A note on compressed sensing and the complexity of matrix multiplication

Information Processing Letters

Volumn 109, Issue 10, 2009, Pages 468-471

  Iwen, M A ^a   Spencer, C V ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

Algorithms; Analysis of algorithms; Approximation algorithms; Computational complexity

Indexed keywords

COMPUTATIONAL COMPLEXITY; SIGNAL RECONSTRUCTION;

ANALYSIS OF ALGORITHMS; COMPRESSED SENSING; EXACT COMPUTATIONS; EXPLICIT CONSTRUCTIONS; MATRIX MULTIPLICATIONS; MATRIX PRODUCTS; N MATRIXES; SPARSE SIGNALS; TIME COMPLEXITY;

APPROXIMATION ALGORITHMS;

EID: 62549166190     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ipl.2009.01.010     Document Type: Article

References (18)

1. Alon N., Matias Y., and Szegedy M. The space complexity of approximating the frequency moments. J. Comput. System Sci. 58 1 (1999) 137-147
2. R. Berinde, A.C. Gilbert, P. Indyk, H. Karloff, M.J. Strauss, Combining geometry and combinatorics: A unified approach to sparse signal recovery, preprint, 2008
3. Candes E., Romberg J., and Tao T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52 (2006) 489-509
4. H. Cohn, R. Kleinberg, B. Szegedy, C. Umans, Group-theoretic algorithms for matrix multiplication, preprint
5. Coppersmith D. Rapid multiplication of rectangular matrices. SIAM J. Comput. 11 (1982) 467-471
6. Coppersmith D. Rectangular matrix multiplication revisited. J. Complexity 13 (1997) 42-49
7. Coppersmith D., and Winograd S. Matrix multiplication via arithmetic progressions. J. Symbolic Comput. 9 (1990) 251-280
8. Cormode G., and Muthukrishnan S. Combinatorial Algorithms for Compressed Sensing (2006), CISS, March
9. Donoho D. Compressed sensing. IEEE Trans. Inform. Theory 52 (2006) 1289-1306
10. Flajolet P., and Martin G. Probabilistic counting algorithms for data base applications. J. Comput. System Sci. 31 (1985) 182-209
11. 1 norm for sparse vectors, in: Proc. 44th Annual Allerton Conf. Communication, Control, and Computing, Allerton, Sep. 2006
12. P. Indyk, Explicit constructions for compressed sensing of sparse signals, in: SODA, 2008
13. P. Indyk, Personal correspondence, 2008
14. M.A. Iwen, A deterministic sub-linear time sparse Fourier algorithm via non-adaptive compressed sensing methods, in: SODA, 2008
15. Landsberg J.M. Geometry and the complexity of matrix multiplication. Bull. Amer. Math. Soc. 45 2 (April 2008)
16. S. Muthukrishnan, Some algorithmic problems and results in compressed sensing, in: Allerton Conference, 2006
17. Salem R., and Spencer D.C. On sets of integers which contain no three terms in arithmetical progression. Proc. Nat. Acad. Sci. USA 28 (1942) 561-563
18. J. Tropp, A. Gilbert, Signal recovery from partial information via orthogonal matching pursuit, 2005, submitted for publication. Preprint available at http://www.dsp.ece.rice.edu/CS/tropp.pdf