Nonlinear basis pursuit

Conference Record - Asilomar Conference on Signals, Systems and Computers

Volumn , Issue , 2013, Pages 115-119

  Ohlsson, Henrik ^a,b   Yang, Allen Y ^a   Dong, Roy ^a   Sastry, S Shankar ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LINKÖPING UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSED SENSING; LINEAR EQUATIONS; RELAXATION PROCESSES;

COMPRESSIVE SENSING; CONVEX RELAXATION; GREEDY METHOD; LINEAR EQUATION SYSTEM; NON-LINEAR RELATIONSHIPS; NON-LINEAR SYSTEMS OF EQUATIONS; NOVEL ALGORITHM; PURSUIT ALGORITHMS;

NONLINEAR EQUATIONS;

EID: 84901285779     PISSN: 10586393     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACSSC.2013.6810285     Document Type: Conference Paper

References (39)

1. A. Beck and Y. C. Eldar. Sparsity constrained nonlinear optimization: Optimality conditions and algorithms. Technical Report arXiv:1203.4580, Technion, 2012.
2. D. P. Bertsekas. Nonlinear Programming. Athena Scientific, 1999.
3. D. P. Bertsekas and J. N. Tsitsiklis. Parallel and Distributed Computation: Numerical Methods. Athena Scientific, 1997.
4. T. Blumensath. Compressed sensing with nonlinear observations and related nonlinear optimization problems. Technical Report arXiv:1205.1650, University of Oxford, 2012.
5. T. Blumensath and M. Davies. Gradient pursuit for non-linear sparse signal modelling. In European Signal Processing Conference, 2008.
6. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 2011.
7. A. Bruckstein, D. Donoho, and M. Elad. From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Review, 51(1):34-81, 2009.
8. E. Candes. Compressive sampling. In Proceedings of the International Congress of Mathematicians, volume 3, pages 1433-1452, Madrid, Spain, 2006.
9. E. Candes, Y. Eldar, T. Strohmer, and V. Voroninski. Phase retrieval via matrix completion. Technical Report arXiv:1109.0573, Stanford University, September 2011.
10. E. Candes, X. Li, Y. Ma, and J. Wright. Robust Principal Component Analysis? Journal of the ACM, 58(3), 2011.
11. E. Candes, T. Strohmer, and V. Voroninski. PhaseLift: Exact and stable signal recovery from magnitude measurements via convex programming. Technical Report arXiv:1109.4499, Stanford University, September 2011.
12. A. Chai, M. Moscoso, and G. Papanicolaou. Array imaging using intensity-only measurements. Technical report, Stanford University, 2010.
13. S. Chen, D. Donoho, and M. Saunders. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 20(1):33-61, 1998.
14. W. Dai and O. Milenkovic. Subspace pursuit for compressive sensing signal reconstruction. IEEE Transactions on Information Theory, 55:2230-2249, 2009.
15. G. Davis, S. Mallat, and M. Avellaneda. Adaptive greedy approximations. Journal of Constructive Approximations, 13:57-98, 1997.
16. D. Donoho and M. Elad. Optimally sparse representation in general (nonorthogonal) dictionaries via -1-minimization. PNAS, 100(5):2197-2202, March 2003.
17. Y. C. Eldar and G. Kutyniok. Compresed Sensing: Theory and Applications. Cambridge University Press, 2012.
18. M. Fazel, H. Hindi, and S. P. Boyd. A rank minimization heuristic with application to minimum order system approximation. In Proceedings of the 2001 American Control Conference, pages 4734-4739, 2001.
19. M. X. Goemans and D. P. Williamson. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM, 42(6):1115-1145, November 1995.
20. M. Grant and S. Boyd. CVX: Matlab software for disciplined convex programming, version 1.21. http://cvxr.com/cvx, August 2010.
21. K. Jaganathan, S. Oymak, and B. Hassibi. Recovery of Sparse 1-D Signals from the Magnitudes of their Fourier Transform. ArXiv e-prints, June 2012.
22. H. Konno, J. Gotoh, T. Uno, and A. Yuki. A cutting plane algorithm for semi-definite programming problems with applications to failure discriminant analysis. Journal of Computational and Applied Mathematics, 146(1):141-154, 2002.
23. L. Li and B. Jafarpour. An iteratively reweighted algorithm for sparse reconstruction of subsurface flow properties from nonlinear dynamic data. Technical Report arXiv:0911.2270, University of Southern California, 2009.
24. I. Loris. On the performance of algorithms for the minimization of -1-penalized functionals. Inverse Problems, 25:1-16, 2009.
25. L. Lov́asz and A. Schrijver. Cones of matrices and set-functions and 0-1 optimization. SIAM Journal on Optimization, 1:166-190, 1991.
26. S. Marchesini. Ab Initio Undersampled Phase Retrieval. Microscopy and Microanalysis, 15, July 2009.
27. M. Moravec, J. Romberg, and R. Baraniuk. Compressive phase retrieval. In SPIE International Symposium on Optical Science and Technology, 2007.
28. D. Needell and J. Tropp. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Appl. Comp. Harmonic Anal., 26:301-321, 2008.
29. Y. Nesterov. Semidefinite relaxation and nonconvex quadratic optimization. Optimization Methods &Software, 9:141-160, 1998.
30. H. Ohlsson, A. Yang, R. Dong, and S. S. Sastry. CPRL-an extension of compressive sensing to the phase retrieval problem. In P. Bartlett, F.C.N. Pereira, C.J.C. Burges, L. Bottou, and K.Q. Weinberger, editors, Advances in Neural Information Processing Systems 25, pages 1376-1384. 2012.
31. H. Ohlsson, A. Y. Yang, R. Dong, and S. Sastry. Compressive Phase Retrieval From Squared Output Measurements Via Semidefinite Programming. Technical Report arXiv:1111.6323, University of California, Berkeley, November 2011.
32. H. Ohlsson, A. Y. Yang, R. Dong, M. Verhaegen, and S. Sastry. Quadratic basis pursuit. Technical Report arXiv:1301.7002, University of California, Berkeley, 2013.
33. E. Osherovich, Y. Shechtman, A. Szameit, P. Sidorenko, E. Bullkich, S. Gazit, S. Shoham, E. B. Kley, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev. Sparsity-based single-shot subwavelength coherent diffractive imaging. CLEO: Science and Innovations, 2012. CF3C.7.
34. P. Schniter and S. Rangan. Compressive phase retrieval via generalized approximate message passing. In Proceedings of Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA, October 2012.
35. Y. Shechtman, A. Beck, and Y. C. Eldar. GESPAR: Efficient Phase Retrieval of Sparse Signals. ArXiv e-prints, January 2013.
36. Y. Shechtman, Y. C. Eldar, A. Szameit, and M. Segev. Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing. Opt. Express, 19(16):14807-14822, Aug 2011.
37. N.Z. Shor. Quadratic optimization problems. Soviet Journal of Computer and Systems Sciences, 25:1-11, 1987.
38. A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev. Sparsity-based single-shot subwavelength coherent diffractive imaging. Nature Materials, 11(5):455-459, May 2012.
39. A. Yang, A. Ganesh, Z. Zhou, S. Sastry, and Y. Ma. Fast -1-minimization algorithms for robust face recognition. Technical Report arXiv:1007.3753, University of California, Berkeley, 2012.