Improved denoising of images using modelling of a redundant contourlet transform

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5914, Issue , 2005, Pages 1-12

  Matalon, Boaz ^a   Elad, Michael ^a   Zibulevsky, Michael ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Basis pursuit; Contourlet transform; Denoising; Gaussian scale mixtures; Inter coefficient dependency; Laplacian distribution; Redundancy; Sparsity

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; REDUNDANCY; SPURIOUS SIGNAL NOISE;

COUNTERLET TRANSFORM; DENOISING; GAUSSIAN SCALE MIXTURES; LAPLACIAN DISTRIBUTION; SPARSITY;

IMAGE PROCESSING;

EID: 30844456197     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.614449     Document Type: Conference Paper

References (25)

1. D. L. Donoho, "De-noising by soft thresholding," IEEE Trans. on Information Theory 41, pp. 613-627, May 1995.
2. M. Elad, "Why simple shrinkage is still relevant for redundant representations?," IEEE Trans. on Information Theory, submitted, Jan. 2005.
3. D. D. Y. Po and M. N. Do, "Directional multiscale modeling of images using the contourlet transform," IEEE Trans. on Image Processing, to appear, 2005.
4. J. Portilla, V. Strela, M. Wainwright, and E. Simoncelli, "Image denoising using scale mixtures of gaussians in the wavelet domain," IEEE Trans. on Image Processing 12, pp. 1338-1351, Nov. 2003.
5. L. Sendur and I. W. Selesnick, "Bivariate shrinkage functions for wavelet-based denoising exploiting inter-scale dependency," IEEE Trans. Signal Processing 50, pp. 2744-2755, Nov. 2002.
6. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM Journal on Scientific Computing 20(1), pp. 33-61, 1999.
7. F. Dibos and G. Koepfler, "Global total variation minimization," SIAM Journal on Numerical Analysis 37(2), pp. 646-664, 2000.
8. M. N. Do and M. Vetterli, "The contourlet transform: An efficient directional multiresolution image representation," IEEE Trans. on Image Processing, to appear, 2004.
9. S. Mallat, A Wavelet Tour of Signal Processing, Accademic Press, 2 ed., 1999.
10. E. J. Candés and D. Donoho, "New tight frames of curvelets and optimal representations of objects with smooth singularities," tech. rep., 2002.
11. E. L. Pennec and S. Mallat, "Sparse geometric image representation with bandelets," IEEE Trans. on Image Processing 14, pp. 423-438, April 2005.
12. M. N. Do and M. Vetterli, "Framing pyramids," IEEE Trans. on Signal Processing 51, pp. 2329-2342, Sep. 2003.
13. R. H. Bamberger and M. J. T. Smith, "A filter bank for the directional decomposition of images: Theory and design," IEEE Trans. on Signal Processing 40, pp. 882-893, April 1992.
14. A. L. Cunha, J. Zhou, and M. N. Do, "The nonsubsampled contourlet transform: Theory, design, and applications," IEEE Trans. on Image Processing, submitted, 2005.
15. E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, "Shiftable multi-scale transforms," IEEE Trans. on Information Theory 38(2), pp. 587-607, 1992.
16. S. G. Mallat, "A theory for multiresolution signal decomposition: the wavelet representation," IEEE Trans. on Pattern Analysis and Machine Intelligence 11(7), pp. 674-693, 1989.
17. R. W. Buccigrossi and E. P. Simoncelli, "Image compression via joint statistical characterization in the wavelet domain," Tech. Rep. 414, Munich, Germany, 1997.
18. M. J. Wainwright, E. P. Simoncelli, and A. S. Willsky, "Random cascades on wavelet trees and their use in modeling and analyzing natural imagery," Applied and Computational Harmonic Analysis 11, pp. 89-123, July 2001.
19. G. E. P. Box and C. Tiao, Bayesian Inference in Statistical Analysis, Addison Wesley, Reading, MA, 1992.
20. S. M. Lopresto, K. Ramchandran, and M. T. Orchard, "Image coding based on mixture modeling of wavelet coefficients and a fast estimation-quantization framework," in Proceedings DCC'97 (IEEE Data Compression Conference), March 1997.
21. S. G. C. B. Yu and M. Vetterli, "Spatially adaptive wavelet thresholding with context modeling for image denoising," IEEE Trans. on Image Processing 9, pp. 1522-1531, Sep. 2000.
22. J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. on Signal Processing 41, pp. 3445-3462, Dec. 1992.
23. B. Matalon, M. Zibulevsky, and M. Elad, "A new method for image denoising," tech. rep., to appear, 2005.
24. S. G. Nash, "A survey of truncated-newton methods," Journal of Computational and Applied Mathematics 124, pp. 45-59, 2000.
25. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization, Academic Press, New York, 1981.