Multiscale Sharpening and Smoothing in Besov Spaces with Applications to Image Enhancement

Applied and Computational Harmonic Analysis

Volumn 11, Issue 1, 2001, Pages 2-31

  Berkner, Kathrin ^a   Gormish, Michael J ^a   Schwartz, Edward L ^a  

^a Ricoh Innovations Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035391996     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.2000.0339     Document Type: Article

References (37)

1. Abramovich F., Sapatinas T., Silverman B. W. Wavelet thresholding via a Bayesian approach. J. Roy. Statist. Soc. Ser. B. 60:1998;725-749.
2. Abramovich F., Silverman B. W. Wavelet decomposition approaches to statistical inverse problems. Biometrika. 85:1998;115-129.
3. Andrews H. C., Hunt B. R. Digital Image Restoration. 1977;Prentice-Hall, Englewood Cliffs.
4. K. Berkner, and, R. O. Wells, Jr, Smoothness estimates for soft-threshold denoising via translation invariant wavelet transforms, Technical Report CML TR98-01, Rice University, 1998.
5. Blatner D., Roth S. Real World Scanning and Halftones. 1993;Peachpit Press, Berkeley.
6. H. Choi, and, R. Baraniuk, Analysis of wavelet-domain Wiener filters, in, IEEE Int. Symp. Time-Frequency and Time-Scale Analysis, Pittsburg, 1998.
7. H. Choi, and, R. Baraniuk, Interpolation and denoising of nonuniform sampled data using wavelet-domain processing, in, Proceedings of ICASSP, Phoenix, 1999.
8. Coifman R. R., Donoho D. L. Translation invariant denoising. Antoniades A. Wavelets and Statistics. Lecture Notes in Math. 1995;Springer-Verlag, New York/Berlin.
9. Crouse M. S., Novak R. D., Baraniuk R. G. Wavelet-based statistical signal processing using hidden Markov models. IEEE Trans. Signal Process. 46:1998;886-902.
10. Daubechies I. Ten Lectures on Wavelets. 1992;SIAM.
11. Deslauriers G., Dubuc S. Symmetric iterative interpolation processes. Constr. Approx. 5:1989;49-68.
12. DeVore R. A., Jawerth B., Lucier B. J. Image compression through wavelet transform coding. IEEE Trans. Inform. Theory. 38:1992;719-746.
13. DeVore R. A., Jawerth B., Popov V. Compression of wavelet coefficients. Amer. J. Math. 114:1992;737-785.
14. D. L. Donoho, Interpolating wavelet transforms, Technical Report, Department of Statistics, Stanford University, 1992.
15. Donoho D. L. De-noising by soft-thresholding. IEEE Trans. Inform. Theory. 41:1995;613-627.
16. Donoho D. L. Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmonic Anal. 2:1995;101-115.
17. Donoho D. L., Johnstone I. M. Ideal spatial adaption by wavelet shrinkage. Biometrika. 81:1994;425-455.
18. Donoho D. L., Johnstone I. M. Adaption to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 1995;1200-1224.
19. Donoho D. L., Vetterli M., DeVore R. A., Daubechies I. Data compression and harmonic analysis. IEEE Trans. Inform. Theory. 44:1998;2435-2476.
20. Federal Bureau of Investigation, WSQ gray-scale fingerprint image compression specification, 1993; Drafted by, and, IAFIS-IC-0110-v2.
21. Frazier M., Jawerth B., Weiss G. Littlewood-Paley Theory and the Study of Function Spaces. NSF-CBMS Regional Conf. Series in Mathematics. 79:1991;Amer. Math. Soc. Providence.
22. Galatsanos N. P., Katsaggelos A. K. Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation. IEEE Trans. Image Process. 1:1992;322-336.
23. Jaffard S. Oscillation spaces: Properties and applications to fractal and multifractal functions. J. Math. Phys. 39:1998;4129-4141.
24. Jain A. K. Fundamentals of Digital Image Processing. 1989;Prentice Hall, Englewood Cliffs.
25. Johnstone I. M., Silverman B. W. Wavelet threshold estimators for data with correlated noise. J. Roy. Statist. Soc. Ser. B. 59:1997;319-351.
26. N. Kingsbury, The dual-tree complex wavelet transform: A new efficient tool for image restoration and enhancement, inProc. European Signal Processing Conf., 1988, pp. 319-322.
27. A. F. Laine, J. Fan, and S. Schuler, On discrete dyadic wavelets for contrast enhancement, inProceedings of SPIE, San Diego, 1994, Vol. 2303, pp. 456-460.
28. 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.
29. J. Lévy Véhel, and, B. Guiheneuf, Multifractal image denoising, in, Proceedings of International Wavelet Conference, Tanger, Marocco, 1998.
30. Mallat S. A Wavelet Tour of Signal Processing. 1998;Academic Press, San Diego.
31. Mallat S., Zhong S. Characterization of signals from multiscale edges. IEEE Trans. Patt. Anal. Mach. Intell. 14:1992;710-732.
32. Meyer Y. Wavelets and Operators. 1992;Cambridge Univ. Press, Cambridge.
33. A. Munoz, T. Blu, and M. Unser, Non-Euclidean pyramids, inProceedings of SPIE Conference, San Diego, 2000, Vol. 4119, pp. 710-720.
34. R. Neelamani, H. Choi, and R. Baraniuk, Wavelet-based deconvolution for ol-conditioned systems, inProceedings of ICASSP, 1998, Vol. 6, pp. 3241-3244.
35. Triebel H. Theory of Function Spaces. 1983;Birkhäuser, Basel.
36. P. P. Vuylsteke, and, E. P. Schoeters, Method and apparatus for contrast enhancement, U.S. Patent 5,805,721, 1998.
37. X. Zong, A. F. Laine, E. Geiser, and D. C. Wilson, De-noising and contrast enhancement via wavelet shrinkage and nonlinear adaptive gain, inProceedings of SPIE, 1996, Vol. 2762, pp. 566-574.