Multiwavelets and applications to image denoising with effective iteration method

International Journal of Wavelets, Multiresolution and Information Processing

Volumn 7, Issue 5, 2009, Pages 535-551

  Jung, Tae Kwon ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Image denoising; Multiwavelet; Multiwavelet iteration

Indexed keywords

ANTI-SYMMETRIC; CORE PART; EXTENSION PRINCIPLES; IMAGE DENOISING; ITERATION METHOD; MULTI-WAVELETS; MULTISCALING FUNCTIONS; MULTIWAVELET; MULTIWAVELET ITERATION; NUMERICAL RESULTS; PARAUNITARY; SCALING FUNCTIONS; SINGLE LEVEL; SUB-BANDS;

IMAGE PROCESSING; SIMULATED ANNEALING;

HIGH PASS FILTERS;

EID: 70350238175     PISSN: 02196913     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219691309003070     Document Type: Article

References (41)

1. F. Abramovich, T. Sapatinas and B. W. Silverman, Wavelet thresholding via a Bayesian approach, Int. J. R. Statist. Soc. Ser. B 60 (1998) 725-749.
2. B. K. Alpert, Sparse representation of smooth linear operators, Thesis, Yale University, New Haven, CT, USA (1990).
3. Ofer Amrani, Amir Averbuch, Tamir Cohen and Valery A. Zheludev, Symmetric interpolatary framelets and their erasure recovery properties, Int. J. Wavelets Multiresolut. Inf. Process. 5(4) (2007) 541-566.
4. S. Bacchelli, M. Cotronei and D. Lazzaro, An algebraic construction of k-balanced multiwavelets via the lifting scheme, Numer. Algorithms 23 (2000) 329-356.
5. S. Bacchelli and S. Pappi, A note on a matrix approach to multiwavelet applications, Int. J. Wavelets Multiresolut. Inf. Process. 4(3 (2006) 509-522.
6. S. Bacchelli and S. Pappi, Statistically based multiwavelet denoising, J. Computat. Appl. Math. 210 (2007) 47-55.
7. A. Chambolle, R. A. DeVore, N. Lee and B. J. Lucier, Nonlinear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage, IEEE Trans. Image Proces. 7 (1998) 319-335.
8. C. K. Chui and J.-A. Lian, A study of orthonormal multi-wavelets, Appl. Numer. Math. 20 (1996) 273-298.
9. M. Contronei, L. B. Montefusco and L. Puccio, Multiwavelet analysis and signal processing, IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 41 (1998) 970-987.
10. S. Grace Chang, B. Yu and M. Vetterli, Adaptive wavelet thresholding for image denoising and compression, IEEE Trans. Image Process. 9 9) (2000) 1532-1546.
11. D. L. Donoho and I. M. Johnstone, Ideal spatial adaptation via wavelet shrinkage, Biometrica 81 (1994) 425-455.
12. D. L. Donoho and I. M. Johnstone, Adapting to unknown smoothness via wavelet shrinkage, J. Amer. Statist. Assoc. 90(432) (1995) 1200-1224.
13. G. C. Donovan, J. S. Geronimo, D. P. Hardin and P. R. Massopust, Construction of orthogonal wavelets using fractal interpolation functions, SIAM J. Math. Anal. 27 (1996) 1158-1192.
14. T. R. Downie and B. W. Silverman, The discrete multiple wavelet transform and thresholding methods, IEEE Trans. Signal Process. 46 (1998) 2558-2561.
15. J. Geronimo, D. Hardin and P. R. Massopust, Fractal functions and wavelet expansions based on several functions, J. Approx. Theory 78 (1994) 373-401.
16. T. N. T. Goodman and S. L. Lee, Multiwavelets of multiplicity r, Trans. Amer. Math. Soc. 342 (1994) 307-324.
17. D. P. Hardin and D. W. Roach, Multiwavelet prefilters-I: Orthogonal prefilters preserving approximation order p ≤ 2, IEEE Trans. Circuits Syst.-II, Analog Digital Signal Process. 45(8) (1998) 1106-1112.
18. C. Heil, G. Strang and V. Strela, Approximation by translates refinable functions, Numer. Math. 73 (1996) 75-94.
19. M. Jesen, Noise Reduction by Wavelet Thresholding, Lecture Notes in Statistics (Springer, New York, 2001).
20. F. Keinert, Wavelets and Multiwavelets (Chapman & Hall/CRC, 2004).
21. W. Kim and C.-C. Li, On preconditioning multiwavelet systems for image compression, Int. J. Wavelets Multiresolut. Inf. Process. 1(1) (2003) 51-74.
22. W. Lawton, S. L. Lee and Z. Shen, An algorithm of matrix extension and wavelet construction, Math. Comp. 65 (1996) 723-737.
23. J. Lebrun and M. Vetterli, Balanced multiwavelets theory and design, IEEE Trans. Signal Process. 46 (1998) 1119-1125.
24. J. Lebrun and M. Vetterli, High-order balanced multiwavelets: Theory, factorization, and design, IEEE Trans. Signal Process. 49 (2001) 1918-1930.
25. J. Lu, L. Wang, Y. Li and T. Yahagi, Noise removal for degraded images by IBS shrink method in multiwavelet domain, Electron. Commun. 90(7) (2007) 15-24.
26. J. Lu, L. Wang, Y. Li and T. Yahagi, Noise removal for medical X-ray images in multiwavelet domain, Int. J. Image Graphics 8(1) (2008) 25-46.
27. A. Morimoto, R. Ashino and R. Vaillancourt, Pre-processing desing for multiwavelet filters using neural networks, Int. J. Wavelets Multiresolut. Inf. Process. 2(2) (2004) 133-148.
28. M. Martin and A. Bell, New image compression techniques using multiwavelets and multiwavelet packets, IEEE Trans. Image Process. 10(4) (2001) 500-510.
29. J. T. Miller and C.-C. Li, Adaptive multiwavelet initialization, IEEE Trans. Signal Process. 46(12) (1998) 3282-3291.
30. B. Uma Shankar, S. K. Meher and A. Ghosh, Neuro-wavelet classifier for multispectral remote sensing images, Int. J. Wavelets Multiresolut. Inf. Process. 4(3) (2006) 509-522.
31. L. Shen and H. H. Tan, On a family of orthonormal scalar wavelets and related balanced multiwavelets, IEEE Trans. Signal Process. 49 (2001) 1447-1453.
32. L. Shen, H. H. Tan and J. Y. Tham, Symmetric-antisymmetric orthonormal multiwavelets and related scalar wavelets, Appl. Comput. Harmon. Anal. 8 (2000) 258-279.
33. G. Strang and T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge Press, 1995).
34. G. Strang and V. Strela, Short wavelets and matrix dilation equations, IEEE Trans. Signal Process. 43 (1995) 108-115.
35. V. Strela, P. N. Heller, G. Strang, P. Topiwala and C. Heil, The application of multiwavelet filter banks to image processing, IEEE Trans. Signal Process. 8 (1999) 548-563.
36. V. Strela and A. T. Walden, Denoising via wavelet shrinkage: Orthogonal, biorthogonal and multiple wavelet transforms, Technical Report, Imperial College of Science, UK (1995).
37. V. Strela and A. T. Walden, Signal and image denoising via wavelet thresholding: Orthogonal and biorthogonal, scalar and multiple wavelet transforms, Technical Report TR-98-01, Imperial College Statistics Section, UK (1998).
38. R. Turcajová, An algorithm for the construnction of symmetric orthogonal multiwavelets, SIAM J. Matrix Anal. Appl. 25(2) (2003) 532-550.
39. M. J. Vrhel and A. Aldroubi, Projection based prefiltering for multiwavelet transforms, IEEE Trans. Signal Process. 46(11) (1998) 3088-3092.
40. N. Weyrich and G. T. Warhola, Wavelet shrinkage and generalized cross validation for image denoising, IEEE Trans. Image Process. 7 1) (1998) 82-90.
41. X.-G. Xia, A new prefilter design for discrete multiwavelet transform, IEEE Trans. Signal Process. 46(6) (1998) 1558-1570.