Abstract
Wavelets are widely used in numerous applied fields involving for example signal analysis, image compression or function approximation. The idea of adapting wavelet to specific problems, it means to create and use problem and data dependent wavelets, has been developed for various purposes. In this paper, we are interested in to define, starting from a given pattern, an efficient design of FIR adapted wavelets based on the lifting scheme. We apply the constructed wavelet for pattern detection in the 1D case. To do so, we propose a three stages detection procedure which is finally illustrated by spike detection in EEG.
Keywords
- Discrete Wavelet Transform
- Continuous Wavelet Transform
- Pattern Detection
- Lift Scheme
- Biorthogonal Wavelet
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Chapter PDF
References
Zhang, J.K., Davidson, T.N., Wong, K.M.: Efficient design of orthonormal wavelet bases for signal representation. IEEE Transactions on Signal Processing 52, 1983–1996 (2004)
Lucas, M.F., Hitti, E., Doncarli, C.: Optimisation d’ondelettes pour la classification. 18ième colloque GRETSI sur le traitement du Signal et des Images, Toulouse, France (2001)
Du, M., Chan, F.H.Y., Lam, F.K., Sun, J.: Crackle detection and classification based on matched wavelet analysis. In: Engineering in Medicine and Biology Society, Chicago, IL, USA. 19th Annual International Conference of the IEEE, vol. 4, pp. 1638–1641 (1997)
Brunelli, R., Poggio, T.: Template matching: Matched spatial filters and beyond. Pattern Recognition 30, 751–768 (1997)
Ozdamar, O., Kalayci, T.: Detection of spikes with artificial neural networks using raw EEG. Computers and Biomedical Research 31, 122–142 (1998)
Kalayci, T., Ozdamar, O.: Wavelet processing for automated neural network detection of EEG spikes. IEEE Med. Engng. Biol. 14, 160–166 (1995)
Mallat, S.: A wavelet tour of signal processing. Academic Press, London (1998)
Misiti, M., Misiti, Y., Oppenheim, G., Poggi, J.M.: Les ondelettes et leurs applications. Hermes (2003)
Chapa, J.O., Rao, R.M.: Algorithms for designing wavelets to match a specified signal. IEEE Transactions on Signal Processing 48, 3395–3406 (2000)
Fung, C.C., Shi, P.: Design of compactly supported wavelet to match singularities in medical images. Applications of Digital Image Processing XXV, 358–369 (2002)
Abry, P.: Ondelettes et turbulences. Diderot Editeur, Paris (1997)
Aldroubi, A., Unser, M.: Families of multiresolution and wavelet spaces with optimal properties. Numer. Funct. Anal. and Optimiz. 14, 417–446 (1993)
Abry, P., Aldroubi, A.: Designing multiresolution analysis-type wavelets and their fast alghorithm. The journal of Fourier Analysis and Applications 2, 135–159 (1995)
Sweldens, W.: The lifting scheme: A new philosophy in biorthogonal wavelet constructions. In: Laine, A., Unser, M. (eds.) Wavelet Applications in Signal and Image Processing III, Proc. SPIE, vol. 2569, pp. 68–79 (1995)
Sweldens, W.: The lifting scheme: A custom-design construction of biorthogonal wavelets. Appl. Comput. Harmon. Anal. 3, 186–200 (1996)
Sweldens, W.: The lifting scheme: A construction of second generation wavelets. SIAM J. Math. Anal. 29, 511–546 (1997)
Sweldens, W., Daubechies, I.: Factoring wavelets transform into lifting steps. J. Fourier Anal. Appl. 4, 247–269 (1998)
Strang, G., Nguyen, T.: Wavelets and Filters Banks. Wellesley-Cambridge Press (1996)
Daubechies, I.: Ten Lectures on Wavelets. 3rd. edn. CBMS-NSF (1994)
Wilson, S.B., Emerson, R.: Spike detection: a review and comparison of algorithms. Clinical Neurophysiology 113, 1873–1881 (2002)
Varsta, M., Heikkonen, J., Millan, J.R.: Epileptic activity detection in EEG with neural networks. Research Reports B3, Laboratory of Computational Engineering, Helsinki University of Technology (1998)
Gloor, P.: Contributions of electroencephalography and electrocorticography in the neurosurgical treatment of the epilepsies. Adv. Neurol. 8, 59–105 (1975)
Wilson, S.B., Turner, C.A., Emerson, R.G., Scheuer, M.L.: Spike detection. Clinical Neurophysiology 110, 404–411 (1999)
Scott, C., Nowak, R.: TEMPLAR: A wavelet based framework for pattern learning and analysis. IEEE Transactions on Signal Processing 52, 2264–2274 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mesa, H. (2005). Adapted Wavelets for Pattern Detection. In: Sanfeliu, A., Cortés, M.L. (eds) Progress in Pattern Recognition, Image Analysis and Applications. CIARP 2005. Lecture Notes in Computer Science, vol 3773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11578079_96
Download citation
DOI: https://doi.org/10.1007/11578079_96
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29850-2
Online ISBN: 978-3-540-32242-9
eBook Packages: Computer ScienceComputer Science (R0)
Publish with us
-
Published in cooperation with
http://www.iapr.org/
