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5 - Compressive Sensing

from Part I - Fundamentals

Published online by Cambridge University Press:  23 December 2021

Marco Tartagni
By
Marco Chiani
Marco Tartagni
Affiliation:
University of Bologna
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Summary

This chapter provides the essential concepts of compressive sensing (CS), also called compressed sensing, compressive sampling, or sparse sampling. A basic knowledge of signal processing is assumed. The treatment is rigorous but limited: more details can be found on the recommended textbooks given at the end of the chapter.

Keywords

compressive sensingcompressible signalsmeasurement matrixsparse recovery algorithms
Type
Chapter
Information
Electronic Sensor Design Principles , pp. 236 - 248
Publisher: Cambridge University Press
Print publication year: 2022

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References

Logan, B. F., Properties of High-Pass Signals. PhD thesis, Columbia University, New York, 1965.Google Scholar
Donoho, D. L. and Logan, B. F., Signal recovery and the large sieve, SIAM J. Appl. Math., vol. 52, no. 2, pp. 577–591, 1992.Google Scholar
Donoho, D. L. and Huo, X., Uncertainty principles and ideal atomic decomposition, IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2845–2862, Nov. 2001.Google Scholar
Candes, E. and Tao, T., Decoding by linear programming, IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203–4215, Dec. 2005.CrossRefGoogle Scholar
Cai, T. and Zhang, A., Sharp RIP bound for sparse signal and low-rank matrix recovery, Appl. Comput. Harmon. Anal., vol. 35, no. 1, pp. 74–93, Aug. 2013.Google Scholar
Candès, E. J. and Wakin, M. B., An introduction to compressive sampling, IEEE Signal Proc. Magazine, vol. 25, no. 2, pp. 21–30, 2008.Google Scholar
Donoho, D. L. and Tanner, J., Precise undersampling theorems, Proc. IEEE, vol. 98, no. 6, pp. 913–924, May 2010.Google Scholar
Baraniuk, R., Davenport, M. A., and Duarte, M. F., An introduction to compressive sensing. Connexions e-textbook, 2011.Google Scholar
Foucart, S. and Rauhut, H., A Mathematical Introduction to Compressive Sensing. New York: Springer Science+Business Media, 2013.Google Scholar
Donoho, D., Compressed sensing, IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289–1306, April 2006.Google Scholar
Candes, E. J., Romberg, J., and Tao, T., Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489–509, Feb 2006.Google Scholar
Candes, E. J. and Tao, T., Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5406–5425, Dec. 2006.CrossRefGoogle Scholar
Elzanaty, A., Giorgetti, A., and Chiani, M., Limits on sparse data acquisition: RIC analysis of finite Gaussian matrices, IEEE Trans. Inf. Theory, vol. 65, no. 3, pp. 1578–1588, Mar. 2019.CrossRefGoogle Scholar
Elzanaty, A., Giorgetti, A., and Chiani, M., Weak RIC analysis of finite Gaussian matrices for joint sparse recovery, IEEE Signal Proc. Lett., vol. 24, no. 10, pp. 1473–1477, Oct. 2017.Google Scholar
Candès, E. J., The restricted isometry property and its implications for compressed sensing, Comptes Rendus Math., vol. 346, no. 9, pp. 589–592, May 2008.Google Scholar
Maleki, A. and Donoho, D. L., Optimally tuned iterative reconstruction algorithms for compressed sensing, IEEE J. Sel. Topics Signal Proc., vol. 4, no. 2, pp. 330–341, Apr. 2010.Google Scholar
Yang, A. Y., Zhou, Z., Balasubramanian, A. G., Sastry, S. S., and Ma, Y., Fast ℓ1 minimization algorithms for robust face recognition, IEEE Trans. Image Proc., vol. 22, no. 8, pp. 3234–3246, Aug. 2013.Google Scholar
Wakin, M., Becker, S., Nakamura, E., Grant, M., Sovero, E., Ching, D., et al. A nonuniform sampler for wideband spectrally-sparse environments, IEEE J. Emerg. Sel. Topics Circuits Syst., vol. 2, no. 3, pp. 516–529, 2012.CrossRefGoogle Scholar
Chen, F., Chandrakasan, A. P., and Stojanovic, V. M., Design and analysis of a hardware-efficient compressed sensing architecture for data compression in wireless sensors, IEEE J. Solid-State Circuits, vol. 47, no. 3, pp. 744–756, Mar. 2012.Google Scholar
Haboba, J., Mangia, M., Pareschi, F., Rovatti, R., and Setti, G., A pragmatic look at some compressive sensing architectures with saturation and quantization, IEEE J. Emerg. Sel. Topics Circuits Syst., vol. 2, no. 3, pp. 443–459, Sept. 2012.Google Scholar
Gangopadhyay, D., Allstot, E. G., Dixon, A. M. R., Natarajan, K., Gupta, S., and Allstot, D. J., Compressed sensing analog front-end for bio-sensor applications, IEEE J. Solid-State Circuits, vol. 49, no. 2, pp. 426–438, Feb 2014.Google Scholar
Chen, F., Lim, F., Abari, O., Chandrakasan, A., and Stojanovic, V., Energy-aware design of compressed sensing systems for wireless sensors under performance and reliability constraints, IEEE Trans. Circuits Syst., vol. 60, no. 3, pp. 650–661, March 2013.Google Scholar
Elzanaty, A., Giorgetti, A., and Chiani, M., Lossy compression of noisy sparse sources based on syndrome encoding, IEEE Trans. Commun., vol. 67, no. 10, pp. 7073–7087, Oct. 2019.Google Scholar
Yoo, J., Becker, S., Loh, M., Monge, M., Candes, E., and Emami-Neyestanak, A., A 100 MHz–2GHz 12.5 x sub-Nyquist rate receiver in 90 nm CMOS,” in Proc. of 2012 IEEE Radio Frequency Integrated Circuits Symposium, June 2012, pp. 31–34.Google Scholar
Duarte, M. F., Davenport, M. A., Takhar, D., Laska, J. N., Sun, T., Kelly, K. E., et al., Single-pixel imaging via compressive sampling, IEEE Signal Process. Mag., vol. 25, no. 2, p. 83, March 2008.CrossRefGoogle Scholar
Lustig, M., Donoho, D. L., Santos, J. M., and Pauly, J. M., Compressed sensing MRI, IEEE Signal Process. Mag., vol. 25, no. 2, pp. 72–82, March 2008.Google Scholar
Craven, D., McGinley, B., Kilmartin, L., Glavin, M., and Jones, E., Compressed sensing for bioelectric signals: a review, IEEE J. Biomed. Health Inform., vol. 19, no. 2, pp. 529–540, 2015.CrossRefGoogle ScholarPubMed

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