Smooth Wavelet Tight Frames with Zero Moments

Applied and Computational Harmonic Analysis

Volumn 10, Issue 2, 2001, Pages 163-181

  Selesnick, Ivan W ^a  

^a POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Overcomplete signal expansions; wavelets; frames

Indexed keywords

EID: 0035276530     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.2000.0332     Document Type: Editorial

References (39)

1. Benedetto J. J., Li S. The theory of multiresolution an analysis frames and applications to filter banks. Appl. Comput. Harmon. Anal. 5:1998;389-427.
2. Benno S. A., Moura J. M. F. Scaling functions robust to translations. IEEE Trans. Signal Process. 46:1998;3269-3281.
3. K. Berkner, and, R. O. Wells, Jr, A correlation-dependent model for denoising via nonorthogonal wavelet transforms, Technical Report CML TR98-07, Computational Mathematics Laboratory, Rice University, 1998.
4. Bölcskei H., Hlawatsch F., Feichtinger H. G. Frame-theoretic analysis of oversampled filter banks. IEEE Trans. Signal Process. 46:1998;3256-3268.
5. Burrus C. S., Gopinath R. A., Guo H. Introduction to Wavelets and Wavelet Transforms. 1997;Prentice Hall, Englewood Cliffs.
6. Burt P. J., Adelson E. H. The Laplacian pyramid as a compact image code. IEEE Trans. Comm. 31:1983;532-540.
7. Chui C., He W. Compactly supported tight frames associated with refinable functions. Appl. Comput. Harmon. Anal. 8:2000;293-319.
8. Chui C. K., Shi X., Stöckler J. Affine frames, quasi-affine frames, and their duals. Adv. Comp. Math. 8:1998;1-17.
9. Coifman R. R., Donoho D. L. Translation-invariant de-noising. Antoniadis A. Wavelets and Statistics. Springer-Verlag Lecture Notes. 1995;Springer-Verlag, Berlin.
10. Cox D., Little J., OrShea D. Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. 1991;Springer-Verlag, Berlin.
11. Cvetkovic̀ Z., Vetterli M. Oversampled filter banks. IEEE Trans. Signal Process. 46:1998;1245-1255.
12. Daubechies I. Ten Lectures on Wavelets. 1992;SIAM, Philadelphia.
13. Faugère J.-C., de Saint-Martin F. M., Rouillier F. Design of regular nonseparable bidimensional wavelets using Gröbner basis techniques. IEEE Trans. Signal Process. 46:1998;845-856.
14. Freeman W. T., Adelson E. H. The design and use of steerable filters. IEEE Trans. Pattern Anal. Mach. Intell. 13:1991;891-906.
15. N : Analysis, synthesis and algorithms. IEEE Trans. Inform. Theory. 44:1998;16-31.
16. G.-M. Greuel, G. Pfister, and, H. Schönemann, Singular reference manual, in, Reports on Computer Algebra, number, 12, Centre for Computer Algebra, University of Kaiserslautern, May 1997. Available at, http://www.singular.uni-kl.de/ .
17. Hermann O. On the approximation problem in nonrecursive digital filter design. IEEE Trans. Circuit Theory. 18:1971;411-413.
18. Holschneider M., Kronland-Martinet R., Morlet J., Tchamitchian Ph. A real-time algorithm for signal analysis with the help of the wavelet transform. Combes J. M., Grassman A., Tchamitchian Ph. Wavelets, Time-Frequency Methods and Phase Space. 1989;286-297 Springer-Verlag, Berlin.
19. N. G. Kingsbury, The dual-tree complex wavelet transform: A new technique for shift invariance and directional filters, in, Proceedings of the Eighth IEEE DSP Workshop, Utah, August 9-12, 1998.
20. Kingsbury N. G. Image processing with complex wavelets. Phil. Trans. R. Soc. London A. 1999.
21. N. G. Kingsbury, Shift invariant properties of the dual-tree complex wavelet transform, in, Proc IEEE Int. Conf. Acoust, Speech, Signal Processing (ICASSP), Phoenix, March 16-19, 1999.
22. Kliewer J., Mertins A. Oversampled cosine-modulated filter banks with arbitrary system delay. IEEE Trans. Signal Process. 46:1998;941-955.
23. Lang M., Guo H., Odegard J. E., Burrus C. S., Wells R. O. Jr. Noise reduction using an undecimated discrete wavelet transform. IEEE Signal Process. Lett. 3:1996;10-12.
24. J. Lebrun, and, M. Vetterli, High order balanced multiwavelets: Theory, factorization and design, preprint, 1998.
25. Munch N. J. Noise reduction in tight Weyl-Heisenberg frames. IEEE Trans. Inform. Theory. 38:1992;608-616.
26. Nason G. P., Silverman B. W. Stationary wavelet transform and some statistical applications. Antoniadis A. Wavelets and Statistics. Springer-Verlag Lecture Notes. 1995;281-299 Springer-Verlag, Berlin.
27. Park H., Kalker T., Vetterli M. Groebner bases and multidimensional FIR multirate systems. J. Multidimen. Syst. Signal Process. 8:1997;11-30.
28. Rabiner L. R., Rader C. M. Digital Signal Processing. 1972;IEEE Press, New York.
29. Rioul O., Duhamel P. Fast algorithms for discrete and continuous wavelet transforms. IEEE Trans. Inform. Theory. 38:1992;569-586.
30. d ): The analysis of the analysis operator. J. Funct. Anal. 148:1997;408-447.
31. d ). Lau K. S. Advances in Wavelets. 1998;Springer-Verlag, Berlin.
32. Selesnick I. W. Interpolating multiwavelet bases and the sampling theorem. IEEE Trans. Signal Process. 47:1999;1615-1621.
33. Selesnick I. W. Balanced multiwavelet based on symmetric FIR filters. IEEE Trans. Signal Process. 48:2000;184-191.
34. Selesnick I. W., Burrus C. S. Maximally flat low-pass FIR filters with reduced delay. IEEE Trans. Circuits Syst. II. 45:1998;53-68.
35. I. W. Selesnick, and, L. Sendur, Iterated oversampled filter banks and wavelet frames, in, Wavelet Applications in Signal and Image Processing VIII, San Diego, 2000, Proceedings of SPIE, Vol, 4119.
36. Shensa M. J. The discrete wavelet transform: Wedding the à trous and Mallat algorithms. IEEE Trans. Signal Process. 40:1992;2464-2482.
37. Strang G., Nguyen T. Wavelets and Filter Banks. 1996;Wellesley-Cambridge Press.
38. Vetterli M., Kovačević J. Wavelets and Subband Coding. 1995;Prentice-Hall, Englewood Cliffs.
39. Xiong Z., Orchard M. T., Zhang Y.-Q. A deblocking algorithm for JPEG compressed images using overcomplete wavelet representations. IEEE Trans. Circuits Syst. Video Technol. 7:1997;433-437.