A box constrained gradient projection algorithm for compressed sensing

Signal Processing

Volumn 91, Issue 8, 2011, Pages 1985-1992

  Broughton, R L ^a   Coope, I D ^a   Renaud, P F ^a   Tappenden, R E H ^a  

^a UNIVERSITY OF CANTERBURY   (New Zealand)

Author keywords

Compressed sensing; Projected BarzilaiBorwein algorithm; Signal reconstruction

Indexed keywords

COMPRESSED SENSING; GRADIENT PROJECTION ALGORITHMS; NUMERICAL EXPERIMENTS; PROJECTED BARZILAIBORWEIN ALGORITHM; PROJECTION ALGORITHMS; SOLUTION VECTORS; SPARSE SOLUTIONS; SPECIAL STRUCTURE; STEP LENGTH; UNDER-DETERMINED; UPPER BOUND;

ALGORITHMS; SIGNAL ANALYSIS; SIGNAL RECONSTRUCTION;

PROBLEM SOLVING;

EID: 79955463420     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2011.03.003     Document Type: Article

References (33)

1. J. Barzilai, and J.M. Borwein Two-point step size gradient methods IMA Journal of Numerical Analysis 8 1988 141 148
2. A. Beck, and M. Teboulle A fast iterative shrinkage-thresholding algorithm for linear inverse problems SIAM Journal of Imaging Sciences 2 1 2009 183 202
3. S. Boyd, and L. Vandenberghe Convex Optimization 2004 Cambridge University Press
4. E. Candès The restricted isometry property and its implications for compressed sensing Comptes Rendus Mathematique 346 2008 9 10
5. 1-magic: recovery of sparse signals via convex programming, Technical Report, California Institute of Technology, October 2005.
6. E. Candès, J. Romberg, and T. Tao Stable signal recovery from incomplete and inaccurate measurements Communications on Pure and Applied Mathematics 59 8 2006 1207 1223 (Pubitemid 43988295)
7. E.J. Candès, Compressive sampling, in: Proceedings of the International Congress of Mathematics (Madrid, Spain), European Mathematical Society, 2006, pp. 14331452.
8. E.J. Candès, and T. Tao Near-optimal signal recovery from random projections and universal encoding strategies IEEE Transactions on Information Theory 52 12 2006 5406 5425 (Pubitemid 46445381)
9. R. Chartrand, Nonconvex compressive sensing and reconstruction of gradientsparse images: random vs. tomographic Fourier sampling, in: IEEE Conference on Image Processing, vol. 15, 2008, pp. 26242627.
10. J. Claerbout, and F. Muir Robust modelling of erratic data Geophysics 38 5 1973 826 844
11. Y.H. Dai, and R. Fletcher Projected BarzilaiBorwein methods for large-scale box-constrained quadratic programming Numerische Mathematik 100 2005 21 47 (Pubitemid 40405555)
12. Y.H. Dai, W.W. Hager, K. Schittkowski, and H. Zhang The cyclic Barzilai-Borwein method for unconstrained optimization IMA Journal of Numerical Analysis 26 2006 604 627 (Pubitemid 44048227)
13. Y.H. Dai, and L.Z. Liao R-linear convergence of the Barzilai and Borwein gradient method IMA Journal of Numerical Analysis 22 1 2002 1 10
14. M.A.T. Figueiredo, J.M. Bioucas-Dias, M.V. Afonso, Fast frame-based image deconvolution using variable splitting and constrained optimization, in: IEEE Workshop on Statistical Signal Processing, 2009, pp. 109112.
15. M.A.T. Figueiredo, R.D. Nowak, and S.J. Wright Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems IEEE Journal of Selected Topics in Signal Processing 1 4 2007 586 597 (Pubitemid 351276802)
16. R. Fletcher Practical Methods of Optimization second ed. March 1991 John Wiley and Sons
17. R. Fletcher On the BarzilaiBorwein Method, Numerical Analysis Report October 2001 University of Dundee
18. R. Garg, R. Khandekar, Gradient descent with sparsification: an iterative algorithm for sparse recovery with restricted isometry property, in: Proceedings of the 26th International Conference on Machine Learning 2009, pp. 337344.
19. G. Golub, P.C. Hansen, and D. O'Leary Tikhonov regularization and total least squares SIAM Journal on Matrix Analysis and Applications 21 1 1999 185 194
20. E.T. Hale, W. Yin, and Y. Zhang Fixed-point continuation applied to compressed sensing: implementation and numerical experiments Journal of Computational Mathematics 28 2 2010 170 194
21. P.C. Hansen Rank-deficient and Discrete Ill-posed Problems 1998 SIAM
22. S.J. Kim, K. Koh, M. Lustig, S. Boyd, An efficient method for compressed sensing, in: IEEE International Conference on Image Processing, 2007, pp. 117120.
23. 1-regularized least squares IEEE Journal of Selected Topics in Signal Processing 1 4 2007 606 617 (Pubitemid 351266626)
24. 1-constrained signal recovery by steplength selection rules Applied and Computational Harmonic Analysis 27 2 2009 247 254
25. F. Luengo, and M. Raydan Gradient method with dynamical retards for large-scale optimization problems Electronic Transactions on Numerical Analysis 16 2003 186 193 (Pubitemid 38816942)
26. J. Nocedal, and S.J. Wright Numerical Optimization. Springer Series in Operations Research and Financial Engineering second ed. 2006 Springer
27. R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin A simple proof of the restricted isometry property for random matrices Constructive Approximation 28 3 2008 253 263
28. M. Raydan On the Barzilai and Borwein choice of steplength for the gradient method IMA Journal of Numerical Analysis 13 3 1993 321 326
29. M. Raydan The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem SIAM Journal of Optimization 7 1 1997 26 33
30. M. Raydan, and B.F. Svaiter Relaxed steepest descent and CauchyBarzilaiBorwein method Computational Optimization and Applications 21 2 2002 155 167 (Pubitemid 34168103)
31. Y. Wang, and S. Ma Projected BarzilaiBorwein method for large-scale non-negative image restoration Inverse Problems in Science and Engineering 15 6 2007 559 583 (Pubitemid 47338654)
32. S.J. Wright, R.D. Nowak, M.A.T. Figueiredo, Sparse reconstruction by separable approximation, in: IEEE International Conference on Acoustics, Speech and Signal Processing, 2008, pp. 33733376.
33. S.J. Wright, R.D. Nowak, and M.A.T. Figueiredo Sparse reconstruction by separable approximation IEEE Transactions on Signal Processing 57 7 2009 2479 2493