38
Views
2
CrossRef citations to date
0
Altmetric
Chapter 10

Wavelets

Pages 209-224 | Published online: 05 Jun 2011

References

  • Bakshi , B. B. and Stepnanopolous , G. Wavelets as basis functions for localised learning in a multi-resolution hierarchy . Proceedings of 2nd IJCNN Neural Network Conference . Baltimore , MD . pp. 140 – 145 .
  • Besag , J. E. 1986 . On the statistical analysis of dirty pictures . Journal of the Royal Statistical Society, Series B , 48 : 259 – 302 . with discussion
  • Cheng , B. and Kay , J. W. 1992a . “ Multiresolution reconstruction of a corrupted image using the wavelet transform ” . In Computational Statistics , Edited by: WHITTAKER , J. and DODGE , Y. Vol. 2 , 293 – 298 . Heidelberg : Physics .
  • CHENG, B. & KAY, J. W. (1992b) Multiresolution image reconstruction using the wavelet transform, submitted for publication.
  • Chui , C. K. 1992 . An Introduction to Wavelets , New York : Academic Press) .
  • Daubechies , I. 1988 . Orthonormal bases of compactly supported wavelets . Communications in Pure and Applied Mathematics , 41 : 909 – 996 .
  • Daubechies , I. 1992 . Ten lectures on wavelets , CBMS : SIAM publication) .
  • Devore , R. A. , Jawerth , B. and LUCIER , B. J. 1992 . Image compression through wavelet transform coding . IEEE Transactions on Information Theory , 38 : 719 – 746 .
  • Donoho , D. L. and Johnstone , I. M. 1990 . “ Wavelets and optimal nonlinear function estimates ” . In Technical Report 281 , CA : Department of Statistics, University of Stanford .
  • Donoho , D. L. and Johnstone , I. M. 1993 . Journal of Applied Statistics , in press
  • Dym , H. and Mckean , H. P. 1972 . Fourier Series and Integrals , New York : Academic Press) .
  • Geman , S. and Geman , D. 1984 . Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images . IEEE Transactions on Pattern Analysis and Machine Intelligence , 6 : 721 – 741 .
  • Geman , D. and Reynolds , G. 1992 . Constrained restoration and the recovery of discontinuities . IEEE Transactions on Pattern Analysis and Machine Intelligence , 14 : 367 – 383 .
  • Graybill , F. A. 1986 . Introduction to Matrices with Applications in Statistics , 2nd , Belmont , CA : Wadsworth .
  • Green , P. J. 1990 . On the use of the EM algorithm for penalised likelihood estimation . Journal of the Royal Statistical Society, Series B , 52 : 443 – 452 .
  • Healy , D. M. and Weaver , J. B. 1992 . Two applications of wavelet transforms in magnetic resonance imaging . IEEE Transactions on Information Theory , 38 : 840 – 860 .
  • Hitchcock , D. and Kay , J. W. On the use of the wavelet transform for multiresolution reconstruction of images degraded by blur and Poisson noise . Proceedings of the 8th International Scandinavian Conference on Image Analysis .
  • Jubb , M. and Jennison , C. 1991 . “ Aggregation and refinement in binary image restoration ” . In Lecture Notes-Monograph Series , Edited by: POSSOLO , A. Hayward , CA : Institute of Mathematical Statistics .
  • Kovacevic , J. and Vetterli , M. 1992 . Non-separable multi-dimensional perfect reconstruction filter banks and wavelet bases for R . IEEE Transactions on Information Theory , 38
  • Mallat , S. 1989a . Multiresolution approximation and wavelet orthonormal bases of L2 (R) . Transactions of the American Mathematical Society , 315 : 69 – 87 .
  • Mallat , S. 1989b . A theory for multiresolution signal decomposition: the wavelet representation . IEEE Transactions on Pattern Analysis and Machine Intelligence , 11 : 674 – 693 .
  • Mallat , S. 1991 . Zero-crossings of a wavelet transform . IEEE Transactions on Information Theory , 37 : 1019 – 1033 .
  • Mallat , S. and Hwang , W. L. 1992 . Singularity detection and processing with wavelets . IEEE Transactions on Information Theory , 38 : 617 – 643 .
  • Meyer , Y. 1990 . Ondelettes , Paris : Hermann) .
  • Nason , G. P. 1993 . “ The discrete wavelet transform in S ” . In Technical Report , University of Bath . The software is available via anonymous ftp from gdr.bath.ac.uk in directory /pub/masgpn
  • Rioul , O. and Vetterli , M. 1991 . Wavelets and signal processing . IEEE SP Magazine , October : 14 – 36 .
  • Strang , G. 1989 . Wavelets and dilatation equations . SIAM Review , 31 : 614 – 627 .
  • SZU, H. (1992) Neural network wavelet transforms, Tutorial No.10,2nd IJCNN, Baltimore, MD.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.