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Multi-Dimensional Wireless Tomography Using Tensor-Based Compressed Sensing

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Abstract

Wireless tomography is a technique for inferring a physical environment within a monitored region by analyzing RF signals traversed across the region. In this paper, we consider wireless tomography in a two and higher dimensionally structured monitored region, and propose a multi-dimensional wireless tomography scheme based on compressed sensing to estimate a spatial distribution of shadowing loss in the monitored region. In order to estimate the spatial distribution, we consider two compressed sensing frameworks: vector-based compressed sensing and tensor-based compressed sensing. When the shadowing loss has a high spatial correlation in the monitored region, the spatial distribution has a sparsity in its frequency domain. Existing wireless tomography schemes are based on the vector-based compressed sensing and estimates the distribution by utilizing the sparsity. On the other hand, the proposed scheme is based on the tensor-based compressed sensing, which estimates the distribution by utilizing its low-rank property. With simulation experiments, we reveal that the tensor-based compressed sensing has a potential for highly accurate estimation as compared with the vector-based compressed sensing. In order to show the possibility of the wireless tomography schemes in practical environments, we also show an experimental result in an anechoic chamber.

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Notes

  1. \(s_n\) (\(n = 1, 2, \ldots , N\)) can be defined over complex number field \(\mathcal {C}\) when \(\varvec{\varPhi }\) is defined by a complex number matrix such as an inverse Fourier transform matrix. In this paper, however, we define \(s_n\) as a real number by using an inverse DCT (Discrete Cosine Transform) matrix in order to simplify the description.

References

  1. Agrawal, P., & Patwari, N. (2009). Correlated link shadow fading in multi-hop wireless networks. IEEE Transactions on Wireless Communications, 8(8), 4024–4036.

    Article  Google Scholar 

  2. Beck, A., & Teboulle, M. (2009). A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1), 183–202.

    Article  MathSciNet  MATH  Google Scholar 

  3. Caiafa, C. F., & Cichocki, A. (2013). Computing sparse representations of multidimensional signals using Kronecker bases. Neural Computation, 25(1), 186–220.

    Article  MathSciNet  MATH  Google Scholar 

  4. Candès, E. J., & Wakin, M. B. (2008). An introduction to compressive sampling. IEEE Signal Processing Magazine, 25(2), 21–30.

    Article  Google Scholar 

  5. Chen, J., & Saad, Y. (2009). On the tensor SVD and the optimal low rank orthogonal approximation of tensors. SIAM Journal on Matrix Analysis and Applications, 30(4), 1709–1734.

    Article  MathSciNet  MATH  Google Scholar 

  6. Dapena, A., & Ahalt, S. (2002). A hybrid DCT-SVD image-coding algorithm. IEEE Transactions on Circuits and Systems for Video Technology, 12(2), 114–121.

    Article  Google Scholar 

  7. Gandy, S., Recht, B., & Yamada, I. (2011). Tensor completion and low-n-rank tensor recovery via convex optimization. Inverse Problems, 27(2), 025010.

    Article  MathSciNet  MATH  Google Scholar 

  8. Hashemi, H. (1993). The indoor radio propagation channel. Proceedings of the IEEE, 81(7), 943–968.

    Article  Google Scholar 

  9. Hayashi, K., Nagahara, M., & Tanaka, T. (2013). A user’s guide to compressed sensing for communications systems. IEICE Transactions on Communications, E96–B(3), 685–712.

    Article  Google Scholar 

  10. Jain, A. K. (1989). Fundamentals of digital image processing. Upper Saddle River: Prentice Hall.

    MATH  Google Scholar 

  11. Kaltiokallio, O., Bocca, M., & Patwari, N. (2014). A fade level-based spatial model for radio tomographic imaging. IEEE Transactions on Mobile Computing, 13(6), 1159–1172.

    Article  Google Scholar 

  12. Kanso, M. A., & Rabbat, M. G. (2009). Compressed RF tomography for wireless sensor networks: Centralized and decentralized approaches. In Proceedings of the 5th IEEE international conference on distributed computing in sensor systems (pp. 173–186).

  13. Kolda, T. G., & Bader, B. W. (2009). Tensor decompositions and applications. SIAM Review, 51(3), 455–500.

    Article  MathSciNet  MATH  Google Scholar 

  14. Lathauwer, L. D., Moor, B. D., & Vandewalle, J. (2000). A multilinear singular value decomposition. SIAM Journal on Matrix Analysis and Applications, 21(4), 1253–1278.

    Article  MathSciNet  MATH  Google Scholar 

  15. Mostofi, Y. (2011). Compressive cooperative sensing and mapping in mobile networks. IEEE Transactions on Mobile Computing, 10(12), 1769–1784.

    Article  Google Scholar 

  16. Patwari, N., & Agrawal, P. (2008). Effects of correlated shadowing: Connectivity, localization, and RF tomography. In Proceedings of the international conference on information processing in sensor networks (pp. 82–93).

  17. Recht, B., Fazel, M., & Parrilo, P. A. (2010). Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Review, 52(3), 471–501.

    Article  MathSciNet  MATH  Google Scholar 

  18. Takemoto, K., Matsuda, T., Hara, S., Takizawa, K., Ono, F., & Miura, R. (2014). Multi-dimensional wireless tomography with tensor-based compressed sensing. arXiv:1407.2394, http://arxiv.org/abs/1407.2394.

  19. Toh, K. C., & Yun, S. (2010). An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems. Pacific Journal of Optimization, 6(3), 615–640.

    MathSciNet  MATH  Google Scholar 

  20. Wilson, J., & Patwari, N. (2010). Radio tomographic imaging with wireless networks. IEEE Transactions on Mobile Computing, 9(5), 621–632.

    Article  Google Scholar 

  21. Yokota, K., Hara, S., Matsuda, T., Takizawa, K., Ono, F., & Miura, R. (2016). Experimental evaluation on a joint attenuation map estimation/indoor localization by means of compressed sensing-based wireless tomography. In Proceedings of the 3rd international conference on information and communication technologies for disaster management 2016 (ICT-DM 2016) (accepted).

  22. Yokota, K., Hara, S., Matsuda, T., Mukamoto, M., Uemura, Y., Takizawa, K., Ono, F., & Miura, R. (2015). Experimental evaluation on wireless tomography with compressed sensing in a three-dimensional space. In Proceedings of the 18th international symposium on wireless personal multimedia communications (WPMC 2015).

  23. Zibulevsky, M., & Elad, M. (2010). L1-L2 optimization in signal and image processing. IEEE Signal Processing Magazine, 27(3), 76–88.

    Article  Google Scholar 

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Authors and Affiliations

  1. Graduate School of Engineering, Osaka University, Osaka, 565-0871, Japan

    Takahiro Matsuda & Kazushi Takemoto

  2. National Institute of Information and Communications Technology, Yokosuka, Kanagawa, 2390847, Japan

    Takahiro Matsuda, Fumie Ono, Kenichi Takizawa & Ryu Miura

  3. Graduate School of Engineering, Osaka City University, Osaka, 558-8585, Japan

    Kengo Yokota & Shinsuke Hara

Authors
  1. Takahiro Matsuda
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  2. Kengo Yokota
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  3. Kazushi Takemoto
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  4. Shinsuke Hara
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  5. Fumie Ono
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  6. Kenichi Takizawa
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  7. Ryu Miura
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Corresponding author

Correspondence to Takahiro Matsuda.

Additional information

This paper is presented in part at arXiv:1407.2394 [18] and the 18th International Symposium on Wireless Personal Multimedia Communications (WPMC 2015) [22]. This work was supported in part by the R&D on “Cooperative Technologies and Frequency Sharing Between Unmanned Aircraft Systems (UAS) Based Wireless Relay Systems and Terrestrial Networks” by the Ministry of Internal Affairs and Communications of Japan, and the Grant-in-Aid for Scientific Researches (Nos. 25289115, JP16K14270, and JP16K00124) from the Ministry of Education, Science, Sport and Culture of Japan.

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Matsuda, T., Yokota, K., Takemoto, K. et al. Multi-Dimensional Wireless Tomography Using Tensor-Based Compressed Sensing. Wireless Pers Commun 96, 3361–3384 (2017). https://doi.org/10.1007/s11277-017-4061-2

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  • DOI: https://doi.org/10.1007/s11277-017-4061-2

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