Abstract
Signal acquisition in ultra-high frequency is a challenging problem due to high cost of analog-digital converter. While compressed sensing (CS) provides an alternative way to sample signal with low sampling rate, the construction of measurement matrix is still challenging due to hardware complexity and random generation. To address this challenge, a variable dimension deterministic measurement matrix construction method is proposed in this paper based on cross-correlation characteristics of m sequences. Specifically, a lower bound of the spark of measurement matrix is derived theoretically. The proposed measurement matrix construction method is applicable to compressive sampling system to improve the quality of signal reconstruction, especially for modulated wideband converter (MWC) architecture. Simulation results demonstrate that the proposed measurement matrix is superior to random Gauss matrix and random Bernoulli matrix.
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References
Candes, E.J., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. J. IEEE Trans. Inf. Theory. 52, 489–509 (2006)
Candes, E.J., Tao, T.: Decoding by linear programming. J. IEEE Trans. Inf. Theory 51, 4203–4215 (2005)
Sun, R., Zhao, H., Xu, H.: The application of improved Hadamard measurement matrix in compressed sensing. In: International Conference on Systems and Informatics, pp. 1994–1997. IEEE, Yantai (2012)
Donoho, D.L., Elad, M.: Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1minimization. J. Proc. Natl. Acad. Sci. U.S.A. 100, 2197–2202 (2003)
Xia, S.T., Liu, X.J., Jiang, Y., Zheng, H.T.: Deterministic constructions of binary measurement matrices from finite geometry. J. IEEE Trans. Sig. Process. 63, 1017–1029 (2013)
Tropp, J.A.: Greed is good: algorithmic results for sparse approximation. J. IEEE Trans. Inf. Theory 50, 2231–2242 (2004)
Dang, K., Ma, L., Tian, Y., Zhang, H., Ru, L., Li, X.: Construction of the compressive sensing measurement matrix based on m sequences. J. Xian Dianzi Keji Daxue Xuebao/J. Xidian Univ. 42, 186–192 (2015)
Mishali, M., Eldar, Y.: From theory to practice: sub-nyquist sampling of sparse wideband analog signals. J. IEEE J. Sel. Top. Sig. Process. 4, 375–391 (2010)
Karahanoglu, N.B., Erdogan, H.: A* orthogonal matching pursuit: best-first search for compressed sensing signal recovery. J. Digit. Sig. Process. 22, 555–568 (2012)
Acknowledgments
This work was supported by the Fundamental Research Funds for the Center Universities (Grant No. HIT.MKSTISP.2016 13).
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© 2018 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering
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Xiao, J., Zhang, R., Zhao, H. (2018). Variable Dimension Measurement Matrix Construction for Compressive Sampling via m Sequence. In: Gu, X., Liu, G., Li, B. (eds) Machine Learning and Intelligent Communications. MLICOM 2017. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 226. Springer, Cham. https://doi.org/10.1007/978-3-319-73564-1_22
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DOI: https://doi.org/10.1007/978-3-319-73564-1_22
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