Sparse solutions to underdetermined Kronecker product systems

Linear Algebra and Its Applications

Volumn 431, Issue 12, 2009, Pages 2437-2447

  Jokar, Sadegh ^a   Mehrmann, Volker ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Compressed sensing; Kronecker product; Mutual incoherence; Restricted isometry property; Spark; Sparse solution of linear systems

Indexed keywords

COMPRESSED SENSING; KRONECKER PRODUCT; MUTUAL INCOHERENCE; RESTRICTED ISOMETRY PROPERTY; SPARK; SPARSE SOLUTION OF LINEAR SYSTEMS;

LINEAR SYSTEMS; SIGNAL RECONSTRUCTION;

ELECTRIC SPARKS;

EID: 70349823220     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2009.08.005     Document Type: Article

References (25)

1. E.J. Candès, Compressive sampling, in: Proceedings of the International Congress of Mathematics, Madrid, Spain, 2006, pp. 1433-1452.
2. E.J. Candès, The restricted isometry property and its implications for compressed sensing, Technical Report, California Institute of Technology, 2008.
3. Candès E.J., and Romberg J. Quantitative robust uncertainty principles and optimally sparse decompositions. Found. Comput. Math. 6 2 (2006) 227-254
4. Candès E.J., Romberg J., and Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52 2 (2006) 489-509
5. Candès E.J., Romberg J., and Tao T. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59 8 (2006) 1207-1223
6. Candès E.J., and Tao T. Decoding by linear programming. IEEE Trans. Inform. Theory 51 12 (2005) 4203-4215
7. Chen S.S., Donoho D.L., and Saunders M.A. Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20 1 (1999) 33-61
8. Cohen A., Dahmen W., and DeVore R. Compressed sensing and best k-term approximation. J. Amer. Math. Soc. 22 (2009) 211-231
9. Donoho D.L. Compressed sensing. IEEE Trans. Inform. Theory 52 4 (2006) 1289-1306
10. 1 minimization. Proc. Natl. Acad. Sci. USA 100 5 (2003) 2197-2202
11. Donoho D.L., Elad M., and Temlyakov V. Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inform. Theory 52 1 (2006) 6-18
12. Donoho D.L., and Huo X. Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inform. Theory 47 7 (2001) 2845-2862
13. D.L. Donoho, Y. Tsaig, I. Drori, J.-L. Starck, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit, Tech. Report 2006-02, Stanford, Department of Statistics, 2006.
14. Elad M., and Bruckstein A.M. A generalized uncertainty principle and sparse representation in pairs of bases. IEEE Trans. Inform. Theory 48 9 (2002) 2558-2567
15. Fuchs J.J. Recovery of exact sparse representations in the presence of bounded noise. IEEE Trans. Inform. Theory 51 10 (2005) 1601-1608
16. Gribonval R., and Nielsen M. Sparse representations in unions of bases. IEEE Trans. Inform. Theory 49 12 (2003) 3320-3325
17. Hadamard J. Résolution d'une question relative aux déterminants. Bull. des Sciences Math. 17 2 (1893) 240-246
18. Horadam K.J. Hadamard Matrices and Their Applications (2007), Princeton University Press, Princeton, NJ
19. Horn R., and Johnson C.R. Topics in Matrix Analysis (1991), Cambridge University Press, Cambridge
20. Jokar S., and Pfetsch M. Exact and approximate sparse solutions of underdetermined linear equations. SIAM J. Sci. Comput. 31 1 (2008) 23-44
21. Lancaster P., and Tismenetsky M. The Theory of Matrices. second ed. (1985), Academic Press, New York
22. Natarajan B.K. Sparse approximate solutions to linear systems. SIAM J. Comput. 24 2 (1995) 227-234
23. Strang G. Computational Science and Engineering (2007), Wellesley-Cambridge Press
24. Strohmer T., and Heath R. Grassmannian frames with applications to coding and communication. Appl. Comput. Harmon. Anal. 14 3 (2003) 257-275
25. Tropp J.A. Greed is good: algorithmic results for sparse approximation. IEEE Trans. Inform. Theory 50 10 (2004) 2231-2242