Abstract

In this paper, a frequency-wavenumber decoupling algorithm with high-efficiency and high-precise for three-dimensional (3-D) multiple-input-multiple-output synthetic aperture radar (MIMO-SAR) imaging is proposed. Based on one-dimensional (1-D) MIMO array combined with synthetic aperture scan along another dimension, MIMO-SAR imaging scheme allows the number of array elements to be greatly reduced compared with the two-dimensional (2-D) MIMO arrays. By multi-dimensional Fourier transforming and Method of Stationary Phase (MSP), analytical expression of the object function in the frequency-wavenumber domain was derived. By further expanding the range Fourier transform factor to its Taylor series form, the range compression can be realized by a simple fast Fourier transform (FFT) without multi-dimensional interpolation. After that, a decoupling factor was multiplied to compensate for the cross-range and range coupling in frequency domain. Finally, 2-D IFFT is carried out after rearrangement in the MIMO spatial frequency to get a fully focused 3-D image. Simulation and experimental results demonstrated that the algorithm can obtain the same high-precision images as back projection (BP) algorithm, and has the same high efficiency as range migration algorithm (RMA) while avoiding cumbersome multi-dimensional interpolation. A bistatic prototype imaging system in 0.1 THz band was designed for the proof-of-principle experiments. The 3-D reconstruction results of different targets were presented to verify the theoretical results and effectiveness of the proposed algorithm for MIMO-SAR imaging.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (2)

H. Gao, C. Li, S. Zheng, S. Wu, and G. Fang, “Implementation of the Phase Shift Migration in MIMO-Sidelooking Imaging at Terahertz Band,” IEEE Sens. J. 19(20), 9384–9393 (2019).
[Crossref]

N. Mohammadian, O. Furxhi, R. Short, and R. Driggers, “Performance comparison of sparse array millimeter wave imager configurations,” Opt. Express 27(14), 19292–19308 (2019).
[Crossref]

2018 (5)

J. Gao, B. Deng, Y. Qin, H. Wang, and X. Li, “An Efficient Algorithm for MIMO Cylindrical Millimeter-Wave Holographic 3-D Imaging,” IEEE Trans. Microwave Theory Tech. 66(11), 5065–5074 (2018).
[Crossref]

J. Gao, Y. Qin, B. Deng, H. Wang, and X. Li, “Novel Efficient 3D Short-Range Imaging Algorithms for a Scanning 1D-MIMO Array,” IEEE Trans. on Image Process. 27(7), 3631–3643 (2018).
[Crossref]

J. Gao, Z. Cui, B. Cheng, Y. Qin, X. Deng, B. Deng, X. Li, and H. Wang, “Fast Three-Dimensional Image Reconstruction of a Standoff Screening System in the Terahertz Regime,” IEEE Trans. Terahertz Sci. Technol. 8(1), 38–51 (2018).
[Crossref]

D. M. Mittleman, “Twenty years of terahertz imaging [Invited],” Opt. Express 26(8), 9417–9431 (2018).
[Crossref]

K. Tan, S. Wu, X. Liu, and G. Fang, “A Modified Omega-K Algorithm for Near-Field MIMO Array-Based 3-D Reconstruction,” IEEE Geosci. Remote Sensing Lett. 15(10), 1555–1559 (2018).
[Crossref]

2017 (2)

R. Zhu, J. Zhou, G. Jiang, and Q. Fu, “Range Migration Algorithm for Near-Field MIMO-SAR Imaging,” IEEE Geosci. Remote Sensing Lett. 14(12), 2280–2284 (2017).
[Crossref]

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

2016 (1)

2014 (1)

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
[Crossref]

2012 (4)

F. Qi, I. Ocket, D. Schreurs, and B. Nauwelaers, “A system-level simulator for indoor mmW SAR imaging and its applications,” Opt. Express 20(21), 23811–23820 (2012).
[Crossref]

S. S. Ahmed, A. Schiessl, F. Gumbmann, M. Tiebout, S. Methfessel, and L. Schmidt, “Advanced microwave imaging,” IEEE Microwave 13(6), 26–43 (2012).
[Crossref]

S. M. Gu, C. Li, X. Gao, Z. Y. Sun, and G. Y. Fang, “Terahertz aperture synthesized imaging with fan-beam scanning for personnel screening,” IEEE Trans. Microwave Theory Tech. 60(12), 3877–3885 (2012).
[Crossref]

X. Zhuge and A. G. Yarovoy, “Three-Dimensional Near-Field MIMO Array Imaging Using Range Migration Techniques,” IEEE Trans. on Image Process. 21(6), 3026–3033 (2012).
[Crossref]

2011 (4)

S. S. Ahmed, A. Schiessl, and L.-P. Schmidt, “A novel fully electronic active real-time imager based on a planar multistatic sparse array,” IEEE Trans. Microwave Theory Tech. 59(12), 3567–3576 (2011).
[Crossref]

F. Gumbmann and L. Schmidt, “Millimeter-wave imaging with optimized sparse periodic array for short-range applications,” IEEE Trans. Geosci. Remote Sensing 49(10), 3629–3638 (2011).
[Crossref]

S. Yeom, D. Lee, J. Son, M. Jung, Y. Jang, S. Jung, and S. Lee, “Real-time outdoor concealed-object detection with passive millimeter wave imaging,” Opt. Express 19(3), 2530–2536 (2011).
[Crossref]

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

2010 (2)

C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, “Millimeter-wave compressive holography,” Appl. Opt. 49(19), E67–E82 (2010).
[Crossref]

X. Zhuge, A. G. Yarovoy, T. Savelyev, and L. Ligthart, “Modified Kirchhoff Migration for UWB MIMO Array-Based Radar Imaging,” IEEE Trans. Geosci. Remote Sensing 48(6), 2692–2703 (2010).
[Crossref]

2009 (1)

2008 (1)

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
[Crossref]

2007 (1)

R. Appleby and H. B. Wallace, “Standoff detection of weapons and contraband in the 100 GHz to 1 THz region,” IEEE Trans. Antennas Propag. 55(11), 2944–2956 (2007).
[Crossref]

2003 (1)

2001 (1)

D. M. Sheen, D. L. McMakin, and T. E. Hall, “Three-dimensional millimeter-wave imaging for concealed weapon detection,” IEEE Trans. Microwave Theory Tech. 49(9), 1581–1592 (2001).
[Crossref]

1971 (1)

N. H. Farhat and W. R. Guard, “Millimeter wave holographic imaging of concealed weapons,” Proc. IEEE 59(9), 1383–1384 (1971).
[Crossref]

Agostini, P.

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

Ahmed, S. S.

S. S. Ahmed, A. Schiessl, F. Gumbmann, M. Tiebout, S. Methfessel, and L. Schmidt, “Advanced microwave imaging,” IEEE Microwave 13(6), 26–43 (2012).
[Crossref]

S. S. Ahmed, A. Schiessl, and L.-P. Schmidt, “A novel fully electronic active real-time imager based on a planar multistatic sparse array,” IEEE Trans. Microwave Theory Tech. 59(12), 3567–3576 (2011).
[Crossref]

Alderman, B.

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
[Crossref]

Alexander, N. E.

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
[Crossref]

Allona, F.

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
[Crossref]

Appleby, R.

R. Appleby and H. B. Wallace, “Standoff detection of weapons and contraband in the 100 GHz to 1 THz region,” IEEE Trans. Antennas Propag. 55(11), 2944–2956 (2007).
[Crossref]

Baccouche, B.

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

Bauer, M.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Bianca Jackson, J.

Bolivar, P. H.

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Boppel, S.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Bowen, J. W.

Brady, D. J.

Bryllert, T.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
[Crossref]

Chattopadhyay, G.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
[Crossref]

Cheng, B.

J. Gao, Z. Cui, B. Cheng, Y. Qin, X. Deng, B. Deng, X. Li, and H. Wang, “Fast Three-Dimensional Image Reconstruction of a Standoff Screening System in the Terahertz Regime,” IEEE Trans. Terahertz Sci. Technol. 8(1), 38–51 (2018).
[Crossref]

Choi, K.

Citrin, D. S.

Collins, H. D.

H. D. Collins, D. L. McMakin, T. E. Hall, and R. P. Gribble, “Real-time holographic surveillance system,” U.S. Patent 5455590, Oct. 3, 1995.

Cooper, K. B.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
[Crossref]

Cui, Z.

J. Gao, Z. Cui, B. Cheng, Y. Qin, X. Deng, B. Deng, X. Li, and H. Wang, “Fast Three-Dimensional Image Reconstruction of a Standoff Screening System in the Terahertz Regime,” IEEE Trans. Terahertz Sci. Technol. 8(1), 38–51 (2018).
[Crossref]

Cull, C. F.

Cumming, I. G.

I. G. Cumming and F. H. Wong, Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation. sArtech House, Norwood, MA, USA, 2004

Deng, B.

J. Gao, Y. Qin, B. Deng, H. Wang, and X. Li, “Novel Efficient 3D Short-Range Imaging Algorithms for a Scanning 1D-MIMO Array,” IEEE Trans. on Image Process. 27(7), 3631–3643 (2018).
[Crossref]

J. Gao, Z. Cui, B. Cheng, Y. Qin, X. Deng, B. Deng, X. Li, and H. Wang, “Fast Three-Dimensional Image Reconstruction of a Standoff Screening System in the Terahertz Regime,” IEEE Trans. Terahertz Sci. Technol. 8(1), 38–51 (2018).
[Crossref]

J. Gao, B. Deng, Y. Qin, H. Wang, and X. Li, “An Efficient Algorithm for MIMO Cylindrical Millimeter-Wave Holographic 3-D Imaging,” IEEE Trans. Microwave Theory Tech. 66(11), 5065–5074 (2018).
[Crossref]

Deng, X.

J. Gao, Z. Cui, B. Cheng, Y. Qin, X. Deng, B. Deng, X. Li, and H. Wang, “Fast Three-Dimensional Image Reconstruction of a Standoff Screening System in the Terahertz Regime,” IEEE Trans. Terahertz Sci. Technol. 8(1), 38–51 (2018).
[Crossref]

Dengler, R. J.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
[Crossref]

Dong, J.

Driggers, R.

Fang, G.

H. Gao, C. Li, S. Zheng, S. Wu, and G. Fang, “Implementation of the Phase Shift Migration in MIMO-Sidelooking Imaging at Terahertz Band,” IEEE Sens. J. 19(20), 9384–9393 (2019).
[Crossref]

K. Tan, S. Wu, X. Liu, and G. Fang, “A Modified Omega-K Algorithm for Near-Field MIMO Array-Based 3-D Reconstruction,” IEEE Geosci. Remote Sensing Lett. 15(10), 1555–1559 (2018).
[Crossref]

Fang, G. Y.

S. M. Gu, C. Li, X. Gao, Z. Y. Sun, and G. Y. Fang, “Terahertz aperture synthesized imaging with fan-beam scanning for personnel screening,” IEEE Trans. Microwave Theory Tech. 60(12), 3877–3885 (2012).
[Crossref]

Farhat, N. H.

N. H. Farhat and W. R. Guard, “Millimeter wave holographic imaging of concealed weapons,” Proc. IEEE 59(9), 1383–1384 (1971).
[Crossref]

Friederich, F.

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Frijlink, P.

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
[Crossref]

Fu, Q.

R. Zhu, J. Zhou, G. Jiang, and Q. Fu, “Range Migration Algorithm for Near-Field MIMO-SAR Imaging,” IEEE Geosci. Remote Sensing Lett. 14(12), 2280–2284 (2017).
[Crossref]

Furxhi, O.

Gao, H.

H. Gao, C. Li, S. Zheng, S. Wu, and G. Fang, “Implementation of the Phase Shift Migration in MIMO-Sidelooking Imaging at Terahertz Band,” IEEE Sens. J. 19(20), 9384–9393 (2019).
[Crossref]

Gao, J.

J. Gao, Z. Cui, B. Cheng, Y. Qin, X. Deng, B. Deng, X. Li, and H. Wang, “Fast Three-Dimensional Image Reconstruction of a Standoff Screening System in the Terahertz Regime,” IEEE Trans. Terahertz Sci. Technol. 8(1), 38–51 (2018).
[Crossref]

J. Gao, B. Deng, Y. Qin, H. Wang, and X. Li, “An Efficient Algorithm for MIMO Cylindrical Millimeter-Wave Holographic 3-D Imaging,” IEEE Trans. Microwave Theory Tech. 66(11), 5065–5074 (2018).
[Crossref]

J. Gao, Y. Qin, B. Deng, H. Wang, and X. Li, “Novel Efficient 3D Short-Range Imaging Algorithms for a Scanning 1D-MIMO Array,” IEEE Trans. on Image Process. 27(7), 3631–3643 (2018).
[Crossref]

Gao, X.

S. M. Gu, C. Li, X. Gao, Z. Y. Sun, and G. Y. Fang, “Terahertz aperture synthesized imaging with fan-beam scanning for personnel screening,” IEEE Trans. Microwave Theory Tech. 60(12), 3877–3885 (2012).
[Crossref]

Gill, J.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
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Giovanacci, D.

Gonzalo, R.

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
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Gribble, R. P.

H. D. Collins, D. L. McMakin, T. E. Hall, and R. P. Gribble, “Real-time holographic surveillance system,” U.S. Patent 5455590, Oct. 3, 1995.

Gu, S. M.

S. M. Gu, C. Li, X. Gao, Z. Y. Sun, and G. Y. Fang, “Terahertz aperture synthesized imaging with fan-beam scanning for personnel screening,” IEEE Trans. Microwave Theory Tech. 60(12), 3877–3885 (2012).
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N. H. Farhat and W. R. Guard, “Millimeter wave holographic imaging of concealed weapons,” Proc. IEEE 59(9), 1383–1384 (1971).
[Crossref]

Gumbmann, F.

S. S. Ahmed, A. Schiessl, F. Gumbmann, M. Tiebout, S. Methfessel, and L. Schmidt, “Advanced microwave imaging,” IEEE Microwave 13(6), 26–43 (2012).
[Crossref]

F. Gumbmann and L. Schmidt, “Millimeter-wave imaging with optimized sparse periodic array for short-range applications,” IEEE Trans. Geosci. Remote Sensing 49(10), 3629–3638 (2011).
[Crossref]

Hagelen, M.

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
[Crossref]

Hall, T. E.

D. M. Sheen, D. L. McMakin, and T. E. Hall, “Three-dimensional millimeter-wave imaging for concealed weapon detection,” IEEE Trans. Microwave Theory Tech. 49(9), 1581–1592 (2001).
[Crossref]

H. D. Collins, D. L. McMakin, T. E. Hall, and R. P. Gribble, “Real-time holographic surveillance system,” U.S. Patent 5455590, Oct. 3, 1995.

Han, F.

H. Liu, Y. X. Zhang, Z. J. Long, F. Han, and Q. H. Liu, “Three-dimensional reverse-time migration applied to a MIMO GPR system for subsurface imaging,” in Proc. Int. Conf. Ground Penetrating Radar, Jun. 2016, pp. 1–4.

Henneberger, R.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Hils, B.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Horisaki, R.

Huhn, A. K.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Ibanzez, V.

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
[Crossref]

Inoue, H.

Jang, Y.

Jiang, G.

R. Zhu, J. Zhou, G. Jiang, and Q. Fu, “Range Migration Algorithm for Near-Field MIMO-SAR Imaging,” IEEE Geosci. Remote Sensing Lett. 14(12), 2280–2284 (2017).
[Crossref]

Jonuscheit, J.

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

Jung, M.

Jung, S.

Kahl, M.

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

Kawase, K.

Keil, A.

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Krozer, V.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Langford, M.

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
[Crossref]

Lee, C.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
[Crossref]

Lee, D.

Lee, S.

Li, C.

H. Gao, C. Li, S. Zheng, S. Wu, and G. Fang, “Implementation of the Phase Shift Migration in MIMO-Sidelooking Imaging at Terahertz Band,” IEEE Sens. J. 19(20), 9384–9393 (2019).
[Crossref]

S. M. Gu, C. Li, X. Gao, Z. Y. Sun, and G. Y. Fang, “Terahertz aperture synthesized imaging with fan-beam scanning for personnel screening,” IEEE Trans. Microwave Theory Tech. 60(12), 3877–3885 (2012).
[Crossref]

Li, X.

J. Gao, B. Deng, Y. Qin, H. Wang, and X. Li, “An Efficient Algorithm for MIMO Cylindrical Millimeter-Wave Holographic 3-D Imaging,” IEEE Trans. Microwave Theory Tech. 66(11), 5065–5074 (2018).
[Crossref]

J. Gao, Z. Cui, B. Cheng, Y. Qin, X. Deng, B. Deng, X. Li, and H. Wang, “Fast Three-Dimensional Image Reconstruction of a Standoff Screening System in the Terahertz Regime,” IEEE Trans. Terahertz Sci. Technol. 8(1), 38–51 (2018).
[Crossref]

J. Gao, Y. Qin, B. Deng, H. Wang, and X. Li, “Novel Efficient 3D Short-Range Imaging Algorithms for a Scanning 1D-MIMO Array,” IEEE Trans. on Image Process. 27(7), 3631–3643 (2018).
[Crossref]

Ligthart, L.

X. Zhuge, A. G. Yarovoy, T. Savelyev, and L. Ligthart, “Modified Kirchhoff Migration for UWB MIMO Array-Based Radar Imaging,” IEEE Trans. Geosci. Remote Sensing 48(6), 2692–2703 (2010).
[Crossref]

Lim, S.

Limiti, E.

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
[Crossref]

Lisauskas, A.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Liu, H.

H. Liu, Y. X. Zhang, Z. J. Long, F. Han, and Q. H. Liu, “Three-dimensional reverse-time migration applied to a MIMO GPR system for subsurface imaging,” in Proc. Int. Conf. Ground Penetrating Radar, Jun. 2016, pp. 1–4.

Liu, Q. H.

H. Liu, Y. X. Zhang, Z. J. Long, F. Han, and Q. H. Liu, “Three-dimensional reverse-time migration applied to a MIMO GPR system for subsurface imaging,” in Proc. Int. Conf. Ground Penetrating Radar, Jun. 2016, pp. 1–4.

Liu, X.

K. Tan, S. Wu, X. Liu, and G. Fang, “A Modified Omega-K Algorithm for Near-Field MIMO Array-Based 3-D Reconstruction,” IEEE Geosci. Remote Sensing Lett. 15(10), 1555–1559 (2018).
[Crossref]

Llombart, N.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
[Crossref]

Locquet, A.

Loffler, T.

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Long, Z. J.

H. Liu, Y. X. Zhang, Z. J. Long, F. Han, and Q. H. Liu, “Three-dimensional reverse-time migration applied to a MIMO GPR system for subsurface imaging,” in Proc. Int. Conf. Ground Penetrating Radar, Jun. 2016, pp. 1–4.

Mait, J. N.

Marks, D. L.

Mattheiss, M.

McMakin, D. L.

D. M. Sheen, D. L. McMakin, and T. E. Hall, “Three-dimensional millimeter-wave imaging for concealed weapon detection,” IEEE Trans. Microwave Theory Tech. 49(9), 1581–1592 (2001).
[Crossref]

H. D. Collins, D. L. McMakin, T. E. Hall, and R. P. Gribble, “Real-time holographic surveillance system,” U.S. Patent 5455590, Oct. 3, 1995.

Mehdi, I.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
[Crossref]

Melis, M.

Meng, F. Z.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Methfessel, S.

S. S. Ahmed, A. Schiessl, F. Gumbmann, M. Tiebout, S. Methfessel, and L. Schmidt, “Advanced microwave imaging,” IEEE Microwave 13(6), 26–43 (2012).
[Crossref]

Mittleman, D. M.

Mohammadian, N.

Mohammadzadeh, S.

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

Nauwelaers, B.

Ocket, I.

Ogawa, Y.

Platt, D.

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
[Crossref]

Qi, F.

Qin, Y.

J. Gao, Z. Cui, B. Cheng, Y. Qin, X. Deng, B. Deng, X. Li, and H. Wang, “Fast Three-Dimensional Image Reconstruction of a Standoff Screening System in the Terahertz Regime,” IEEE Trans. Terahertz Sci. Technol. 8(1), 38–51 (2018).
[Crossref]

J. Gao, B. Deng, Y. Qin, H. Wang, and X. Li, “An Efficient Algorithm for MIMO Cylindrical Millimeter-Wave Holographic 3-D Imaging,” IEEE Trans. Microwave Theory Tech. 66(11), 5065–5074 (2018).
[Crossref]

J. Gao, Y. Qin, B. Deng, H. Wang, and X. Li, “Novel Efficient 3D Short-Range Imaging Algorithms for a Scanning 1D-MIMO Array,” IEEE Trans. on Image Process. 27(7), 3631–3643 (2018).
[Crossref]

Roskos, H. G.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Sauer-Greff, W.

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

Savelyev, T.

X. Zhuge, A. G. Yarovoy, T. Savelyev, and L. Ligthart, “Modified Kirchhoff Migration for UWB MIMO Array-Based Radar Imaging,” IEEE Trans. Geosci. Remote Sensing 48(6), 2692–2703 (2010).
[Crossref]

Schiessl, A.

S. S. Ahmed, A. Schiessl, F. Gumbmann, M. Tiebout, S. Methfessel, and L. Schmidt, “Advanced microwave imaging,” IEEE Microwave 13(6), 26–43 (2012).
[Crossref]

S. S. Ahmed, A. Schiessl, and L.-P. Schmidt, “A novel fully electronic active real-time imager based on a planar multistatic sparse array,” IEEE Trans. Microwave Theory Tech. 59(12), 3567–3576 (2011).
[Crossref]

Schikora, M.

N. E. Alexander, B. Alderman, F. Allona, P. Frijlink, R. Gonzalo, M. Hagelen, V. Ibanzez, M. Langford, E. Limiti, D. Platt, M. Schikora, H. Wang, and M. Weber, “TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks,”Proc. SPIE 9078,907802 (2014).
[Crossref]

Schlecht, E.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
[Crossref]

Schmidt, L.

S. S. Ahmed, A. Schiessl, F. Gumbmann, M. Tiebout, S. Methfessel, and L. Schmidt, “Advanced microwave imaging,” IEEE Microwave 13(6), 26–43 (2012).
[Crossref]

F. Gumbmann and L. Schmidt, “Millimeter-wave imaging with optimized sparse periodic array for short-range applications,” IEEE Trans. Geosci. Remote Sensing 49(10), 3629–3638 (2011).
[Crossref]

Schmidt, L.-P.

S. S. Ahmed, A. Schiessl, and L.-P. Schmidt, “A novel fully electronic active real-time imager based on a planar multistatic sparse array,” IEEE Trans. Microwave Theory Tech. 59(12), 3567–3576 (2011).
[Crossref]

Schreurs, D.

Sheen, D. M.

D. M. Sheen, D. L. McMakin, and T. E. Hall, “Three-dimensional millimeter-wave imaging for concealed weapon detection,” IEEE Trans. Microwave Theory Tech. 49(9), 1581–1592 (2001).
[Crossref]

Short, R.

Siegel, P. H.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
[Crossref]

Skalare, A.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microwave Theory Tech. 56(12), 2771–2778 (2008).
[Crossref]

Son, J.

Spickermann, G.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Spiegel, W. V.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Sun, Z. Y.

S. M. Gu, C. Li, X. Gao, Z. Y. Sun, and G. Y. Fang, “Terahertz aperture synthesized imaging with fan-beam scanning for personnel screening,” IEEE Trans. Microwave Theory Tech. 60(12), 3877–3885 (2012).
[Crossref]

Tan, K.

K. Tan, S. Wu, X. Liu, and G. Fang, “A Modified Omega-K Algorithm for Near-Field MIMO Array-Based 3-D Reconstruction,” IEEE Geosci. Remote Sensing Lett. 15(10), 1555–1559 (2018).
[Crossref]

Thomson, M. D.

F. Friederich, W. V. Spiegel, M. Bauer, F. Z. Meng, M. D. Thomson, S. Boppel, A. Lisauskas, B. Hils, V. Krozer, A. Keil, T. Loffler, R. Henneberger, A. K. Huhn, G. Spickermann, P. H. Bolivar, and H. G. Roskos, “THz Active imaging systems with Real-time Capabilities,” IEEE Trans. Terahertz Sci. Technol. 1(1), 183–200 (2011).
[Crossref]

Tiebout, M.

S. S. Ahmed, A. Schiessl, F. Gumbmann, M. Tiebout, S. Methfessel, and L. Schmidt, “Advanced microwave imaging,” IEEE Microwave 13(6), 26–43 (2012).
[Crossref]

Urbansky, R.

B. Baccouche, P. Agostini, S. Mohammadzadeh, M. Kahl, C. Weisenstein, J. Jonuscheit, A. Keil, T. Loffler, W. Sauer-Greff, R. Urbansky, P. H. Bolivar, and F. Friederich, “Three-dimensional terahertz imaging with sparse multistatic line arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–11 (2017).
[Crossref]

Walker, G. C.

Wallace, H. B.

R. Appleby and H. B. Wallace, “Standoff detection of weapons and contraband in the 100 GHz to 1 THz region,” IEEE Trans. Antennas Propag. 55(11), 2944–2956 (2007).
[Crossref]

Wang, H.

J. Gao, B. Deng, Y. Qin, H. Wang, and X. Li, “An Efficient Algorithm for MIMO Cylindrical Millimeter-Wave Holographic 3-D Imaging,” IEEE Trans. Microwave Theory Tech. 66(11), 5065–5074 (2018).
[Crossref]

J. Gao, Z. Cui, B. Cheng, Y. Qin, X. Deng, B. Deng, X. Li, and H. Wang, “Fast Three-Dimensional Image Reconstruction of a Standoff Screening System in the Terahertz Regime,” IEEE Trans. Terahertz Sci. Technol. 8(1), 38–51 (2018).
[Crossref]

J. Gao, Y. Qin, B. Deng, H. Wang, and X. Li, “Novel Efficient 3D Short-Range Imaging Algorithms for a Scanning 1D-MIMO Array,” IEEE Trans. on Image Process. 27(7), 3631–3643 (2018).
[Crossref]

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H. Gao, C. Li, S. Zheng, S. Wu, and G. Fang, “Implementation of the Phase Shift Migration in MIMO-Sidelooking Imaging at Terahertz Band,” IEEE Sens. J. 19(20), 9384–9393 (2019).
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X. Zhuge, A. G. Yarovoy, T. Savelyev, and L. Ligthart, “Modified Kirchhoff Migration for UWB MIMO Array-Based Radar Imaging,” IEEE Trans. Geosci. Remote Sensing 48(6), 2692–2703 (2010).
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[Crossref]

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[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

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[Crossref]

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[Crossref]

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[Crossref]

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I. G. Cumming and F. H. Wong, Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation. sArtech House, Norwood, MA, USA, 2004

H. Liu, Y. X. Zhang, Z. J. Long, F. Han, and Q. H. Liu, “Three-dimensional reverse-time migration applied to a MIMO GPR system for subsurface imaging,” in Proc. Int. Conf. Ground Penetrating Radar, Jun. 2016, pp. 1–4.

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Figures (9)

Fig. 1.
Fig. 1. Imaging system geometry of the MIMO-SAR configuration.
Fig. 2.
Fig. 2. MIMO-SAR set up used in the numerical simulation, with the 1-D MIMO array in front of nine distributed point scatters at a distance of 1 m.
Fig. 3.
Fig. 3. Horn antenna for simulation and experiment with detailed dimensions.
Fig. 4.
Fig. 4. Approximation error analysis from (16) to (26). (a) Minimum relative error along ${k_{y}}$ at ${k_{xt}}$ = 0 and ${k_{xr}}$ = 0 for different k. (b) Maximum relative error along ${k_{y}}$ at $\left|k_{x t}\right|=k_{x t_{m}}$ and $\left|k_{x r}\right|=k_{x r_{m}}$ for different k.
Fig. 5.
Fig. 5. Imaging results of the simulation shown in Fig. 2 with the MIMO-SAR configuration. (a) 3-D image by BP. (b) 3-D image by MIMO-SAR RMA. (c) 3-D image by the proposed algorithm. (d) Front view of the image obtained by BP.(e) Front view of the image obtained by MIMO-SAR RMA. (f) Front view of the image obtained by the proposed algorithm. (g) Side view by BP. (h) Side view by MIMO-SAR RMA. (i) Side view by the proposed algorithm. The front/side views are obtained by maximum projection of the 3-D image on to the x-y and z-y planes, respectively.
Fig. 6.
Fig. 6. PSFs of different algorithms.
Fig. 7.
Fig. 7. Photograph of the 2-D-scanner of the experiment setup.
Fig. 8.
Fig. 8. Adaptive focusing experiment 1 for three targets distributed in different ranges. (a) Photo of front view of three targets located in different ranges. (b)Adaptive focusing result reconstructed by BP algorithm. (c) Adaptive focusing result reconstructed RMA algorithm. (d) Adaptive focusing result reconstructed by the proposed algorithm.
Fig. 9.
Fig. 9. Adaptive focusing experiment 2 for three targets distributed in different ranges. (a) Photo of front view of three targets located in different ranges. (b)Adaptive focusing result reconstructed by BP algorithm. (c) Adaptive focusing result reconstructed RMA algorithm. (d) Adaptive focusing result reconstructed by the proposed algorithm.

Tables (4)

Tables Icon

Table 1. Overview of the proposed algorithm

Tables Icon

Table 2. Computational cost of the proposed algorithm

Tables Icon

Table 3. Comparison on computational times of different algorithm of the simulation

Tables Icon

Table 4. Comparison on computational times of different algorithm of the experiments

Equations (35)

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s ( x t , x r , y , z 0 , k ) = D G t O ( x , y , z ) G r d x d y d z
G t = exp ( j k R t ) 4 π R t
G r = exp ( j k R r ) 4 π R r
R t = ( x t x ) 2 + ( y y ) 2 + ( z 0 z ) 2
R r = ( x r x ) 2 + ( y y ) 2 + ( z 0 z ) 2
s ( x t , x r , y , z 0 , k ) = D O ( x , y , z ) exp ( j k ( R t + R r ) ) d x d y d z
s ~ ( k x t , k x r , k y , z 0 , k ) = D O ( x , y , z ) E ( k x t , k x r , k y , k ) d x d y d z
E ( k x t , k x r , k y , k ) = E ( k x t , y , k ) E ( k x r , y , k ) exp ( j k y y ) d y
E ( k x t , y , k ) = exp ( j k R t ) exp ( j k x t x t ) d x t
E ( k x r , y , k ) = exp ( j k R r ) exp ( j k x r x r ) d x r
E ( k x t , y , k ) = exp ( j k x t x j k 2 k x t 2 ( y y ) 2 + ( z 0 z ) 2 )
E ( k x r , y , k ) = exp ( j k x r x j k 2 k x r 2 ( y y ) 2 + ( z 0 z ) 2 )
E ( k x t , k x r , k y , k ) = exp ( j ( k x t + k x r ) x ) exp ( j ( k 2 k x t 2 + k 2 k x r 2 ) ( y y ) 2 + ( z 0 z ) 2 ) exp ( j k y y ) d y
E ( k x t , k x r , k y , k ) = exp ( j ( k x t + k x r ) x j k y y ) exp ( j ( ( k 2 k x t 2 + k 2 k x r 2 ) 2 k y 2 ) ( z z 0 ) )
s ~ ( k x t , k x r , k y , z 0 , k ) = D O ( x , y , z ) exp ( j ( k x t + k x r ) x j k y y ) exp ( j ( ( k 2 k x t 2 + k 2 k x r 2 ) 2 k y 2 ) ( z z 0 ) ) d x d y d z
{ k ^ x = k x t + k x r k ^ y  =  k y k ^ z = ( k 2 k x t 2 + k 2 k x r 2 ) 2 k y 2
s ~ ( k x t , k x r , k y , k ) = F ( k ^ x , k ^ y , k ^ z )
F ( k ^ x , k ^ y , k ^ z )  =  D O ( x , y , z ) exp ( j k ^ x x j k ^ y y j k ^ z z ) d x d y d z
s ~ ( k x t , k x r , k y , k )  =  s ~ ( k x t , k x r , k y , z 0 , k ) exp ( j k ^ z z 0 )
F ( k ^ x , k ^ y , z ) = s ~ ( k x t , k x r , k y , k ) exp ( j k ^ z z ) d k ^ z
a 1 = 2 k + k k 2 k 2 x t k 2 k 2 x r + k k 2 k 2 x r k 2 k 2 x t ( k 2 k x t 2 + k 2 k x r 2 ) 2 k y 2
F ( k ^ x , k ^ y , z ) = s ~ ( k x t , k x r , k y , k ) exp ( j k ^ z z ) d k
s ~ ( k x t , k x r , k y , k ) = s ~ ( k x t , k x r , k y , k ) a 1
k ^ z = 2 k 2 k x t 2 k x r 2 + 2 k 2 1 k x t 2 + k x r 2 k 2 + k x t 2 k x r 2 k 4 k y 2
1 k x t 2 + k x r 2 k 2 + k x t 2 k x r 2 k 4 = 1 k x t 2 + k x r 2 2 k 2 ( k x t 2 k x r 2 ) 2 8 k 4 + ( k x t 2 + k x r 2 ) k x t 2 k x r 2 4 k 6 k x t 4 k x r 4 8 k 8 + o [ ( k x t 2 + k x r 2 k 2 + k x t 2 k x r 2 k 4 ) 3 ]
k ^ z 2 k k 1
k 1 = 2 ( k x t 2 + k x r 2 ) k 2 y 4 k c + 8 ( k x t 4 + k x r 4 ) + 4 ( k x t 2 + k x r 2 ) k 2 y + k 4 y 64 k c 3
F ( k ^ x , k ^ y , z ) = s ~ ( k x t , k x r , k y , k ) exp ( j 2 k z ) d k exp ( j k 1 z )
O ( x , y , z ) = F ( k ^ x , k ^ y , z ) exp ( j k ^ x x ) exp ( j k ^ y y ) d k ^ x d k ^ y
{ d x t λ min ( L x t + D x ) 2 / 4 + z 0 2 L x t + D x d x r λ min ( L x r + D x ) 2 / 4 + z 0 2 L x r + D x d y λ min min ( 4 sin ( θ H B W / 2 ) , 2 D y z 0 )
{ δ x = 0 .886 λ c z L t x + L r x δ y = 0 .443 λ c z L y δ z = 0 .44 c B
C p r o p o s e d = 5 N f N x t N x r N y log 2 ( N f N x t N x r N y )  + 4 N x t N x r N y ( 1 .5 N f  + 2 N z ) + 5 N z N x N y log 2 ( N x N y )  - 2 N z N x N y F L O P
C B P = 5 N x t N x r N y N f log 2 N f + 12 N x t N x r N y N x N y N z F L O P
C R M A = 5 N x t N x r N y [ N f log 2 ( N x t N x r N y ) + 1.2 N f + 1.6 N z ] + 5 N x N z N y [ log ( N x N z N y ) 0.4 ] FLOP
R E ( k x t , k x r , k y , k ) = | k ^ z ( 2 k k 1 ) k ^ z |

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