Parametrization construction of biorthogonal wavelet filter banks for image coding

Signal, Image and Video Processing

Volumn 1, Issue 1, 2007, Pages 63-76

  Liu, Zaide ^a,b   Zheng, Nanning ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b CHANGSHU INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Biorthogonal wavelets; Coding gain; Compression performance; Computational complexity; Diophantine equation; Discrete wavelet transform (DWT); Filter bank

Indexed keywords

EID: 34547588952     PISSN: 18631703     EISSN: 18631711     Source Type: Journal    
DOI: 10.1007/s11760-007-0001-z     Document Type: Article

References (35)

1. Cohen A., Daubechies I. and Feauveau J.C. (1992). Biorthogonal Bases of Compactly Supported Wavelets. Commun. Pure Appl. Math. 45: 485-560
2. Vetterli M. and Herley C. (1992). Wavelets and filter banks: theory and design. IEEE Trans. Image Process. 40(9): 2207-2232
3. Ansari R., Guillemot C. and Kaiser J.F. (1991). Wavelet construction using lagrange halfband filters., IEEE Trans. Circ. Syst. 38(9): 1116-1118
4. Villasenor J.D., Belzer B. and Liao J. (1995). Wavelet filter evaluation for image compression. IEEE Trans. Image Process. 4(8): 1053-1060
5. Sweldens W. (1996). The Lifting Scheme: A Custom-design Construction of Biorthogonal Wavelets. Appl. Comput. Harmon. Anal. 3: 186-200
6. Tsai M.J., Villasenor J.D. and Chen F. (1996). Stack-run image coding. IEEE Trans. Circ. Syst. Video Tech. 6(5): 519-521
7. Cooklev T., Nishihara A. and Sablatash M. (1997). Regular orthonormal and biorthogonal wavelet filters. Signal Process. 57: 121-137
8. Wei D., Wells R.O., Burrus C.S. and Tian J (1998). A new class of biorthogonal wavelet systems for image transform coding. IEEE Trans. Image Process. 7(7): 1000-1013
9. Dahmen W., Kunoth A. and Urban K. (1999). Biorthogonal Spline Wavelets on the Interval-Stability and Moment Conditions. Appl. Comput. Harmon. Anal. 6: 132-196
10. Tay D.B.H. (2000). Rationalizing the coefficients of popular biorthogonal wavelet filters. IEEE Trans. Circ. Syst. Video Tech. 10(6): 998-1005
11. Tay, D.B.H.: Families of binary coefficient biorthogonal wavelet filters. Proc. of IEEE ISCAS 2000, Geneva, Switzerland 3(28-31), 371-374 (2000)
12. He T.-X. (2001). Biorthogonal wavelets with certain regularities. Appl. Comput. Harmon. Anal. 11: 227-242
13. Winger L.L. and Venetsanopoulos A.N. (2001). Biorthogonal nearly coiflet wavelets for image compression. Signal Processing: Image Commu. 16: 859-869
14. Shui P.-L., Bao Z., Zhang X. and Tang Y. (2002). Two-channel Adaptive Biorthogonal Filterbanks via Lifting. Signal Process. 82: 881-893
15. Averbuch A.Z. and Zheludev V.A. (2002). Construction of biorthogonal discrete wavelet transforms using interpolatory splines. Appl. Comput. Harmon. Anal. 12: 25-56
16. Kotteri K.A., Bell A.E. and Carletta J.E. (2004). Design of Multiplierless, high-performance, wavelet filter banks with image compression applications. IEEE Trans. Circuits and Systems-I: Regular Papers 51(3): 483-494
17. Liu Z. and Zheng N. (2006). Parametrization construction of integer wavelet transforms for embedded image coding. Lecture Notes in Computer Science 4153: 26-29
18. Liu, Z., Zheng, N., Liu, Y., van de Wetering, H.: Optimization design of biorthogonal wavelets for embedded image coding. IEICE Trans. Info. Syst. (2007) (in press)
19. Daubechies I. and Sweldens W. (1998). Factoring wavelet transforms into lifting steps. J. Fourier Anal. Appl. 4(3): 247-269
20. ISO/IEC 15444-1 (2nd Edition), Information Technology-JPEG 2000 Image Coding System: Core Coding System (2004)
21. Katto J. and Yasuda Y. (1991). Performance evaluation of subband coding and optimization of its filter coefficients. In: Proceeding of SPIE Symposium on Visual Comm.and Image Processing vol. 1605: 95-106
22. Lightstone M., Majani E. and Mitra S.K. (1997). Low bit-rate design considerations for wavelet-based image coding. Multidimensional Syst.Signal Process 8(1): 111-128
23. Tay D.B.H. and Kingsbury N.G. (1993). Flexible design of multidimensional perfect reconstruction FIR 2-Band filters using transformations of variables. IEEE Trans.Image Process. 2(4): 466-480
24. Deslauriers G. and Dubuc S. (1989). Symmetric iterative interpolation processes. Constructive Approx. 5: 49-68
25. Strang G. and Nguyen T. (1996). Wavelets and filter banks. Wellesley-Cambridge Press, Wellesley, 214-218
26. Calderbank A.R., Daubechies I., Sweldens W. and Yeo B.-L. (1998). Wavelet transforms that map integers to integers. Appl. Comput. Harmon. Anal. 5: 332-369
27. Adams M.D. and Kossentini F. (2000). Reversible integer-to-integer wavelet transforms for image compression: performance evaluation and analysis. IEEE Trans. Image Process. 9(6): 1010-1024
28. Burt P.J. and Adelson E.H. (1983). The laplacian pyramid as a compact image code. IEEE Trans.Commu. 31(4): 532-540
29. Antonini M., Barlaud M., Mathieu P. and Daubechies I. (1992). Image coding using wavelet transform. IEEE Trans. Image Process 1(2): 205-220
30. ISO/IEC 15444-2, Information Technology-JPEG 2000 Image Coding System: Extensions (2004)
31. Mallat S.G. (1989). Multifrequency Channel Decompositions of Images and Wavelet Models. IEEE Trans. Acoust. Speech Signal Processing, 37(12): 2091-2110
32. Woods J.W. and Naveen T. (1992). A filter based bit allocation scheme for subband compression of HDTV. IEEE Trans.Image Process 1(3): 436-440
33. Said A. and Pearlman W.A. (1996). A new, fast, efficient image codec based on set partitioning in hierarchical trees. IEEE Trans. Circ. Syst. Video Tech. 6(3): 243-250
34. Pearlman W.A., Islam A., Nagaraj N. and Said A. (2004). Efficient, low-complexity image coding with a Set-partitioning embedded block coder. IEEE Trans. Circ. Syst. Video Tech. 14(11): 1219-1235
35. Wang E.-P. and Wang C.-z. (1992). Polynomial and Polynomial Matrix (Chinese Edition). Defense Industry Press, Beijing, China