A simple method to build oversampled filter banks and tight frames

IEEE Transactions on Image Processing

Volumn 16, Issue 11, 2007, Pages 2682-2687

  Yang, Bo ^a   Jing, Zhongliang ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Filter bank; Frame; Shift invariant; Wavelet transform

Indexed keywords

OVERSAMPLED FILTER BANKS; SHIFT INVARIANT; TIGHT FRAMES;

FILTER BANKS; IMAGE RECONSTRUCTION; SAMPLING; WAVELET TRANSFORMS;

IMAGE FUSION;

ALGORITHM; ARTICLE; COMPUTER AIDED DESIGN; COMPUTER ASSISTED DIAGNOSIS; COMPUTER PROGRAM; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; METHODOLOGY; REPRODUCIBILITY; SAMPLE SIZE; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING;

ALGORITHMS; COMPUTER-AIDED DESIGN; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; INFORMATION STORAGE AND RETRIEVAL; REPRODUCIBILITY OF RESULTS; SAMPLE SIZE; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED; SOFTWARE; SOFTWARE DESIGN;

EID: 36348940621     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2007.908077     Document Type: Article

References (38)

1. S. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Anal. Mach. Intell., vol. 11, no. 7, pp. 674-693, Jul. 1989.
2. I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: SIAM, 1992.
3. M. Vetterli and C. Herley, "Wavelets and filter banks: Theory and design," IEEE Trans. Signal Process., vol. 40, no. 9, pp. 2207-2232, Sep. 1992.
4. M. Vetterli, J. Kovačević, and D. J. LeGall, "Perfect reconstruction filter banks for HDTV representation and coding," Image Commun., vol. 2, no. 3, pp. 349-364, Oct. 1990.
5. M. Antonini, M. Barlaud, P. Mathieu, and I. Daubeclues, "Image coding using wavelet transform," IEEE Trans. Image Process., vol. 1, no. 2, pp. 205-220, Apr. 1992.
6. O. Rioul and M. Vetterli, "Wavelets and signal processing," IEEE Signal Process. Mag., vol. 8, no. 4, pp. 11-38, Oct. 1991.
7. J. Luo, R. L. de Queiroz, and Z. Fan, "A robust technique for image descreening based on the wavelet transform," IEEE Trans. Signal Process., vol. 46, no. 4, pp. 1179-1185, Apr. 1998.
8. P. L. Dragotti and M. Vetterli, "Wavelet footprints: Theory, algorithms and applications," IEEE Trans. Signal Process., vol. 51, no. 5, pp. 1306-1323, May 2003.
9. G. T. Strang, "Wavelets and dilation equations: A brief introduction," SIAM Rev., vol. 31, no. 4, pp. 614-627, Dec. 1989.
10. E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, "Shiftable multiscale transforms," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 587-607, Mar. 1992.
11. N. G. Kingsbury, "Complex wavelets for shift invariant analysis and filtering of signals," Appl. Comput. Harmon. Anal., vol. 10, no. 3, pp. 234-253, May 2001.
12. M. J. Shensa, "The discrete wavelet transform: Wedding the à trous and mallat algorithms," IEEE Trans. Signal Process., vol. 40, no. 10, pp. 2464-2482, Oct. 1992.
13. M. Unser, "Texture classification and segmentation using wavelet frames," IEEE Trans. Image Process., vol. 4, no. 11, pp. 1549-1560, Nov. 1995.
14. J. G. Rosiles and M. J. T. Smith, "A low complexity overcomplete directional image pyramid," in Proc. Int. Conf. Image Processing, 2003, vol. 1, pp. 1049-1052.
15. A. L. da Cunha, J. Zhou, and M. N. Do, "The nonsubsampled contourlet transform: Theory, design, and applications," IEEE Trans. Image Process., vol. 15, no. 10, pp. 3089-3101, Oct. 2006.
16. I. W. Selesnick, R. G. Baraniuk, and N. Kingsbury, "The dual-tree complex wavelet transform - A coherent framework for multiscale signal and image processing," IEEE Signal Process. Mag., vol. 22, no. 6, pp. 123-151, Nov. 2005.
17. I. W. Selesnick, "The double density DWT," in Wavelets in Signal and Image Analysis: From Theory to Practice, A. Petrosian and F. G. Meyer, Eds. Norwell, MA: Kluwer, 2001.
18. I. W. Selesnick, "The double-density dual-tree DWT," IEEE Trans. Signal Process., vol. 52, no. 5, pp. 1304-1314, May 2004.
19. I. W. Selesnick, "A higher-density discrete wavelet transform," IEEE Trans. Signal Process., vol. 54, no. 8, pp. 3039-3048, Aug. 2006.
20. A. F. Abdelnour and I. W. Selesnick, "Symmetric nearly shift-invariant tight frame wavelets," IEEE Trans. Signal Process., vol. 53, no. 1, pp. 231-239, Jan. 2005.
21. T. O'Rourke and R. Stevenson, "Human visual system based wavelet decomposition for image compression," J. Vis. Commun. Image Represent., vol. 6, no. 4, pp. 109-121, Jun. 1995.
22. n," SIAM J. Math. Anal., vol. 30, no. 3, pp. 678-697, 1999, (electronic).
23. J. Kovačević and W. Sweldens, "Wavelet families of increasing order in arbitrary dimensions," IEEE Trans. Image Process., vol. 9, no. 3, pp. 480-496, Mar. 2000.
24. A. Gouze, M. Antonini, M. Barlaud, and B. Macq, "Design of signal-adapted multidimensional lifting scheme for lossy coding," IEEE Trans. Image Process., vol. 13, no. 12, pp. 1589-1603, Dec. 2004.
25. M. Feilner, D. Van De Ville, and M. Unser, "An orthogonal family of quincunx wavelets with continuously adjustable order," IEEE Trans. Image Process., vol. 14, no. 4, pp. 499-5 10, Apr. 2005.
26. D. Van De Ville, T. Blu, and M. Unser, "Isotropic polyharmonic B-splines: Scaling functions and wavelets," IEEE Trans. Image Process., vol. 14, no. 11, pp. 1798-11813, Nov. 2005.
27. J. Cassels, An Introduction to the Geometry of Numbers. Berlin: Springer-Verlag, 1971.
28. E. Viscito and J. P. Allebach, "The analysis and design of multidimensional FIR perfect reconstruction filter banks for arbitrary sampling lattices," IEEE Trans. Circuits Syst., vol. 38, no. 1, pp. 29-42, Jan. 1991.
29. n," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 533-555, Mar. 1992.
30. S. Park, M. J. T. Smith, and R. M. Mersereau, "Improved structures of maximally decimated directional filter banks for spatial image analysis," IEEE Trans. Image Process., vol. 13, no. 11, pp. 1424-1431, Nov. 2004.
31. R. R. Coilman and D. L. Donoho, "Translation-invariant denoising," in Lect. Notes Stat.. New York: Springer Verlag, 1995, pp. 125-150.
32. A. Temizel and T. Vlachos, "Wavelet domain image resolution enhancement using cycle-spinning," IEE Electron. Lett., vol. 41, no. 3, pp. 119-121, Feb. 2005.
33. D. Van De Ville, T. Blu, and M. Unser, "On the multidimensional extension of the quincunx subsampling matrix," IEEE Signal Process. Lett., vol. 12, no. 2, pp. 112-115, Feb. 2005.
34. Z. Zhang and R. S. Blum, "A categorization of multiscale-decomposition-based image fusion schemes with a performance study for a digital camera application," Proc. IEEE, vol. 87, no. 8, pp. 1315-1326, Aug. 1999.
35. H. Li, B. S. Manjunath, and S. K. Mitra, "Mulitsensor image fusion using the wavelet transform," Graph. Models Image Process., vol. 57, no. 3, pp. 235-245, May 1995.
36. O. Rockinger, "Image sequence fusion using a shift invariant wavelet transform," in Proc. Int. Conf. Image Processing, 1997, vol. 3, pp. 288-291.
37. P. Hill, N. Canagarajah, and D. Bull, "Image fusion using complex wavelets," in Proc. BMVC, 2002, pp. 487-496.
38. B. Forster, D. Van De Ville, J. Berent, D. Sage, and M. Unser, "Complex wavelets for extended depth-of-field: A new method for the fusion of multichannel microscopy images," Microscopy Res. Tech., vol. 65, no. 1-2, pp. 33-42, Sep. 2004.