Image de-noising by integer wavelet transforms and generalized cross validation

Medical Physics

Volumn 26, Issue 4, 1999, Pages 622-630

  Jansen, Maarten ^a   Uytterhoeven, Geert ^b   Bultheel, Adhemar ^b  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b NONE

Author keywords

Cross validation; Integer transforms; Noise reduction; Thresholding; Wavelets

Indexed keywords

IMAGE DENOISING; NOISE ABATEMENT;

CROSS VALIDATION; DE-NOISING ALGORITHM; GENERALIZED CROSS VALIDATION; INTEGER TRANSFORM; INTEGER WAVELET TRANSFORMS; THRESHOLDING; WAVELET THRESHOLDING; WAVELETS;

WAVELET TRANSFORMS;

ALGORITHM; ARTICLE; AUDITORY THRESHOLD; IMAGE ANALYSIS; IMAGE PROCESSING; IMAGING SYSTEM; NOISE REDUCTION; NUCLEAR MAGNETIC RESONANCE IMAGING; PRIORITY JOURNAL; SIGNAL NOISE RATIO; VALIDATION PROCESS; WHITE NOISE;

EID: 0032891258     PISSN: 00942405     EISSN: None     Source Type: Journal    
DOI: 10.1118/1.598562     Document Type: Article

References (26)

1. D. L. Donoho, "De-noising by soft-thresholding," IEEE Trans. Inf. Theory 41, 613-627 (1995).
2. R. Calderbank, I. Daubechies, W. Sweldens, and B.-L. Yeo, "Wavelet transforms that map integers to integers," Technical report, Department of Mathematics, Princeton University, 1996.
3. W. Sweldens, "The lifting scheme: A new philosophy in biorthogonal wavelet constructions," Proc. SPIE 2569, 68-79 (1995).
4. W. Sweldens, "The lifting scheme: A custom-design construction of biorthogonal wavelets," Appl. Comput. Harmon. Anal. 3, 186-200 (1996).
5. G. Lang, H. Guo, J. E. Odegard, C. S. Burrus, and R. O. Wells, "Noise reduction using an undecimated discrete wavelet transform," IEEE Signal Process. Lett. 3, 10-12 (1996).
6. G. P. Nason and B. W. Silverman, "The stationary wavelet transform and some statistical applications," in Wavelets and Statistics, edited by A. Antoniadis and G. Oppenheim, Lecture Notes in Statistics (Springer-Verlag, New York, 1995), pp. 281-299.
7. J.-C. Pesquet, H. Krim, and H. Carfantan, "Time invariant orthonormal wavelet representations," IEEE Trans. Signal Process. 44, 1964-1970 (1996).
8. M. Malfait and D. Roose, "Wavelet based image denoising using a markov random field a priori model," IEEE Trans. Image Process. 6, 549-565 (1997).
9. M. Jansen and A. Bultheel, "Experiments with wavelet based image denoising using generalized cross validation," SPIE Proc. 3034, 206-214, (1997).
10. M. Jansen and A. Bultheel, "Multiple wavelet threshold estimation by generalized cross validation for images with correlated noise," IEEE Trans. Image Process. (to appear).
11. I. Daubechies and W. Sweldens, "Factoring wavelet transforms into lifting steps," Technical report, Bell Laboratories, Lucent Technologies, 1996.
12. I. M. Johnstone and B. W. Silverman, "Wavelet threshold estimators for data with correlated noise," J. Royal Statistical Society, Ser. B 59, 319-351 (1997).
13. D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika 81, 425-455 (1994).
14. D. L. Donoho and I. M. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," J. Amer. Statist. Assoc. 90, 1200-1224 (1995).
15. F. Abramovich, F. Sapatinas, and B. W. Silverman, "Wavelet thresholding via a bayesian approach," J. Royal Statistical Society, Ser. B 60, 725-749 (1998).
16. F. Ruggeri and B. Vidakovic, "A bayesian decision theoretic approach to wavelet thresholding," Preprint 95-35, Duke University, Durham, NC, 1995.
17. B. Vidakovic, "Nonlinear wavelet shrinkage with Bayes rules and Bayes factors," Preprint 94-24, Duke University, Durham, NC, 1994.
18. G. Wahba, Spline Models for Observational Data, CBMS-NSF Regional Conf. Series in Appl. Math. (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990), Chap. 4, pp. 45-65.
19. N. Weyrich and G. T. Warhola, "De-noising using wavelets and cross validation," in Approximation Theory, Wavelets and Applications, Volume 454 of NATO ASI Series C, edited by S. P. Singh (Kluwer Academic, Dordrecht, 1995), pp. 523-532.
20. M. Jansen, M. Malfait, and A. Bultheel, "Generalized cross validation for wavelet thresholding," Signal Process. 56, 33-44 (1997).
21. G. P. Nason, "Wavelet shrinkage using cross validation," J. Royal Statistical Society, Ser. B 58, 463-479 (1996).
22. R. D. Nowak and R. G. Baraniuk, "Wavelet-domain filtering for photon imaging systems," IEEE Trans. Image Process., April (1998), special issue on wavelets and filter banks.
23. R. Fletcher, Practical Methods of Optimization (Wiley-Interscience, Chichester, 1981).
24. A. Cohen, I. Daubechies, and J. Feauveau, "Bi-orthogonal bases of compactly supported wavelets," Commun. Pure Appl. Math. 45, 485-560 (1992).
25. W. Sweldens and P. Schröder, "Building your own wavelets at home," in Wavelets in Computer Graphics, ACM SIGGRAPH Course Notes (ACM, New York, 1996).
26. G. Uytterhoeven, F. Van Wulpen, M. Jansen, D. Roose, and A. Bultheel, "WAILI: Wavelets with Integer Lifting," TW Report 262, Department of Computer Science, Katholieke Universiteit Leuven, Belgium, July 1997.