Combining geometry and combinatorics: A unified approach to sparse signal recovery

46th Annual Allerton Conference on Communication, Control, and Computing

Volumn , Issue , 2008, Pages 798-805

  Berinde, R ^a   Gilbert, A C ^b   Indyk, P ^c   Karloff, H ^d   Strauss, M J ^b  

^a Department of Electrical Engineering and Computer Science   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d AT AND T LABS RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADJACENCY MATRICES; ALGORITHMIC APPROACHES; COMBINATORIAL APPROACHES; COMBINATORIAL TECHNIQUES; COMBINATORICS; DENSE MATRICES; EUCLIDEAN; EUCLIDEAN NORMS; GEOMETRIC APPROACHES; GEOMETRIC PROPERTIES; HIGH PROBABILITIES; MANHATTANS; MEASUREMENT MATRIXES; RECOVERY ALGORITHMS; SIGNAL RECOVERIES; SPARSE GRAPHS; SPARSE MATRICES; SPARSE SIGNALS; UNIFIED APPROACHES;

COMPUTATIONAL EFFICIENCY; SIGNAL RECONSTRUCTION;

COMBINATORIAL MATHEMATICS;

EID: 64549162832     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ALLERTON.2008.4797639     Document Type: Conference Paper

References (41)

1. N. Alon, Y. Matias, and M. Szegedy. The Space Complexity of Approximating the Frequency Moments. J. Comput. System Sci., 58 (1) :137-147, 1999.
2. R. Berinde, A. C. Gilbert, P. Indyk, H. Karloff, and M. J. Strauss. Combining geometry and combinatorics: a unified approach to sparse signal recovery. arXiv:0804.4666, 2008.
3. R. Berinde and P. Indyk. Sparse recovery using sparse random matrices. MIT-CSAIL Technical Report, 2008.
4. M. Charikar, K. Chen, and M. Farach-Colton. Finding frequent items in data streamsiICALP, 2002.
5. A. Cohen, W. Dahmen, and R. DeVore. Compressed sensing and best k-term approximation. Preprint, 2006.
6. V. Chandar. A negative result concerning explicit matrices with the restricted isometry property. Preprint, 2008.
7. G. Cormode and S. Muthukrishnan. Improved data stream summaries: The count-min sketch and its applications. FSTTCS, 2004.
8. G. Cormode and S. Muthukrishnan. Combinatorial algorithms for Compressed Sensing. In Proc. 40th Ann. Conf. Information Sciences and Systems, Princeton, Mar. 2006.
9. E. J. Candès, J. Romberg, and T Tao. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math., 59 (8) :1208-1223, 2006.
10. M. Capalbo, O. Reingold, S. Vadhan, and A. Wigderson. Randomness conductors and constant-degree lossless expanders. STOC-CCC, 2002.
11. M. Duarte, M. Davenport, D. Takhar, J. Laska, T Sun, K. Kelly, and R. Baraniuk. Single-pixel imaging via compressive sampling. IEEE Signal Processing Magazine, 2008.
12. R. DeVore. Deterministic constructions of compressed sensing matrices. preprint, 2007.
13. W. Dai and O. Milenkovic. Subspace pursuit for compressive sensing: Closing the gap between performance and complexity. Arxiv:0803.0811, 2008.
14. C. Dwork, F. McSherry, and K. Talwar. The price of privacy and the limits of lp decoding. STOC, 2007.
15. D. L. Donoho. Compressed Sensing. IEEE Trans. Info. Theory, 52 (4) :1289-1306, Apr. 2006.
16. David L. Donoho. High-dimensional centrally-symmetric polytopes with neighborliness proportional to dimension. Disc. Comput. Geometry, 35 (4) :617-652, 2006.
17. D. L. Donoho and J. Tanner. Thresholds for the recovery of sparse solutions via 11 minimization. Proc. of the 40th Annual Conference on Information Sciences and Systems (CISS), 2006. To appear.
18. M. F. Duarte, M. B. Wakin, and R. G. Baraniuk. Fast reconstruction of piecewise smooth signals from random projections. In Proc. SPARS05, Rennes, France, Nov. 2005.
19. C. Estan and G. Varghese. New directions in traffic measurement and accounting: Focusing on the elephants, ignoring the mice. ACM Transactions on Computer Systems, 2003.
20. A. Gilbert, S. Guha, P. Indyk, M. Muthukrishnan, and M. Strauss. Near-optimal sparse fourier representations via sampling. STOC, 2002.
21. A. C. Gilbert, S. Guha, P. Indyk, Y. Kotidis, S. Muthukrishnan, and M. J. Strauss. Fast, small-space algorithms for approximate histogram maintenance. In ACM Symposium on Theoretical Computer Science, 2002.
22. A. C. Gilbert, Y Kotidis, S. Muthukrishnan, and M. Strauss. One-Pass Wavelet Decompositions of Data Streams. IEEE Trans. Knowl. Data Eng., 15 (3) :541-554, 2003.
23. V. Guruswami, J. Lee, and A. Razborov. Almost euclidean subspaces of l1 via expander codes. SODA, 2008.
24. Rice DSP Group. Compressed sensing resources. Available at http://www.dsp. ece.rice.edu/cs/, 2006.
25. 1 norm for sparse vectors. Submitted for publication, 2006.
26. A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. One sketch for all: fast algorithms for compressed sensing. In ACM STOC 2007, pages 237-246, 2007.
27. P. Indyk. Sketching, streaming and sublinear-space algorithms. Graduate course notes, available at http://stellar.mit.edu/S/course/6/ fa07/6.895/, 2007.
28. P. Indyk. Explicit constructions for compressed sensing of sparse signals. SODA, 2008.
29. P. Indyk and M. Ruzic. Fast and effective sparse recovery using sparse random matrices. Preprint, 2008.
30. B. S. Kashin and V. N. Temlyakov. A remark on compressed sensing. Preprint, 2007.
31. Y. Mansour. Randomized interpolation and approximation of sparse polynomials. ICALP, 1992.
32. S. Muthukrishnan. Data streams: Algorithms and applications (invited talk at soda'03). Available at http://athos.rutgers.edu/~muthu/stream-1-1.ps, 2003.
33. D. Needell and J. A. Tropp. Cosamp: Iterative signal recovery from incomplete and inaccurate samples. Arxiv math. NA 0803.2392, 2008.
34. D. Needell and R. Vershynin. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. 2007.
35. S. Sarvotham, D. Baron, and R. G. Baraniuk. Compressed sensing reconstruction via belief propagation. Technical Report ECE-0601, Electrical and Computer Engineering Department, Rice University, 2006.
36. S. Sarvotham, D. Baron, and R. G. Baraniuk. Sudocodes - fast measurement and reconstruction of sparse signals. IEEE International Symposium on Information Theory, 2006.
37. T. Tao. Open question: deterministic uup matrices. Weblog at http://terrytao.wordpress.com, 2007.
38. V. Temlyakov. Nonlinear methods of approximation. Foundations of Comput. Math., July 2002.
39. J. A. Tropp and A. C. Gilbert. Signal recovery from partial information via Orthogonal Matching Pursuit. Submitted to IEEE Trans. Inform. Theory, April 2005.
40. Dharmpal Takhar, Jason Laska, Michael B. Wakin, Marco F. Duarte, Dror Baron, Shriram Sarvotham, Kevin Kelly, and Richard G. Baraniuk. A new compressive imaging camera architecture using optical-domain compression. In Proc. IS&T/SPIE Symposium on Electronic Imaging, 2006.
41. W. Xu and B. Hassibi. Efficient compressive sensing with determinstic guarantees using expander graphs. IEEE Information Theory Workshop, 2007.