Construction of arbitrary dimensional biorthogonal multiwavelet using lifting scheme

IEEE Transactions on Image Processing

Volumn 18, Issue 5, 2009, Pages 942-955

  Gao, Xieping ^a   Xiao, Fen ^a   Li, Bodong ^a  

^a XIANGTAN UNIVERSITY   (China)

Author keywords

Hermite interpolation filter; Hermite Neville filter; Lifting scheme; Multidimensional biorthogonal multiwavelet

Indexed keywords

DESIGN FRAMEWORKS; FAST TRANSFORMS; HERMITE INTERPOLATION FILTER; HERMITE-NEVILLE FILTER; IN-PLACE COMPUTATIONS; INTEGER-TO-INTEGER TRANSFORMS; LIFTING SCHEME; LIFTING STRUCTURES; MULTIDIMENSIONAL BIORTHOGONAL MULTIWAVELET; MULTIFILTER BANKS; PERFECT RECONSTRUCTION; SHORT SUPPORTS; VANISHING MOMENTS;

FILTER BANKS; MATHEMATICAL TRANSFORMATIONS; SIGNAL FILTERING AND PREDICTION;

INTERPOLATION;

EID: 65149100001     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2009.2017325     Document Type: Article

References (18)

1. A. Z. Averbuch and V. A. Zheludev, "Lifting scheme for biorthogonal multiwavelets originated from Hermite splines," IEEE Trans. Signal Process., vol. 50, pp. 487-500, 2002.
2. T. P.-Y. Yu, "On the regularity analysis of interpolatory Hermite subdivision schemes," J. Math. Anal. Appl., vol. 302, pp. 201-216, 2005.
3. B. Han, T. P.-Y. Yu, and B. Piper, "Multivariate refinable Hermite interpolants," Math. Comput., vol. 73, pp. 1913-1935, 2004.
4. R. F. Warming and R. M. Beam, "Discrete multiresolution analysis using hermite interpolation: Biorthogonal multiwavelets," SIAM J. Sci. Comput., vol. 22, pp. 1269-1317, 2000.
5. B. Han, "Hermite interpolants and biorthogonal multiwavelets with arbitrary order of vanishing moments," Proc. SPIE, vol. 3813, pp. 147-161, 1999.
6. J. Derado, "Nonseparable, compactly supported interpolating refinable functions with arbitrary smoothness," Appl. Comput. Harmon. Anal. vol. 10, pp. 113-138, 2001.
7. B. Han, "Approximation properties and construction of Hermite interpolants and biorthogonal multiwavelets," J. Approx. Theory, vol. 110, pp. 18-53, 2001.
8. W. Sweldens, "The lifting scheme: A custom-design construction of biorthogonal wavelets," Appl. Comput. Harmon. Anal., vol. 3, pp. 186-200, 1996.
9. S. S. Goh, Q. Jiang, and T. Xia, "Construction of biorthogonal multiwavelets using the lifting scheme," Appl. Comput. Harmon. Anal. vol. 9, pp. 336-352, 2000.
10. H. Olkkonen and J. T. O. P. Pesola, "Efficient lifting wavelet transform for microprocessor and VLSI applications," IEEE Signal Process. Lett., vol. 12, pp. 120-122, 2005.
11. J. T. Olkkonen and H. Olkkonen, "Discrete lattice wavelet transform," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 54, pp. 71-75, 2007.
12. J. Kovacevic and W. Sweldens, "Wavelets families of increasing order in arbitrary dimensions," IEEE Trans. Image Process., vol. 9, pp. 480-496, 2000.
13. C. d. Boor and A. Ron, "On multivariate polynomial interpolation," Constructive Approx., vol. 6, pp. 287-302, 1990.
14. T. Laakso, V. Valimaki, M. Karjalainen, and U. K. Laine, "Splitting the unit delay: Tools for fractional delay filter design," IEEE Signal Process. Mag., vol. 13, pp. 30-80, 1996.
15. J. T. Olkkonen and H. Olkkonen, "Fractional time-shift B-spline filter," IEEE Signal Process. Lett., vol. 14, pp. 688-691, 2007.
16. R. Claypoole, G. Davis, W. Sweldens, and R. Baraniuk, "Nonlinear wavelet transforms for image coding via lifting," IEEE Trans. Image Process., vol. 12, pp. 1449-1459, 2003.
17. G. Piella, B. Pesquet-Popescu, and H. J. A. M. Heijmans, "Gradient-driven update lifting for adaptive wavelets," Signal Process.: Image Commun., vol. 20, pp. 813-831, 2005.
18. P. J. Oonincx and P. M. d. Zeeuw, "Adaptive lifting for shape-based image retrieval," Pattern Recognit., vol. 36, pp. 2663-2672, 2003.