Tree-adapted wavelet shrinkage

Advances in Imaging and Electron Physics

Volumn 124, Issue , 2002, Pages 343-394

  Walker, James S ^a  

^a UNIVERSITY OF WISCONSIN EAU CLAIRE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EDGE DETECTION; IMAGE PROCESSING; OPTICAL RESOLVING POWER; SIGNAL TO NOISE RATIO; TREES (MATHEMATICS); WAVELET TRANSFORMS;

ANALOG SIGNALS; DENOISING; TREE-ADAPTED WAVELET SHRINKAGE (TAWS);

WAVELET ANALYSIS;

EID: 34247518619     PISSN: 10765670     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1076-5670(02)80046-5     Document Type: Chapter

References (64)

1. Buccigrossi R.W., and Simoncelli E.P. Image compression via joint statistical characterization in the wavelet domain. IEEE Trans. Image Processing 8 (1999) 1688-1701
2. Burrus C.S., Gopinath R.H., and Guo H. Introduction to Wavelets and Wavelet Transforms: A Primer (1998), Prentice Hall, Englewood Cliffs, NJ
3. Burt P.J., and Adelson E.H. The Laplacian pyramid as a compact image code. IEEE Trans. Commun. 31 (1983) 532-540
4. Calderbank A.R., Daubechies I., Sweldens W., and Yeo B.-L. Wavelet transforms that map integers to integers. Appl. Comput. Harmonic Anal. 5 (1998) 332-369
5. Chambolle A., and Lucier B. Interpreting translation-invariant wavelet shrinkage as a new image smoothing scale space. IEEE Trans. Image Processing 10 (2001) 993-1000
6. Chang S.G., Yu B., and Vetterli M. Adaptive wavelet thresholding for image denoising and compression. IEEE Trans. Image Processing 9 (2000) 1532-1546
7. Choi H., and Baraniuk R. Wavelet statistical models and Besov spaces. Proceedings of the SPIE Conference on Wavelet Applications in Signal and Image Processing VII. Denver, CO (1999) 489-501
8. Choi H., Romberg J., Baraniuk R., and Kingsbury N. Hidden Markov tree modeling of complex wavelet transforms. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP'00. Istanbul, Turkey (2000)
9. Chui C.K. Wavelets: A Mathematical Tool for Signal Analysis (1997), Soc. for Industr. & Appl. Math., Philadelphia
10. Cohen A., Daubechies I., and Feauveau J.-C. Biorthogonal bases of compactly supported wavelets. Commun. Pure Appl. Math. 45 (1992) 485-560
11. Coifman R., and Donoho D. Translation-invariant denoising. Wavelets and Statistics. Lecture Notes in Statistics (1995), Springer-Verlag, Berlin/New York
12. Daubechies I. Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41 (1988) 909-996
13. Daubechies I. Ten Lectures on Wavelets (1992), Soc. for Industr. & Appl. Math., Philadelphia
14. Donoho D. Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data. In: Daubechies I. (Ed). Different Perspectives on Wavelets (1993), Am. Math. Soc., Providence, RI 173-205
15. Donoho D., and Johnstone I. Ideal spatial adaptation via wavelet shrinkage. Biometrika 81 (1994) 425-455
16. Donoho D., and Johnstone I. Adapting to unknown smoothness via wavelet shrinkage. Am. Stat. Assoc. 90 (1995) 1200-1224
17. Donoho D., Johnstone I., Kerkyacharian G., and Picard D. Wavelet shrinkage: Asymptopia?. J. R. Stat. Soc. B 57 (1995) 301-369
18. Field D.J. Scale invariance and self-similar "wavelet" transforms: An analysis of natural scenes and mammalian visual systems. In: Farge M., Hunt J.C.R., and Vassilicos J.C. (Eds). Wavelets, Fractals and Fourier Transforms (1993), Clarendon, Oxford 151-193
19. Field D.J. What is the goal of sensory coding?. Neural Comput. 6 (1994) 559-601
20. Field D.J. Wavelets, vision and the statistics of natural scenes. Philos. Trans. R. Soc. 357 (1999) 2527-2542
21. Field D.J., and Brady N. Wavelets, blur and the sources of variability in the amplitude spectra of natural scenes. Vision Res. 37 (1997) 3367-3383
22. Gormish M.J., Lee D., and Marcellin M.W. JPEG 2000: Overview, architecture, and applications. Sept. 2000. IEEE International Conference on Image Processing, Vancouver Vol. 2 (2000) 29-32
23. Haar L. Zur theorie der orthogonalen funktionsensysteme. Math. Ann. 69 (1910) 331-371
24. Hernandez E., and Weiss G. A First Course on Wavelets (1996), CRC Press, Boca Raton, FL
25. Huang J. Statistics of natural images and models. Ph.D. thesis (2000), Brown University, Providence, R.I.
26. Huang J., and Mumford D. Statistics of natural images and models. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 1999 (1999) 541-547
27. Johnstone I. Function estimation and wavelets. Lecture Notes (1999), Dept. of Statistics Stanford University, Palo Alto, CA
28. Kingsbury N. The dual-tree complex wavelet transform: A new efficient tool for image restoration and enhancement. Proceedings of the European Signal Processing Conference, EUSIPCO 98. Rhodes (1998) 319-322
29. Lang M., Guo H., Odegard J.E., and Burrus C.S. Nonlinear processing of a shift-invariant DWT for noise reduction. Proceedings of SPIE Conference 2491, Wavelet Applications II. Orlando, Apr. 1995 (1995) 640-651
30. Lee J.S. Digital image enhancement and noise filtering by use of local statistics. IEEE Pattern Anal. Machine Intell. 2 (1980) 165-168
31. Liu J., and Moulin P. Information-theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients. IEEE Trans. Image Processing 10 (2001) 1647-1658
32. Mallat S. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Pattern Anal. Machine Intell. 11 (1989) 674-693
33. Mallat S. A Wavelet Tour of Signal Processing (1999), Academic Press, New York
34. Mallat S., and Hwang W.L. Singularity detection and processing with wavelets. IEEE Trans. Inf. Theory 38 (1992) 617-643
35. Mallat S., and Zhong S. Characterization of signals from multiscale edges. IEEE Trans. Pattern Anal. Machine Intell. 14 (1992) 710-732
36. Marr D. Vision (1982), Freeman, San Francisco
37. Meyer Y. Wavelets and Operators (1992), Cambridge Univ. Press, Cambridge, UK
38. de Queiroz R.L., Nguyen T.Q., and Rao K.R. The GenLOT: Generalized linear-phase lapped orthogonal transform. IEEE Trans. Image Processing 44 (1996) 497-507
39. Resnikoff H.L., and Wells R.O. Wavelet Analysis. The Scalable Structure of Information (1998), Springer-Verlag, New York
40. Romberg J.K., Choi H., and Baraniuk R.G. Bayesian tree-structured image modeling using wavelet-domain hidden Markov models. Proceedings of the SPIE Technical Conference on Mathematical Modeling, Bayesian Estimation, and Inverse Problems. July 1999, Denver (1999) 31-44
41. Romberg R.K., Choi H., and Baraniuk R.G. Shift-invariant denoising using wavelet-domain hidden Markov trees. Proceedings of the Thirty-third Asilomar Conference. Oct. 1999, Pacific Grove, CA (1999)
42. Said A., and Pearlman W.A. An image multi-resolution representation for lossless and lossy image compression. IEEE Trans. Image Processing 5 (1996) 1303-1310
43. Said A., and Pearlman W.A. A new, fast, and efficient image codec based on set partitioning in hierarchical trees. IEEE Trans. Circuits Syst. Video Technol. 6 (1996) 243-250
44. Shapiro J.M. Embedded image coding using zerotrees of wavelet coefficients. IEEE Trans. Signal Processings 41 (1993) 3445-3462
45. Simoncelli E.P., and Freeman W.T. The steerable pyramid: A flexible architecture for multi-scale derivative computation. Second International Conference on Image Processing, IEEE Signal Proc. Soc. (Washington, DC), Oct. 1995 Vol. III (1995) 444-447
46. Stein C. Estimation of the mean of a multivariate normal distribution. Ann. Stat. 9 (1981) 1135-1151
47. Strang G., and Nguyen T.Q. Wavelets and Filter Banks (1996), Wellesley-Cambridge Press, Boston
48. Strela V., Portilla J., and Simoncelli E.P. Image denoising using a local Gaussian scale mixture model in the wavelet domain. Proceedings of the SPIE 45th Annual Meeting. San Diego, CA (2000)
49. Tian J., and Wells R.O. A lossy image codec based on index coding. IEEE Data Compression Conference, DCC'96 (1996) 456-460
50. Tian J., and Wells R.O. Embedded image coding using wavelet-difference-reduction. In: Topiwala P. (Ed). Wavelet Image and Video Compression (1998), Kluwer Academic, Norwell, MA 289-301
51. Tran T.D. Linear phase perfect reconstruction filter banks: Theory, structure, design, and applications in image compression. Ph.D. thesis (1999), Univ. of Wisconsin-Madison
52. Tran T.D., and Nguyen T.Q. A progressive transmission image coder using linear phase uniform filter banks as block transforms. IEEE Trans. Image Processing 8 (1999) 1493-1507
53. Vetterli M., and Kovačević J. Wavelets and Subband Coding (1995), Prentice Hall, Englewood Cliffs, NJ
54. Walker J.S. Fourier analysis and wavelet analysis. Notices Am. Math. Soc. 44 (1997) 658-670
55. Walker J.S. A Primer on Wavelets and Their Scientific Applications (1999), CRC Press, Boca Raton, FL
56. Walker J.S. Lossy image codec based on adaptively scanned wavelet difference reduction. Opt. Eng. 39 (2000) 1891-1897
57. Walker J.S. New methods in wavelet-based image denoising. Proceedings of the Third International Conference of the International Society for Analysis, Its Applications and Computations. Berlin, Aug. 2001 (2001), World Scientific, Singapore
58. Walker J.S. Combined image compressor and denoiser based on tree-adapted wavelet shrinkage. Opt. Eng. 41 (2002) 1520-1527
59. Walker J.S., and Chen Y.-J. Image denoising using tree-based wavelet subband correlations and shrinkage. Opt. Eng. 39 (2000) 2900-2908
60. Walker J.S., and Nguyen T.Q. Adaptive scanning methods for wavelet difference reduction in lossy image compression. IEEE International Conference on Image Processing Vancouver, Sept. 2000 Vol. 3 (2000) 182-185
61. Walker J.S., and Nguyen T.Q. Wavelet-based image compression. In: Rao K.R., and Yip P.C. (Eds). Handbook of Transforms and Data Compression (2000), CRC Press, Boca Raton, FL 267-311
62. Wandell B.A. Foundations of Vision (1995), Sinauer, Sunderland, MA
63. Wang Y. Jump and sharp cusp detection by wavelets. Biometrika 82 (1995) 385-397
64. Watson A.B. Efficiency of a model human image code. J. Opt. Soc. Am. 4 (1987) 2401-2417