Boolean compressed sensing and noisy group testing

IEEE Transactions on Information Theory

Volumn 58, Issue 3, 2012, Pages 1880-1901

  Atia, George K ^a   Saligrama, Venkatesh ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b Boston University   (United States)

Author keywords

Compressed sensing (CS); group testing; ML decoding; sparse models

Indexed keywords

ACHIEVABILITY; AVERAGE ERROR PROBABILITY; BERNOULLI; COMPRESSED SENSING; COMPRESSED SENSING (CS); DEFECTIVE ITEMS; DILUTION EFFECT; GROUP TESTING; LARGE POPULATION; LOWER BOUNDS; MAXIMUM LIKELIHOOD DETECTORS; NOISE FREE CASE; NOISE MODELS; RANDOM CODING; SENSING MODEL; WORST-CASE ERRORS;

INFORMATION THEORY; MAXIMUM LIKELIHOOD ESTIMATION;

SIGNAL RECONSTRUCTION;

EID: 84857771457     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2178156     Document Type: Article

References (29)

1. G. Atia and V. Saligrama, "Noisy group testing: An information theoretic perspective," in 47th Annu. Allerton Conf. Commun., Control, Comput., Monticello, IL, Sep. 2009, pp. 355-362.
2. G. Atia and V. Saligrama, Boolean compressed sensing and noisy group testing 2009 [Online]. Available: http://arxiv.org/abs/0907.1061
3. D.-Z. Du and F. K. Hwang, Combinatorial Group Testing and Its Applications, 2nd ed. , Singapore: World Scientific, 2000.
4. R. Dorfman, "The detection of defective members of large populations," Ann. Math. Stat., vol. 14, pp. 436-440, 1943.
5. G. Atia, A. Sahai, and V. Saligrama, "Spectrum enforcement and liability assignment in cognitive radio systems," in Proc. IEEE Dynamic Spectrum Access Netw. (DySpAN), Chicago, IL, Oct. 2008.
6. G. Atia, V. Saligrama, and A. Sahai, "Codes to unmask spectrum violators," in Asilomar Conf. Signals, Systems and Computers, Pacific Grove, CA, Oct. 2008, pp. 1575-1578.
7. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
8. E. J. Candes, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol. 59, pp. 1207-1223, 2005.
9. M. Wainwright, "Information-theoretic bounds on sparsity recovery in the high-dimensional and noisy setting," in Int. Symp. Information Theory, Nice, France, Jun. 2007, pp. 961-965.
10. M. J. Wainwright, "Sharp thresholds for high-dimensional and noisy sparsity recovery using -constrained quadratic programs," presented at the Allerton Conf. Communication, Control, and Comput., Monticello, IL, 2006.
11. G. Reeves and M. C. Gastpar, "A note on optimal support recovery in compressed sensing," in 43rd Annu. IEEE Asilomar Conf. Signals, Systems, and Comput., Monterey, CA, Nov. 2009, pp. 1576-1580.
12. A. K. Fletcher, S. Rangan, and V. K. Goyal, "Necessary and sufficient conditions for sparsity pattern recovery," IEEE Trans. Inf. Theory, vol. 55, no. 12, pp. 5758-5772, Dec. 2009.
13. A. K. Fletcher, S. Rangan, V. K. Goyal, and K. Ramchandran, "Denoising by sparse approximation: Error bounds based on rate-distortion theory," EURASIP J. Appl. Signal Process., pp. 1-19, 2006.
14. W. H. Kautz and R. C. Singleton, "Nonrandom binary superimposed codes," IEEE Trans. Inf. Theory, vol. 10, no. 4, pp. 363-377, Oct. 1964.
15. A. G. Dyachkov and V. V. Rykov, "A survey of superimposed code theory," Probl. Control Inf. Theory, vol. 12, no. 4, pp. 1-13, 1983.
16. P. Erdös, P. Frankl, and Z. Füredi, "Family of finite sets in which no set is covered by the union of n others," Isr. J. Math., vol. 51, pp. 79-89, 1985.
17. H.-B. Chen and F. K. Hwang, "Exploring the missing link among d-separable, -separable and -disjunct matrices," Discrete Appl. Math., vol. 155, no. 5, pp. 662-664, 2007.
18. A. G. Dyachkov, V. V. Rykov, and A. M. Rashad, "Bounds of the length of disjunct codes," Probl. Control Inf. Theory, vol. 11, pp. 7-13, 1982.
19. M. Ruszinkó, "Family of finite sets in which no set is covered by the union of n others," Isr. J. Math., vol. 51, pp. 79-89, 1985.
20. A. Sebo, "On two random search problems," J. Statist. Plan. Inference, vol. 11, pp. 23-31, 1985.
21. T. Berger and V. I. Levenshtein, "Asymptotic efficiency of two-stage disjunctive testing," IEEE Trans. Inf. Theory, vol. 48, no. 7, pp. 1741-1749, Jul. 2002.
22. A. C. Gilbert, M. A. Iwen, and M. J. Strauss, "Group testing and sparse signal recovery," presented at the 42nd Asilomar Conf. Signals, Systems and Comput., Pacific Grove, CA, 2008.
23. D.-Z. Du and F. K. Hwang, Pooling Designs and Non-Adaptive Group Testing: Important Tools for DNA Sequencing. , Singapore: World Scientific, 2006.
24. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
25. G. Atia and V. Saligrama, "A mutual information characterization for sparse signal processing," presented at the 38th Int. Colloquium on Automata, Languages and Programming, Zurich, Switzerland, Jul. 2011.
26. S. Aeron, V. Saligrama, and M. Zhao, "Information theoretic bounds for compressed sensing," IEEE Trans. Inf. Theory, vol. 56, no. 10, pp. 5111-5130, Oct. 2010.
27. R. G. Gallager, Information Theory and Reliable Communication. New York: Wiley, 1968.
28. M. B. Malyutov, P. S. Mateev, and M. Zhao, "Screening design for non-symmetric response function," Mat. Zemetki, vol. 27, pp. 109-127, 1980.
29. A. Dyachkov, Lectures on Designing Screening Experiments Moscow State Univ., Moscow, Russia, 2003.