Image denoising using a tight frame

IEEE Transactions on Image Processing

Volumn 15, Issue 5, 2006, Pages 1254-1263

  Shen, Lixin ^a   Papadakis, Manos ^b   Kakadiaris, Ioannis A ^c   Konstantinidis, Ioannis ^d   Kouri, Donald ^e   Hoffman, David ^f  

^a WESTERN MICHIGAN UNIVERSITY   (United States)

^b University of Houston   (United States)

^c University of Houston   (United States)

^d Bldg 142   (United States)

^e UNIVERSITY OF HOUSTON   (United States)

^f IOWA STATE UNIVERSITY   (United States)

Author keywords

Image denoising; Tight frame; Wavelets

Indexed keywords

ALGORITHMS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; WAVELET TRANSFORMS;

IMAGE DENOISING; MATHEMATICAL THEORY; PARSEVAL FRAMES; PIECEWISE LINEAR SPLINE; TIGHT FRAME;

IMAGE PROCESSING;

ALGORITHM; ARTICLE; AUTOMATED PATTERN RECOGNITION; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; EVALUATION; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; MATHEMATICAL COMPUTING; METHODOLOGY; SIGNAL PROCESSING; STATISTICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; INFORMATION STORAGE AND RETRIEVAL; MODELS, STATISTICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 33645968985     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2005.864240     Document Type: Article

References (33)

1. D. Donoho and I. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika, vol. 81, pp. 425-455, 1994.
2. D. Donoho, "De-noising by soft thresholding," IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 613-627, May 1995.
3. D. Donoho and I. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," J. Amer. Stat. Assoc., vol. 90, no. 432, pp. 1200-1224, 1995.
4. R. Coifman and D. Donoho, "Translation-invariant de-noising," in Wavelets and Statistics, A. Antoniadis and G. Oppenheim, Eds. Berlin, Germany: Springer-Verlag, 1995, vol. 103, pp. 125-150.
5. E. Simoncelli, "Bayesian denoising of visual images in the wavelet domain," in Bayesian Inference in Wavelet Based Models, P. Müller and B. Vidakovic, Eds. New York: Springer-Verlag, 1999, vol. 141, ch. 18, pp. 291-308.
6. S. Chang, B. Yu, and M. Vetterli, "Spatially adaptive wavelet thresholding with context modeling for image denoising," IEEE Trans. Image Process., vol. 9, no. 9, pp. 1522-1531, Sep. 2000.
7. X. Li and M. Orchard, "Spatially adaptive denoising under overcomplete expansion," in Proc. Int. Conf. Image Processing, vol. 3, Vancouver, BC, Canada, Sep. 2000, pp. 300-303.
8. H. Zhang, A. Nosratinia, and R. Wells, "Modeling the autocorrelation of wavelet coefficients for image denoising," in Proc. Int. Conf. Image Processing, vol. 3, Vancouver, BC, Canada, Sep. 2000, pp. 304-307.
9. E. Simoncelli, W. Freeman, E. Adelson, and D. Heeger, "Shiftable multiscale transforms," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 587-607, Mar. 1992.
10. J. Portilla, V. Strela, M. Wainwright, and E. Simoncelli, "Image denoising using scale mixtures of Gaussians in the wavelet domain," IEEE Trans. Image Process., vol. 12, no. 11, pp. 1338-1351, Nov. 2003.
11. N. Kingsbury, "Complex wavelets for shift invariant analysis and filtering of signals," Appl. Comput. Harmon. Anal., pp. 234-253, 2001.
12. L. Sendur and I. Selesnick, "Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency," IEEE Trans. Signal Process., vol. 50, no. 11, pp. 2744-2756, Nov. 2002.
13. L. Sendur and I. Selesnick, "Bivariate shrinkage with local variance estimation," IEEE Signal Process. Lett., vol. 9, no. 12, pp. 438-441, Dec. 2002.
14. E. Simoncelli and E. Adelson, "Noise removal via Bayesian wavelet coring," in Proc. Int. Conf. Image Processing, vol. I, Lausanne, Switzerland, Sep. 1996, pp. 379-382.
15. S. Chang, B. Yu, and M. Vetterli, "Adaptive wavelet thresholding for image denoising and compression," IEEE Trans. Image Process., vol. 9, no. 9, pp. 1532-1546, Sep. 2000.
16. M. Mihçak, I. Kozintsev, and K. Ramchandran, "Low-complexity image modeling based on statistical modeling of wavelet coefficients," IEEE Signal Process. Lett., vol. 6, no. 2, pp. 300-303, Feb. 1999.
17. A. Pizurica, W. Philips, I. Lemahieu, and M. Acheroy, "A joint inter-and intrascale statistical model for Bayesian wavelet based image denoising," IEEE Trans. Image Process., vol. 11, no. 5, pp. 545-557, May 2002.
18. J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. Acoust., Speech, Signal Process., vol. 41, no. 12, pp. 3445-3462, Dec. 1993.
19. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. New York: Academic, 1999.
20. M. Crouse, R. Nowak, and R. Baraniuk, "Wavelet-based statistical signal processing using hidden Markov models," IEEE Trans. Signal Process., vol. 46, no. 4, pp. 886-902, Apr. 1998.
21. J. Romberg, H. Choi, and R. Baraniuk, "Bayesian tree-structured image modeling using wavelet domain hidden Markov models," IEEE Trans. Image Process., vol. 10, no. 7, pp. 1056-1068, Jul. 2001.
22. G. Fan and X.-G. Xia, "Image denoising using local contextual hidden Markov model in the wavelet domain," IEEE Signal Process. Lett., vol. 8, no. 5, pp. 125-128, May 2001.
23. d : The analysis of the analysis operator," J. Func. Anal., vol. 148, pp. 408-447, 1997.
24. M. Papadakis, G. Gogoshin, I. Kakadiaris, D. Kouri, and D. Hoffman, "Non-separable radial frame multiresolution analysis in multidimensions," Numer. Func. Anal. Optim., vol. 24, pp. 907-928, 2003.
25. I. Selesnick, "Smooth wavelet frames with zero moments," Appl. Comput. Harmon. Anal., vol. 10, pp. 163-181, 2001.
26. C. Chui, W. He, and J. Stöckler, "Compactly supported tight and sibling frames with maximum vanishing moments," Appl. Comput. Harmon. Anal., vol. 13, pp. 224-262, 2002.
27. I. Daubechies, B. Han, A. Ron, and Z. Shen, "Framelets: MRA-based constructions of wavelet frames," Appl. Comput. Harmon. Anal., vol. 14, pp. 1-46, 2003.
28. Q. Jiang, "Parameterizations of masks for tight affine frames with two symmetric/antisymmetric generators," Adv. Comput. Math., vol. 18, pp. 247-268, 2003.
29. A. Petukhov, "Symmetric framelets," Constr. Approx., vol. 19, pp. 309-328, 2003.
30. B. Han and Q. Mo, "Tight wavelet frames generated by three symmetric b-spline functions with high vanishing moments," in Proc. Amer. Math. Soc., vol. 132, 2004, pp. 77-86.
31. J. Benedetto and O. Treiber, "Wavelet frames: Multiresolution analysis and extension principles," in Wavelet Transforms and Time-Frequency Analysis, L. Debnath, Ed. Boston, MA: Birkhauser, 2001, ch. 1, pp. 3-36.
32. Matlab. Natick, MA: The MathWorks, Inc., 1994-2004.
33. M. Papadakis, "Generalized frame multiresolution analysis in abstract Hilbert spaces," in Sampling, Wavelets and Tomography, J. Benedetto and A. Zayed, Eds. Boston, MA: Birkhauser, 2003.