A proximal approach for constrained cosparse modelling

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

Volumn , Issue , 2012, Pages 3433-3436

  Chierchia, G ^a   Pustelnik, N ^b   Pesquet, J C ^c   Pesquet Popescu, B ^a  

^a INSTITUT TELECOM   (France)

^b UNIVERSITÉ DE LYON   (France)

^c UNIVERSITÉ PARIS EST   (France)

Author keywords

compressed sensing; iterative methods; optimization methods; Signal restoration; wavelet transforms

Indexed keywords

COMPRESSIVE SENSING; CONVEX CONSTRAINTS; DATA FIDELITY; OPTIMIZATION METHOD; POISSON NOISE; PROJECTION TECHNIQUES; PROXIMAL ALGORITHM; RECONSTRUCTION PROBLEMS; SIGNAL RESTORATION; TARGET SIGNALS;

IMAGE RECONSTRUCTION; ITERATIVE METHODS; WAVELET TRANSFORMS;

SIGNAL PROCESSING;

EID: 84867606682     PISSN: 15206149     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICASSP.2012.6288654     Document Type: Conference Paper

References (17)

1. D. L. Donoho, "Compressed sensing," IEEE Trans. on Inform. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
2. E. J. Candès and T. Tao, "Near-optimal signal recovery from random projection : universal encoding strategies," IEEE Trans. on Inform. Theory, vol. 52, pp. 5406-5425, Dec. 2006.
3. S. Nam, M. Davies, M. Elad, and R. Gribonval, "Cosparse analysis modeling - uniqueness and algorithms," in Int. Conf. on Acoust., Speech and Sig. Proc., Prague, Czech Republic, May 22-27, 2011, pp. 5804-5807.
4. Y. C. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Trans. on Inform. Theory, vol. 55, no. 11, pp. 5302-5316, Nov. 2009.
5. J.-J. Fuchs, "Extension of the global matched filter to structured groups of atoms: Application to harmonic signals.," in Int. Conf. on Acoust., Speech and Sig. Proc., Prague, Czech Republic, May 22-27, 2011, pp. 3996-3999.
6. G. Peyré and J. Fadili, "Group sparsity with overlapping partition functions," in Proc. Eur. Sig. and Image Proc. Conference, Barcelona, Spain, Aug. 29 - Sept. 2, 2011, pp. x+5.
7. F. Bach, R. Jenatton, J. Mairal, and G. Obozinski, "Structured sparsity through convex optimization," Technical report, 2011, Preprint Hal-00621245.
8. P. L. Combettes, "Inconsistent signal feasibility problems : least-squares solutions in a product space," IEEE Trans. on Signal Proc., vol. 42, no. 11, pp. 2955-2966, Nov. 1994.
9. S. Theodoridis, K. Slavakis, and I. Yamada, "Adaptive learning in a world of projections," IEEE Signal Processing Magazine, vol. 28, no. 1, pp. 97-123, Jan. 2011.
10. P. L. Combettes and J.-C. Pesquet, "Proximal splitting methods in signal processing," in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, H. H. Bauschke, R. Burachik, P. L. Combettes, V. Elser, D. R. Luke, and H. Wolkowicz, Eds. Springer-Verlag, New York, 2010.
11. M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, "An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems," IEEE Trans. on Image Proc., vol. 20, no. 3, pp. 681-695, Mar. 2011.
12. G. Chen and M. Teboulle, "A proximal-based decomposition method for convex minimization problems," Math. Programm., vol. 64, pp. 81-101, 1994.
13. A. Chambolle and T. Pock, "A first-order primal-dual algorithm for convex problems with applications to imaging," J. Math. Imaging. Vis., vol. 40, no. 1, pp. 120-145, 2011.
14. L. M. Briceño-Arias and P. L. Combettes, "A monotone+skew splitting model for composite monotone inclusions in duality," SIAM J. Optim., vol. 21, pp. 1230-1250, 2011.
15. P. L. Combettes and J.-C. Pesquet, "Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators," Set-Valued and Variational Analysis, 2011, To appear, http://arxiv.org/abs/1107.0081.
16. M. Raginsky, S. Jafarpour, Z. Harmany, R. Marcia, R. Willett, and R. Calderbank, "Performance bounds for expander-based compressed sensing in Poisson noise," IEEE Trans. on Signal Proc., vol. 58, no. 8, pp. 3990-4002, Aug. 2011.
17. C. Chaux, L. Duval, and J.-C. Pesquet, "Image analysis using a dual-tree M-band wavelet transform," IEEE Trans. on Image Proc., vol. 15, no. 8, pp. 2397-2412, Aug. 2006.