Matching pursuit by undecimated discrete wavelet transform for non-stationary time series of arbitrary length

Statistics and Computing

Volumn 8, Issue 3, 1998, Pages 205-219

  Walden, A T ^a   Contreras Cristan, A ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Discrete wavelet transform; Matching pursuit; Undecimated discrete wavelet transform

Indexed keywords

EID: 0043226672     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008901226235     Document Type: Article

References (12)

1. Coifman, R. R. and Donoho, D. L. (1995) Translation-invariant de-noising. In Wavelets and Statistics, Antoniadis, A. and Oppenheim, G. (eds). Lecture Notes in Statistics, Vol. 103. Springer-Verlag, New York, pp. 125-50.
2. Davis, G., Mallat, S. G. and Zhang, Z. (1994) Adaptive time-frequency approximations with matching pursuits. In Wavelets: Theory, Algorithms, and Applications, Chui, C.K., Montefusco, L. and Puccio, L. (eds.) Academic Press, San Diego, pp. 271-93.
3. Daubechies, I. (1992) Ten Lectures on Wavelets. SIAM, Philadelphia.
4. Eslava, G. and Marriott, F. H. C. (1994) Some criteria for projection pursuit. Statistics and Computing, 4, 13-20.
5. Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans, on Pattern Analysis and Machine Intelligence 11, 674-93.
6. Mallat, S. G. and Zhang, Z. (1993) Matching pursuits with time-frequency dictionaries. IEEE Trans, on Signal Processing 41, 3397-415.
7. Nason, G. and Silverman, B. W. (1995) The stationary wavelet transform and some statistical applications. In Wavelets and Statistics, Antoniadis, A. and Oppenheim, G. (eds.) Lecture Notes in Statistics, Vol. 103. Springer-Verlag, New York, pp. 281-99.
8. Percival, D. B. and Guttorp, P. (1994) Long-memory processes, the Allan variance and wavelets. In Wavelets in Geophysics, Foufoula-Georgiou, E. and Kumar, P. (eds.) Academic Press, San Diego, pp. 325-44.
9. Percival, D. B. and Mofjeld, H. (1997) Analysis of subtidal coastal sea level fluctuations using wavelets. Journal of the American Statistical Association, 92, 868-80.
10. Rioul, O. and Duhamel, P. (1992) Fast algorithms for discrete and continuous wavelet transforms. IEEE Transactions on Information Theory, 38, 569-86.
11. Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge, UK.
12. Shensa, M. J. (1992) The discrete wavelet transform: wedding the à trous and Mallat algorithms. IEEE Transactions on Signal Processing 40, 2464-82.