Compactly supported tight and sibling frames with maximum vanishing moments

Applied and Computational Harmonic Analysis

Volumn 13, Issue 3, 2002, Pages 224-262

  Chui, Charles K ^a,c   He, Wenjie ^a   Stöckler, Joachim ^a,b  

^a UNIVERSITY OF MISSOURI ST LOUIS   (United States)

^b TU DORTMUND UNIVERSITY   (Germany)

^c STANFORD UNIVERSITY   (United States)

Author keywords

Inter orthogonality; Matrix factorization; Sibling frame; Tight frame; Unitary extension; Vanishing moment recovery

Indexed keywords

COMPUTER AIDED DESIGN; COMPUTER AIDED MANUFACTURING; FUNCTIONS; INTEGER PROGRAMMING; POLYNOMIALS; REDUNDANCY; WAVELET TRANSFORMS;

INTER-ORTHOGONALITY; MATRIX FACTROIZATION; SIBLING FRAME; TIGHT FRAME; UNITARY EXTENSION; VANISHING MOMENT RECOVERY (VMR);

HARMONIC ANALYSIS;

EID: 0242601591     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1063-5203(02)00510-9     Document Type: Article

References (35)

1. Aldroubi A. Portraits of frames. Proc. Amer. Math. Soc. 123:(6):1995;1661-1668.
2. Benedetto J.J., Li S. The theory of multiresolution analysis frames and applications to filter banks. Appl. Comput. Harmon. Anal. 5:(4):1998;389-427.
3. de Boor C., DeVore R., Ron A. On the construction of multivariate (pre)wavelets. Constr. Approx. 9:1993;123-166.
4. Chui C.K. An Introduction to Wavelets. 1992;Academic Press, Boston.
5. Chui C.K., De Villiers J.M. Spline-wavelets with arbitrary knots on a bounded interval: Orthogonal decomposition and computational algorithms. Comm. Appl. Anal. 2:(4):1998;457-486.
6. Chui C.K., He W. Compactly supported tight frames associated with refinable functions. Appl. Comput. Harmon. Anal. 8:2000;293-319.
7. Chui C.K., Shi X.L. Bessel sequences and affine frames. Appl. Comput. Harmon. Anal. 1:(1):1993;29-49.
8. Chui C.K., Smith P.W., Ward J.D. Cholesky factorization of positive definite biinfinite matrices. Numer. Funct. Anal. Optim. 5:(1):1982;1-20.
9. Cohen A., Daubechies I., Feauveau J.-C. Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math. 14:1992;485-560.
10. Cohen A., Daubechies I., Vial P. Wavelets on the interval and fast wavelet transforms. Appl. Comput. Harmon. Anal. 1:(1):1993;54-81.
11. Cohen A., Sun Q. An arithmetic characterization of the conjugate quadrature filters associated to orthonormal wavelet bases. SIAM J. Math. Anal. 24:(5):1993;1355-1360.
12. Daubechies I. Ten Lectures on Wavelets. CBMS-NSF Reg. Conf. Ser. Appl. Math. 61:1992;SIAM, Philadelphia.
13. I. Daubechies, B. Han, Pairs of dual wavelet frames from any two refinable functions, Preprint, 2000.
14. I. Daubechies, B. Han, A. Ron, Z.W. Shen, Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal., to appear.
15. Frazier M., Garrigós G., Wang K., Weiss G. A characterization of functions that generate wavelet and related expansion. Proceedings of the conference dedicated to Professor Miguel de Guzmán (El Escorial, 1996). J. Fourier Anal. Appl. 3:1997;883-906.
16. Gantmacher F.R. The Theory of Matrices, Vol. 2. 1959;Chelsea, New York.
17. Gundy R.F. Low-pass filters, martingales, and multiresolution analyses. Appl. Comput. Harmon. Anal. 9:(2):2000;204-219.
18. Han B. On dual wavelet tight frames. Appl. Comput. Harmon. Anal. 4:(4):1997;380-413.
19. Hernández E., Weiss G. A First Course on Wavelets. 1996;CRC Press, Boca Raton.
20. Kingsbury N.G. The dual-tree complex wavelet transform: A new technique for shift invariance and directional filters. IEEE Digital Signal Processing Workshop, DSP'98. 1998;Bryce Canyon. paper 86.
21. Kingsbury N.G. Complex wavelets for shift invariant analysis and filtering of signals. Appl. Comput. Harmon. Anal. 10:(3):2001;234-253.
22. Lawton W. Necessary and sufficient conditions for constructing orthonormal wavelet bases. J. Math. Phys. 32:(1):1991;57-61.
23. Lawton W., Lee S.L., Shen Z.W. Stability and orthonormality of multivariate refinable functions. SIAM J. Math. Anal. 28:(4):1997;999-1014.
24. Lawton W., Micchelli C.A. Construction of conjugate quadrature filters with specified zeros. Numer. Algorithms. 14:1997;383-399.
25. van der Mee C.V.M., Rodriguez G., Seatzu S. Spectral factorization of biinfinite block Toeplitz matrices with applications. Trigiante D. Recent Trends in Numerical Analysis. 2001;Nova Science Publishers, Hauppage, New York.
26. Piegl L., Tiller W. The NURBS Book. 2nd Edn. 1997;Springer, Berlin/Heidelberg.
27. Rheinboldt W.C., Vandergraft J.S. A simple approach to the Perron-Frobenius theory for positive operators on general partially-ordered finite-dimensional linear spaces. Math. Comp. 27:1973;139-145.
28. Riesz F., Sz.-Nagy B. Functional Analysis. Frederick Ungar. 1955;New York. Dover Publ., New York, 1990.
29. d): The analysis of the analysis operator. J. Funct. Anal. 148:(2):1997;408-447.
30. d): II. Dual systems. J. Fourier Anal. Appl. 3:1997;617-637.
31. d). Math. Comp. 67:1998;191-207.
32. Rosenblatt M. A multidimensional prediction problem. Ark. Mat. 3:1958;407-424.
33. Rosenblum M., Rovnyak J. Hardy Classes and Operator Theory. 1985;Oxford University Press, New York.
34. Stollnitz E.J., DeRose T.D., Salesin D.H. Wavelets for Computer Graphics: Theory and Applications. 1996;Morgan Kaufmann, San Francisco.
35. Vandergraft J.S. Spectral properties of matrices which have invariant cones. SIAM J. Appl. Math. 16:1968;1208-1222.