal features. Traditionally, this is achieved by linear processing such as Wiener filtering. A vast literature has emerged recently on signal denoising using nonlinear techniques, in the setting of additive white Gaussian noise. The seminal work on signal denoising via wavelet thresholding have shown that various wavelet thresholding schemes for denoising have near-optimal properties in the minimax sense and perform well in simulation studies of one-dimensional curve estimation. It has been shown to have better rates of convergence than linear methods for approximating functions. Thresholding is a nonlinear technique, yet it is very simple because it operates on one wavelet coefficient at a time. Alternative approaches to nonlinear wavelet-based denoising can be found in, for example and references therein.


1. K. A. Wahid, V. S. Dimitrov, and G. A. Jullien, “Errorfree arithmetic for discrete wavelet transforms using algebraic integers,” in Proc. 16th IEEE Symp. Computer Arithmetic, 2003, pp. 238–244.
2. S.-C. B. Lo, H. Li, and M. T. Freedman, “Optimization of wavelet decomposition for image compression and feature preservation,” IEEE Trans. Med. Imag., vol. 22, no. 9, pp. 1141–1151, Sep. 2003.
3. M. Martone, “Multiresolution sequence detection in rapidly fading channels based on focused wavelet decompositions,” IEEE Trans. Commun., vol. 49, no. 8, pp. 1388–1401, 2001.
4. P. P. Vaidyanathan,Multirate Systems and Filter Basnks. Englewood Cliffs, NJ: PTR Prentice Hall, 1992, 07632.
5. D. B. H. Tay, “Balanced spatial and frequency localised 2-D nonseparable wavelet filters,” in Proc. IEEE Int. Symp. Circuits Systems ISCAS 2001, 2001, vol. 2, pp. 489–492.
6. M. A. Islam and K. A. Wahid, “Area- and powerefficient design of Daubechies wavelet transforms using folded AIQ mapping,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 57, no. 9, pp. 716–720, Sep. 2010.
7. F. Marino, D. Guevorkian, and J. T. Astola, “Highly efficient high-speed/low-power architectures for the 1-D discrete wavelet transform,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 47, no. 12, pp. 1492–1502, Dec. 2000.
8. K. A.Wahid, V. S. Dimitrov,G. A. Jullien, andW. Badawy, “Error-free computation of Daubechies wavelets for image compression applications,” Electron. Lett., vol. 39, no. 5, pp. 428–429, 2003.
9. T. Acharya and P.-Y. Chen, “Vlsi implementation of a dwt architecture,” in Proc. IEEE Int. Symp. Circuits Syst. ISCAS’98, 1998, vol. 2, pp. 272–275.
10. S. Gnavi, B. Penna, M. Grangetto, E. Magli, and G. Olmo, “DSP performance comparison between lifting and filter banks for image coding,” in Proc. IEEE Int. Acoustics, Speech, Signal Processing (ICASSP) Conf., 2002, vol. 3.
11. A. M. M. Maamoun, M. Neggazi, and D. Berkani, “VLSI design of 2-D disceret wavelet transform for area efficient and high-speed image computing,”World Acad. Science, Eng. Technol., vol. 45, pp. 538–543, 2008.
12. I. Urriza, J. I. Artigas, J. I. Garcia, L. A. Barragan, and D. Navarro, “VLSI architecture for lossless compression of medical images using the discrete wavelet transform,” in Proc. Design, Automat. Test Eur., 1998, pp. 196–201.
13. R. Baghaie and V. Dimitrov, “Computing Haar transform using algebraic integers,” in Proc. Conf. Signals, Systems Computers Record 34th Asilomar Conf., 2000, vol. 1, pp. 438–442.
14. K. A. Wahid, M. A. Islam, and S.-B. Ko, “Lossless implementation of Daubechies 8-tap wavelet transform,” in Proc. IEEE Int. Symp. Circ. Syst., Rio de Janeiro, Brazil, May 2011, pp. 2157–2160.

Wavelet, Filter, 4 tap