An Accelerated Backprojection Algorithm for Monostatic and Bistatic SAR Processing
"> Figure 1
<p>Subaperture summation progress. In the left panel, ‘triangle’ denotes the location where the platform transmits the signal. In the right panel, <math display="inline"> <semantics> <mover accent="true"> <msub> <mi mathvariant="bold">x</mi> <mn mathvariant="bold">1</mn> </msub> <mo stretchy="false">→</mo> </mover> </semantics> </math> and <math display="inline"> <semantics> <mover accent="true"> <msub> <mi mathvariant="bold">x</mi> <mn mathvariant="bold">2</mn> </msub> <mo stretchy="false">→</mo> </mover> </semantics> </math> denote two subapertures and <math display="inline"> <semantics> <mover accent="true"> <msub> <mi mathvariant="bold">x</mi> <mn mathvariant="bold">0</mn> </msub> <mo stretchy="false">→</mo> </mover> </semantics> </math> denote the new synthesized aperture.</p> "> Figure 2
<p>Schematic illustration of the FFBP with eight apertures and three factorization stages. In each processing stage, a common factorization factor of two is used. Narrower “new” beams are formed based on wider “old” beams formed in the previous stage. In the first stage, each of two adjacent subapertures forms a new beam, and <math display="inline"> <semantics> <mrow> <mn>2</mn> <mo>×</mo> <mn>2</mn> </mrow> </semantics> </math> beams are obtained. In the second stage, repeat the summation operation of Stage 1, and <math display="inline"> <semantics> <mrow> <mn>4</mn> <mo>×</mo> <mn>4</mn> </mrow> </semantics> </math> beams are obtained.</p> "> Figure 3
<p>Monostatic SAR case: (<b>a</b>) diagram of subaperture summation; (<b>b</b>) diagram of error analysis.</p> "> Figure 4
<p>Bistatic SAR cases: (<b>a</b>) one-stationary bistatic mode; (<b>b</b>) azimuth-invariant bistatic mode.</p> "> Figure 5
<p>Flowchart of the proposed algorithm. In this flowchart, the MoBulk_FFBP and BiBulk_FFBP are integrated together. Mo, monostatic; Bi, bistatic; FFBP, fast factorization BP.</p> "> Figure 6
<p>Comparative analysis of the residual phase error in Block_FFBP and MoBulk_FFBP. The top yellow plane indicates the residual phase error of Block_FFBP, which is equal to <math display="inline"> <semantics> <mfrac> <mi>π</mi> <mn>8</mn> </mfrac> </semantics> </math> (for a specific offset and squint angel pair, the scene size changes to ensure that the maximum residual phase error is no more than <math display="inline"> <semantics> <mfrac> <mi>π</mi> <mn>8</mn> </mfrac> </semantics> </math>). The offset axis is the range between the “new” and “old” aperture.</p> "> Figure 7
<p>Simulation of slant range error caused by different numbers of pivots and (<b>a</b>) range swaths and (<b>b</b>) azimuth swath.</p> "> Figure 8
<p>Point array simulation results: (<b>a</b>) processed by FFBP; (<b>b</b>) processed by Block_FFBP; (<b>c</b>) processed by MoBulk_FFBP. A 4 km × 4 km scene containing a <math display="inline"> <semantics> <mrow> <mn>5</mn> <mo>×</mo> <mn>5</mn> </mrow> </semantics> </math> point array is shown.</p> "> Figure 9
<p>Magnified image of a point target in the focused results. (<b>a</b>) Processing result with FFBP; (<b>b</b>) processing result with Block_FFBP. The two red arrows note that the third sidelobe of the point processed using Block_FFBP are incorrect. (<b>c</b>) Processing result with MoBulk_FFBP.</p> "> Figure 10
<p>Comparative analysis of the execution times of Block_FBP and MoBulk_FBP. (<b>a</b>) The total processing time when <math display="inline"> <semantics> <mrow> <mi>K</mi> <mo>=</mo> <mfenced separators="" open="{" close="}"> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>6</mn> </mrow> </mfenced> </mrow> </semantics> </math>. (<b>b</b>) Time costs of the factorization and residual BP.</p> "> Figure 11
<p>Focusing results of the synthesized distributed scene. Processing result with (<b>a</b>) BP, (<b>b</b>) MoBulk_FFBP, (<b>c</b>) FFBP, (<b>d</b>) Block_FFBP and (<b>e</b>) BiBulk_FFBP for azimuth-invariant bistatic SAR geometry. The red rectangle is used for focusing performance comparison, and the green rectangle is used for SNR comparison. The five sub-images at bottom-right are the red rectangle areas in (a–e).</p> "> Figure 12
<p>Monostatic spotlight image processed using MoBulk_FBP. (<b>a</b>) The monostatic spotlight image; (<b>b</b>) the optical image of the imaging area from Google Earth.</p> "> Figure 13
<p>Focusing result of point targets. The result is processed with (<b>a</b>) BiBulk_FFBP and (<b>b</b>) FBP in [<a href="#B25-remotesensing-10-00140" class="html-bibr">25</a>].</p> "> Figure 14
<p>Extended target contours. The result is processed with (<b>a</b>) BiBulk_FFBP and (<b>b</b>) FBP in [<a href="#B25-remotesensing-10-00140" class="html-bibr">25</a>].</p> "> Figure 15
<p>The SS-BiSAR image processed by the proposed algorithm. Area A and B are used for demonstrating the focusing performance. Area A contains an athletic field and some trees. Area B contains some buildings.</p> "> Figure 16
<p>Time cost of BiBulk_FFBP in different executing environments. Stages 1–4 represent the factorization step, and Stage 5 is the subsequent focusing with BP. (MT: multi-thread; ST: single-thread).</p> ">
Abstract
:1. Introduction
2. Description of the Fast BP Algorithm
2.1. Fundamental Concept
2.2. Subaperture Processing
3. Accelerated BP Algorithm
3.1. Fundamental Concept
3.2. Monostatic SAR Case
3.3. Bistatic SAR Case
3.4. Summary of the Algorithm
4. Performance Analysis
4.1. Error Analysis
4.2. Parallelization
4.3. Computational Complexity
4.4. Pivot Selection Issue
5. Simulation and Real Data Results
5.1. Monostatic SAR Case
5.2. Bistatic SAR Case
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
- Franceschetti, G.; Lanari, R. Synthetic Aperture Radar Processing; CRC Press: Boca Raton, FL, USA, 1999; pp. 32–58. [Google Scholar]
- Cumming, I.G.; Bennett, J. Digital processing of SeaSAT SAR data. In Proceedings of the IEEE International Conference on ICASSP ’79 Acoustics, Speech, and Signal Processing, Washington, DC, USA, 2–4 April 1979; pp. 710–718. [Google Scholar]
- Raney, R.K.; Runge, H.; Bamler, R.; Cumming, I.G.; Wong, F.H. Precision SAR processing using chirp scaling. IEEE Trans. Geosci. Remote Sens. 1994, 32, 786–799. [Google Scholar] [CrossRef]
- Carrara, W.G.; Majewski, R.M.; Goodman, R.S. Spotlight Synthetic Aperture Radar: Signal Processing Algorithms; Artech House: Norwood, MA, USA, 1995. [Google Scholar]
- Bamler, R.; Eineder, M. ScanSAR processing using standard high precision SAR algorithms. IEEE Trans. Geosci. Remote Sens. 1996, 34, 212–218. [Google Scholar] [CrossRef]
- Mittermayer, J.; Moreira, A. Spotlight SAR processing using the extended chirp scaling algorithm. In Proceedings of the 1997 IEEE International IGARSS’97, Remote Sensing—A Scientific Vision for Sustainable Development, Singapore, 3–8 August 1997; pp. 2021–2023. [Google Scholar]
- Loffeld, O.; Nies, H.; Peters, V.; Knedlik, S. Models and useful relations for bistatic SAR processing. IEEE Trans. Geosci. Remote Sens. 2004, 42, 2031–2038. [Google Scholar] [CrossRef]
- Natroshvili, K.; Loffeld, O.; Nies, H.; Ortiz, A.M.; Knedlik, S. Focusing of general bistatic SAR configuration data with 2-D inverse scaled FFT. IEEE Trans. Geosci. Remote Sens. 2006, 44, 2718–2727. [Google Scholar] [CrossRef]
- Wang, R.; Loffeld, O.; Nies, H.; Knedlik, S.; Ender, J.H.G. Chirp-scaling algorithm for bistatic SAR data in the constant-offset configuration. IEEE Trans. Geosci. Remote Sens. 2009, 47, 952–964. [Google Scholar] [CrossRef]
- Neo, Y.L.; Wong, F.H.; Cumming, I.G. Processing of azimuth-invariant bistatic SAR data using the range Doppler algorithm. IEEE Trans. Geosci. Remote Sens. 2008, 46, 14–21. [Google Scholar] [CrossRef]
- Bamler, R.; Meyer, F.; Liebhart, W. Processing of bistatic SAR data from quasi-stationary configurations. IEEE Trans. Geosci. Remote Sens. 2007, 45, 3350–3358. [Google Scholar] [CrossRef]
- Wong, F.H.; Cumming, I.G.; Neo, Y.L. Focusing bistatic SAR data using the nonlinear chirp scaling algorithm. IEEE Trans. Geosci. Remote Sens. 2008, 46, 2493–2505. [Google Scholar] [CrossRef]
- Qiu, X.; Hu, D.; Ding, C. An improved NLCS algorithm with capability analysis for one-stationary BiSAR. IEEE Trans. Geosci. Remote Sens. 2008, 46, 3179–3186. [Google Scholar] [CrossRef]
- Zeng, T.; Hu, C.; Wu, L.; Liu, L.; Tian, W.; Zhu, M.; Long, T. Extended NLCS algorithm of BiSAR systems with a squinted transmitter and a fixed receiver: Theory and experimental confirmation. IEEE Trans. Geosci. Remote Sens. 2013, 51, 5019–5030. [Google Scholar] [CrossRef]
- Wang, R.; Loffeld, O.; Nies, H.; Ender, J.H.G. Focusing spaceborne/airborne hybrid bistatic SAR data using wavenumber-domain algorithm. IEEE Trans. Geosci. Remote Sens. 2009, 47, 2275–2283. [Google Scholar] [CrossRef]
- Tang, J.; Deng, Y.; Wang, R.; Zhao, S.; Li, N.; Wang, W. A weighted backprojection algorithm for azimuth multichannel SAR imaging. IEEE Geosci. Remote Sens. Lett. 2016, 13, 1265–1269. [Google Scholar] [CrossRef]
- Behner, F.; Reuter, S.; Nies, H.; Loffeld, O. Synchronization and processing in the HITCHHIKER bistatic SAR experiment. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2016, 9, 1028–1035. [Google Scholar] [CrossRef]
- Yegulalp, A.F. Fast backprojection algorithm for synthetic aperture radar. In Proceedings of the The Record of the 1999 IEEE Radar Conference, Waltham, MA, USA, 22 April 1999; pp. 60–65. [Google Scholar]
- Ulander, L.M.H.; Hellsten, H.; Stenstrom, G. Synthetic-aperture radar processing using fast factorized back-projection. IEEE Trans. Geosci. Remote Sens. 2003, 39, 760–776. [Google Scholar] [CrossRef]
- Rodriguez-Cassola, M.; Baumgartner, S.V.; Krieger, G.; Moreira, A. Bistatic TerraSAR-X/F-SAR spaceborne/airborne SAR experiment: Description, data processing, and results. IEEE Trans. Geosci. Remote Sens. 2010, 48, 781–794. [Google Scholar] [CrossRef] [Green Version]
- Duque, S.; Lopez-Dekker, P.; Mallorqui, J.J. Single-pass bistatic SAR interferometry using fixed-receiver configurations: Theory and experimental validation. IEEE Trans. Geosci. Remote Sens. 2010, 48, 2740–2749. [Google Scholar] [CrossRef] [Green Version]
- Walterscheid, I.; Espeter, T.; Brenner, A.R.; Klare, J.; Ender, J.H.G.; Nies, H.; Wang, R.; Loffeld, O. Bistatic SAR experiments with PAMIR and TerraSAR-x;setup, processing, and image results. IEEE Trans. Geosci. Remote Sens. 2010, 48, 3268–3279. [Google Scholar] [CrossRef]
- Vu, V.T.; Sjogren, T.K.; Pettersson, M.I. Fast time-domain algorithms for UWB bistatic SAR processing. IEEE Trans. Aerosp. Electron. Syst. 2013, 49, 1982–1994. [Google Scholar] [CrossRef]
- Rodriguez-Cassola, M.; Prats, P.; Krieger, G.; Moreira, A. Efficient time-domain image formation with precise topography accommodation for general bistatic SAR configurations. IEEE Trans. Aerosp. Electron. Syst. 2011, 47, 2949–2966. [Google Scholar] [CrossRef] [Green Version]
- Shao, Y.; Wang, R.; Deng, Y.; Liu, Y.; Chen, R.; Liu, G.; Loffeld, O. Fast backprojection algorithm for bistatic SAR imaging. IEEE Geosci. Remote Sens. Lett. 2013, 10, 1080–1084. [Google Scholar] [CrossRef]
- Cumming, I.G.; Wong, F.H. Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation; Artech House: Norwood, MA, USA, 2005; pp. 32–58. [Google Scholar]
- Wang, R.; Loffeld, O.; Neo, Y.L.; Nies, H.; Walterscheid, I.; Espeter, T.; Klare, J.; Ender, J.H.G. Focusing bistatic SAR data in airborne/stationary configuration. IEEE Trans. Geosci. Remote Sens. 2010, 48, 452–465. [Google Scholar] [CrossRef]
- Walterscheid, I.; Ender, J.H.G.; Brenner, A.R.; Loffeld, O. Bistatic SAR processing and experiments. IEEE Trans. Geosci. Remote Sens. 2010, 44, 2710–2717. [Google Scholar] [CrossRef]
- Shi, J.; Long, X.; Zhang, X. Streaming BP for non-linear motion compensation SAR imaging based on GPU. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2013, 6, 2035–2050. [Google Scholar] [CrossRef]
- Di Bisceglie, M.; Di Santo, M.; Galdi, C.; Lanari, R.; Ranaldo, N. Synthetic aperture radar processing with GPGPU. IEEE Signal. Proc. Mag. 2010, 27, 69–78. [Google Scholar] [CrossRef]
- Kluge, T. Pricing Swing Options and Other Electricity Derivatives. Ph.D. Dissertation, St Hugh’s College, University of Oxford, Oxford, UK, 2006. Available online: http://kluge.in-chemnitz.de/docs/phd/ (accessed on 11 July 2006).
- Nies, H.; Loffeld, O.; Na, K.; Natroshvili, F. Analysis and focusing of bistatic airborne SAR data. IEEE Trans. Geosci. Remote Sens. 2007, 45, 3342–3349. [Google Scholar] [CrossRef]
- Mao, X.; Zhu, D.; Zhu, Z. Autofocus correction of ape and residual rcm in spotlight SAR polar format imagery. IEEE Trans. Aerosp. Electron. Syst. 2013, 49, 2693–2706. [Google Scholar] [CrossRef]
- Zhang, H.; Deng, Y.; Wang, R.; Li, N.; Zhao, S.; Hong, F.; Wu, L.; Loffeld, O. Spaceborne/stationary bistatic SAR imaging with TerraSAR-X as an illuminator in staring-spotlight modeAnalysis and focusing of bistatic airborne SAR data. IEEE Trans. Geosci. Remote Sens. 2007, 54, 5203–5214. [Google Scholar] [CrossRef]
Parameter | Values |
---|---|
Carrier frequency (GHz) | 9.6 |
Bandwidth (MHz) | 400 |
PRF (Hz) | 160 |
Platform height (km) | 10 |
Look angle (°) | 4 |
Velocity (m/s) | 120 |
Azimuth steering angle (°) | ±1.62 |
IRW (dB) | PSLR (dB) | ISLR (dB) | SNR (dB) | |
---|---|---|---|---|
FFBP | (Rg)0.53/(Az)0.28 | (Rg)-12.35/(Az)-13.04 | (Rg)-9.82/(Az)-9.7 | 52.61 |
Block_FFBP | (Rg)0.53/(Az)0.28 | (Rg)-12.36/(Az)-13.11 | (Rg)-6.9254/(Az)-10.1 | 50.25 |
MoBulk_FFBP | (Rg)0.53/(Az)0.28 | (Rg)-12.33/(Az)-12.99 | (Rg)-10.93/(Az)-9.58 | 53.39 |
Items | Values |
---|---|
CPU | Xeon E5620 |
Clock speed | 2.4 GHz |
Memory | 192 GB |
Parameter | Values |
---|---|
Carrier frequency (GHz) | 9.6 |
Bandwidth (MHz) | 150 |
Sampling rate (MHz) | 180 |
Pulse repetition frequency (Hz) | 8000 |
Synthetic aperture time (s) | 1.27 |
Transmitter center position (km) | (0, 400, 692.8203) |
Synchronization channel position (m) | (0, 0, 533) |
Echo channel position (m) | (0, 0, 533) |
Target for evaluation (m) | (−320, −9216, 0) |
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Zhang, H.; Tang, J.; Wang, R.; Deng, Y.; Wang, W.; Li, N. An Accelerated Backprojection Algorithm for Monostatic and Bistatic SAR Processing. Remote Sens. 2018, 10, 140. https://doi.org/10.3390/rs10010140
Zhang H, Tang J, Wang R, Deng Y, Wang W, Li N. An Accelerated Backprojection Algorithm for Monostatic and Bistatic SAR Processing. Remote Sensing. 2018; 10(1):140. https://doi.org/10.3390/rs10010140
Chicago/Turabian StyleZhang, Heng, Jiangwen Tang, Robert Wang, Yunkai Deng, Wei Wang, and Ning Li. 2018. "An Accelerated Backprojection Algorithm for Monostatic and Bistatic SAR Processing" Remote Sensing 10, no. 1: 140. https://doi.org/10.3390/rs10010140