Morphological diversity and sparsity: New insights into multivariate data analysis

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 6701, Issue , 2007, Pages

  Bobin, J ^a   Fadili, J ^b   Moudden, Y ^a   Starck, J L ^a  

^a UNIVERSITÉ PARIS DIDEROT   (France)

^b Centre National de la Recherche Scientifique   (France)

Author keywords

Blind source separation; Curvelets; Denoising; Inpainting; Morphological diversity; Multichannel data; Overcomplete representation; Sparsity; Wavelets

Indexed keywords

BLIND SOURCE SEPARATION; NUMERICAL ANALYSIS; SENSORS; SIGNAL PROCESSING; WAVELET TRANSFORMS;

CURVELETS; DENOISING; MORPHOLOGICAL DIVERSITY; MULTICHANNEL DATA;

DATA REDUCTION;

EID: 42149107100     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.731589     Document Type: Conference Paper

References (20)

1. J. Bobin, Y. Moudden, J.-L. Starek, and M. Elad, "Morphological diversity and source separation," IEEE Signal Processing Letters 13(7), pp. 409-412, 2006.
2. M. Elad, J.-L. Starek, D. Donoho, and P. Querre, "Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA)," ACHA , 2005. to appear.
3. J.Bobin, J-L.Starek, J.Fadili, Y.Moudden, and D.L.Donoho, "Morphological component analysis: new results.," submitted to IEEE Transactions on Image Processing - revised - available at http://perso.orange. fr/jbobin/articles/TIP_2006.pdf, 2006.
4. J.Bobin, J-L.Starek, J.Fadili, and Y.Moudden, "Sparsity and morphological diversity in blind source separation," IEEE Transactions on Image Processing - accepted - available at http://perso.orange.fr/jbobin/ pubs2.html , 2007.
5. J.-L. Starek, E. J. Candes, and D. L. Donoho, "The curvelet transform for image denoising.," IEEE Transactions on Image Processing 11(6), pp. 670-684, 2002.
6. J.-L. Starek, M. Elad, and D. Donoho, "Image decomposition via the combination of sparse representations and a variational approach," IEEE Transactions on Image Processing , 2004. in press.
7. Y. Li, S.Amari, A.Cichocki, and C. Guan, "Underdetermined blind source separation based on sparse representation," IEEE Transactions on information theory 52, pp. 3139-3152, 2006.
8. M. Zibulevsky and B.B.Pearlmutter, "Blind source separation by sparse decomposition," Neural Computations 13/4, 2001.
9. Olshausen.BA and Field.DJ., "Sparse coding with an overcomplete basis set: A strategy employed by vl?," Vision Research. 37, pp. 3311-3325, 2006.
10. J.-L. Starek, E. Candes, and D. Donoho, "The curvelet transform for image denoising," IEEE Transactions on Image Processing 11(6), pp. 131-141, 2002.
11. J.-L.Starek, J.Fadili, and F.Murtagh, "The undecimated wavelet decomposition and its reconstruction," IEEE Transactions on Image Processing 16, pp. 297-309, 2007.
12. J.Bobin, Y.Moudden, J. Fadili, and J.-L. Starek, "Morphological component analysis for sparse multichannel data: Application to inpainting," Journal of Mathematical Imaging and Vision. , 2007.
13. J.-L. Starek, M. Elad, and D. Donoho, "Redundant multiscale transforms and their application for morphological component analysis," Advances in Imaging and Electron Physics 132, 2004.
14. S.Sardy, A.Bruce, and P.Tseng, "Block coordinate relaxation methods for nonparametric wavelet denoising," Journal of Computational and Graphical Statistics 9(2), pp. 361-379, 2000.
15. J.-F. Cardoso, "Blind signal separation: statistical principles," Proceedings of the IEEE. Special issue on blind identification and estimation 9, pp. 2009-2025, Oct. 1998.
16. M. Zibulevski, "Blind source separation with relative newton method," Proceedings ICA2003, pp. 897-902, 2003.
17. P. Z.Koldovsky and E.Oja, "Efficient variant of algorithm fastica for independent component analysis attaining the cramer-rao lower bound," IEEE Transactions on neural networks 17, pp. 1265-1277, 2006.
18. Curvelab 2.01 for Matlab7.x. (http://www.curvelet.org/), 2006.
19. E. Candès and D. Donoho, "Curvelets," tech. rep., Statistics, Stanford University, 1999.
20. M. J. Fadili and J.-L. Starek, "Em algorithm for sparse representation - based image inpainting," IEEE International Conference on Image Processing ICIP'05 2, pp. 61-63, 2005. Genoa,Italia.