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Compressed sensing is now established as an effective method for dimension reduction when the underlying signals are sparse or compressible with respect to some suitable basis or frame.
P. T. Boufounos and R. G. Baraniuk, “Quantization of sparse representations,” in Rice University ECE Department Technical Report 0701. Summary appears in Proc. Data Compression Conference (DCC) , Snowbird, UT, March 27-29 2007. [Online]. Available: http://hdl.handle.net/1911/13034
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J. Laska, S. Kirolos, Y. Massoud, R. Baraniuk, A. Gilbert, M. Iwen, and M. Strauss, “Random sampling for analog-to-information conversion of wideband signals,” in Design, Applications, Integration and Software, 2006 IEEE Dallas/CAS Workshop on , Oct 2006, pp. 119–122
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P. T. Boufounos and R. G. Baraniuk, “1-bit compressive sensing,” in Proc. Conf. Inform. Science and Systems (CISS) , Princeton, NJ, March 19-21 2008
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C. Güntürk, M. Lammers, A. Powell, R. Saab, and Ö. Yılmaz, “Sobolev duals for random frames and sigma-delta quantization of compressed sensing measurements,” Foundations of Computational mathematics , vol. 13, no. 1, pp. 1–36, 2013
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F. Krahmer, R. Saab, and Ö. Yılmaz, “Sigma-Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing,” Information and Inference , vol. 3, no. 1, pp. 40–58, 2013
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——, “Stabilizing nonuniformly quantized compressed sensing with scalar companders,” IEEE Transactions on Information Theory , vol. 5, no. 12, pp. 7969 – 7984, Jan. 2013
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R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation , vol. 28, no. 3, pp. 253–263, 2008
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A. Cohen, W. Dahmen, and R. DeVore, “Compressed sensing and best k k -term approximation,” Journal of the American mathematical society , vol. 22, no. 1, pp. 211–231, 2009
2009
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A. Zymnis, S. Boyd, and E. Candes, “Compressed sensing with quantized measurements,” IEEE Signal Proc. Lett. , vol. 17, no. 2, pp. 149–152, 2010
2010
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J. Blum, M. Lammers, A. M. Powell, and Ö. Yılmaz, “Sobolev duals in frame theory and Sigma-Delta quantization,” Journal of Fourier Analysis and Applications , vol. 16, no. 3, pp. 365–381, 2010
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O. N. Feldheim and S. Sodin, “A universality result for the smallest eigenvalues of certain sample covariance matrices,” Geometric And Functional Analysis , vol. 20, no. 1, pp. 88–123, 2010
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F. Krahmer and R. Ward, “New and improved johnson-lindenstrauss embeddings via the restricted isometry property,” SIAM Journal on Mathematical Analysis , vol. 43, no. 3, pp. 1269–1281, 2011
2011
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L. Jacques, J. N. Laska, P. T. Boufounos, and R. G. Baraniuk, “Robust 1-bit compressive sensing via binary stable embeddings of sparse vectors,” IEEE Transactions on Information Theory , vol. 59, no. 4, pp. 2082–2102, 2013
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Y. Plan and R. Vershynin, “One-bit compressed sensing by linear programming,” Communications on Pure and Applied Mathematics , vol. 66, no. 8, pp. 1275–1297, 2013
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E. Chou, “Beta-duals of frames and applications to problems in quantization,” Ph.D. dissertation, New York University, 2013
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M. Iwen and R. Saab, “Near-optimal encoding for sigma-delta quantization of finite frame expansions,” Journal of Fourier Analysis and Applications , pp. 1–19, 2013
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2013
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2014
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2014
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P. Boufounos, L. Jacques, F. Krahmer, and R. Saab, “Quantization and compressive sensing,” 2014
2014
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A. Ai, A. Lapanowski, Y. Plan, and R. Vershynin, “One-bit compressed sensing with non-gaussian measurements,” Linear Algebra and its Applications , vol. 441, pp. 222–239, 2014
2014
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2014
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S. Foucart, “Stability and robustness of ℓ 1 \ell_{1} -minimizations with Weibull matrices and redundant dictionaries,” Linear Algebra and its Applications , vol. 441, pp. 4–21, 2014
2014
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2015
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