A construction of multiwavelets

Computers and Mathematics with Applications

Volumn 32, Issue 3, 1996, Pages 23-37

  Ashino, R ^a   Nagase, M ^b   Vaillancourt, R ^c  

^a Dept of Information Processing Engineering College of Industrial Technology 1 27 1 Nishikoya   (Japan)

^b OSAKA UNIVERSITY   (Japan)

^c UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Multiwavelets; Multiwavelets of split type; Regular multiresolution; Split wavelets; Vanishing moments

Indexed keywords

BINARY SEQUENCES; BIT ERROR RATE; FUNCTIONS; IMAGE ANALYSIS; OSCILLATIONS; PATTERN RECOGNITION; SIGNAL PROCESSING; VECTORS;

MULTIWAVELETS; MULTIWAVELETS OF SPLIT TYPE; REGULAR MULTIRESOLUTION; SPLIT WAVELETS; TWO VECTOR SEQUENCE OF BITS; VANISHING MOMENTS;

WAVELET TRANSFORMS;

EID: 0030215127     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/0898-1221(96)00111-3     Document Type: Article

References (20)

1. Y. Meyer, Wavelets and operators, In Cambridge Studies in Advanced Mathematics, Vol. 37, Cambridge University Press, Cambridge, (1992).
2. 2 for the sparse representation of integral operators, SIAM J. Math. Anal. 26, 246-262, (1993).
3. J. Geronimo, D. Hardin, and P.R. Massopust, Fractal functions and wavelet expansions based on several scaling functions, J. Approx. Theory 78, 373-401, (1994).
4. G. Donavan, J. Geronimo, D. Hardin and P.R. Massopust, Construction of orthogonal wavelet using fractal interpolation functions, SIAM J. Math. Anal., (1996) (to appear).
5. G. Strang and V. Strela, Short wavelets and matrix dilation equations, IEEE Trans. on Signal Processing 45, 108-115, (1995).
6. G. Strang and V. Strela, Orthogonal multiwavelets with vanishing moments, J. Optical Engineering 33, 2104-2107, (1994).
7. R. Ashino and M. Kametani, A lemma on matrices and the construction of multi-wavelets, Math. Japan. (to appear).
8. R.Q. Jia and Z. Shen, Multiresolution and wavelets, Proc. Edinburgh Math. Soc. 37, 271-300, (1994).
9. W. Lawton, Applications of complex valued wavelet transforms to subband decomposition, IEEE Trans. on Signal Processing 41 (12), 3566-3568, (1993).
10. T. Cooklev, Regular perfect-reconstruction filter banks and wavelet bases, Ph.D. Thesis, Tokyo Institute of Technology, Tokyo, (1995).
11. T. Cooklev, M. Kato, A. Nishihara and M. Sablatash, Multifilter banks and multiwavelet bases, Technical Report of IEICE (The Institute of Electronics, Information and Communication Engineers) Tokyo, Japan I E95-22, 51-58, (1995).
12. G. Plonka, Factorization of refinement masks of function vectors, In Approximation Theory VIII, (Edited by C.K. Chui and L.L. Schumaker), World Scientific, Singapore, River Edge, NJ, (1995).
13. A. Cohen, I. Daubechies and G. Plonka, Regularity of refinable function vectors, preprint, Rostock University, (1996).
14. G. Plonka and V. Strela, Construction of multi-scaling functions with approximation and symmetry, preprint, Rostock University, (1995).
15. Z. Shen, Refinable function vectors, preprint, National University of Singapore, (1996).
16. V. Strela, Multiwavelets: Regularity, orthogonality and symmetry via two-scale similarity transform, Studies in Appl. Math., (1996) (to appear).
17. I. Daubechies, Ten lectures on wavelets, In CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 61, SIAM, Philadelphia, (1992).
18. G. Strang and T. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA, (1996).
19. n), Computers Math. Applic. 29 (12), 13-25, (1995).
20. R. Ashino, M. Nagase and R. Vaillancourt, A computer search for simple multi-dimensional wavelets, Computers Math. Applic. 28 (5), 57-69, (1994).