Abstract
High resolution three-dimensional (3D) imaging method using MIMO radar with sparse array is studied in this paper. A method based on compressive sensing (CS) is firstly given. However, the CS-based method has the off-grid problem which will reduce the estimation accuracy of scatterers’ position on the target. Moreover, a high dimensional measurement matrix is required in the CS-based method, which will lead to a heavy storage and computation burden. To solve the two problems of CS, a new method based on matrix completion is proposed in this paper. After reshaping the sparse 3D echo into a low-rank structured matrix, the full 3D echo can be recovered by solving a nuclear norm minimization problem. Then the accurate position of scatterers can be estimated by applying multi-dimensional harmonic retrieval methods to the full 3D echo. Finally, the high resolution 3D image of targets is reconstructed. The effectiveness of the method is validated by the results of comparative simulations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Bhalla, R., & Ling, H. (1996). Three-dimensional scattering center extraction using the shooting and bouncing ray technique. IEEE Transactions on Antennas and Propagation, 44(11), 1445–1453.
Cai, J., Candès, E., & Shen, Z. (2008). A singular value thresholding algorithm for matrix completion. SIAM Journal on Optimization, 20(4), 1956–1982.
Candès, E. J., & Plan, Y. (2010). Matrix completion with noise. Proceedings of the IEEE, 98(6), 925–936.
Candès, E. J., & Recht, B. (2009). Exact matrix completion via convex optimization. Foundations of Computational Mathematics, 9(6), 717–772.
Candès, E. J., & Tao, T. (2010). The power of convex relaxation: Near-optimal matrix completion. IEEE Transactions on Information Theory, 56(5), 2053–2080.
Chen, Y., & Chi, Y. (2014). Robust spectral compressed sensing via structured matrix completion. IEEE Transactions on Information Theory, 60(10), 6576–6601.
Chi, Y., Scharf, L., Pezeshki, A., & Calderbank, A. R. (2011). Sensitivity to basis mismatch in compressed sensing. IEEE Transactions on Signal Processing, 59(5), 2182–2195.
Donoho, D. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306.
Duan, G., Wang, D., Ma, X., & Su, Y. (2010). Three-dimensional imaging via wideband MIMO radar system. IEEE Geoscience and Remote Sensing Letters, 7(3), 445–449.
Ghaffari, A., Babaie-Zadeh, M., & Jutten, C. (2009). Sparse decomposition of two dimensional signals. In Proceedings of 2009 IEEE international conference on acoustics, speech and signal processing, Taipei, April, 19–24 (pp. 3157–3160).
Gu, F., Chi, L., Zhang, Q., & Zhu, F. (2013). Single snapshot imaging method in multiple-input multiple-output radar with sparse antenna array. IET Radar, Sonar and Navigation, 7(5), 535–543.
Hu, X., Tong, N., Wang, J., Ding, S., & Zhao, X. (2016a). Matrix completion-based MIMO radar imaging with sparse planar array. Signal Processing. https://doi.org/10.1016/j.sigpro.2016.07.034.
Hu, X., Tong, N., Zhang, Y., Hu, G., & He, X. (2016b). Multiple-input–multiple-output radar super-resolution three-dimensional imaging based on a dimension-reduction compressive sensing. IET Radar, Sonar and Navigation, 10(4), 757–764.
Lin, Z. C., Chen, M. M., & Ma, Y. (2013). The augmented Lagrange multiplier method for exact recovery of corrupted low rank matrices. arXiv preprint arXiv:1009.5055.
Lu, L., Xu, W., & Qiao, S. (2015). A fast SVD for multilevel block Hankel matrices with minimal memory storage. Numerical Algorithms, 69(4), 875–891.
Ma, C., Yeo, T., Tan, C., & Liu, Z. F. (2011a). Three-dimensional imaging of targets using colocated MIMO radar. IEEE Transactions on Geoscience and Remote Sensing, 49(8), 3009–3021.
Ma, C., Yeo, T., Zhao, Y., & Feng, J. (2014). MIMO radar 3D imaging based on combined amplitude and total variation cost function with sequential order one negative exponential form. IEEE Transactions on Image Processing, 23(5), 2168–2183.
Ma, S., Goldfarb, D., & Chen, L. (2011b). Fixed point and Bregman iterative methods for matrix rank minimization. Mathematical Programming, 128(1–2), 321–353.
Mayhan, J. T., Burrows, M. L., Cuomo, K. M., & Piou, J. E. (2001). High resolution 3D “snapshot” ISAR imaging and feature extraction. IEEE Transactions on Aerospace and Electronic System, 37(2), 630–642.
Mohimani, H., Babaie-Zadeh, M., & Jutten, C. (2009). A fast approach for overcomplete sparse decomposition based on smoothed L0 norm. IEEE Transactions on Signal Processing, 57(1), 289–301.
Quinquis, A., Radoi, E., & Totir, F. C. (2004). Some radar imagery results using super resolution techniques. IEEE Transactions on Antennas and Propagation, 52(5), 1–15.
Yang, J., Su, W., & Gu, H. (2014). 3D imaging using narrowband bistatic MIMO radar. Electronic Letters, 50(15), 1090–1092.
Zhang, Q., Yeo, T. S., Du, G., & Zhang, S. H. (2004). Estimation of three dimensional motion parameters in interferometric ISAR imaging. IEEE Transactions on Geoscience and Remote Sensing, 42(2), 292–300.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the National Natural Science Foundation of China (61701526, 61372166, 61571459, 61501495).
Rights and permissions
About this article
Cite this article
Hu, X., Tong, N., He, X. et al. High resolution 3D imaging in MIMO radar with sparse array. Multidim Syst Sign Process 29, 745–759 (2018). https://doi.org/10.1007/s11045-017-0531-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11045-017-0531-7