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Uniqueness in inverse acoustic and electromagnetic scattering with phaseless near-field data at a fixed frequency
Statistical characterization of scattering delay in synthetic aperture radar imaging
Department of Mathematics, North Carolina State University, Campus Box 8205, Raleigh, NC 27695, USA |
Distinguishing between the instantaneous and delayed scatterers in synthetic aperture radar (SAR) images is important for target identification and characterization. To perform this task, one can use the autocorrelation analysis of coordinate-delay images. However, due to the range-delay ambiguity the difference in the correlation properties between the instantaneous and delayed targets may be small. Moreover, the reliability of discrimination is affected by speckle, which is ubiquitous in SAR images, and requires statistical treatment.
Previously, we have developed a maximum likelihood based approach for discriminating between the instantaneous and delayed targets in SAR images. To test it, we employed simple statistical models. They allowed us to simulate ensembles of images that depend on various parameters, including aperture width and target contrast.
In the current paper, we enhance our previously developed methodology by establishing confidence levels for the discrimination between the instantaneous and delayed scatterers. Our procedure takes into account the difference in thresholds for different target contrasts without making any assumptions about the statistics of those contrasts.
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J. C. Allen and S. L. Hobbs,
Spectral estimation of non-stationary white noise, J. Franklin Inst. B, 334 (1997), 99-116.
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M. Basu,
Gaussian-based edge-detection methods–a survey, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 32 (2002), 252-260.
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S. Chen and H. Wang, SAR target recognition based on deep learning, 2014 International Conference on Data Science and Advanced Analytics (DSAA), IEEE, Shanghai, China, 2014, 541–547.
doi: 10.1109/DSAA.2014.7058124. |
[7] |
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[8] |
M. Cheney and B. Borden, Fundamentals of Radar Imaging, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 79, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2009.
doi: 10.1137/1.9780898719291. |
[9] |
F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, (eds.). NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/, Release 1.0.24 of 2019-09-15. Google Scholar |
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M. Ferrara, A. Homan and M. Cheney, Hyperspectral SAR, IEEE Trans. Geoscience and Remote Sensing, 55 (2017), 1682–1695.
doi: 10.1109/TGRS.2016.2629265. |
[11] |
J. Garnier and K. Sølna, A multiscale approach to synthetic aperture radar in dispersive random media, Inverse Problems, 29 (2013), 054006, (18pp).
doi: 10.1088/0266-5611/29/5/054006. |
[12] |
M. Gilman and S. Tsynkov, Mathematical analysis of SAR imaging through a turbulent ionosphere, Application of Mathematics in Technical and Natural Sciences: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences– AMiTaNS'17, Vol. 1895, AIP Conference Proceedings, Albena, Bulgaria, 2017, 020003 (23pp).
doi: 10.1063/1.5007357. |
[13] |
M. Gilman, E. Smith and S. Tsynkov, Transionospheric Synthetic Aperture Imaging, Applied and Numerical Harmonic Analysis, Birkhäuser/Springer, Cham, Switzerland, 2017.
doi: 10.1007/978-3-319-52127-5. |
[14] |
M. Gilman and S. Tsynkov, Detection of delayed target response in SAR, Inverse Problems, 35 (2019), 085005, (38pp).
doi: 10.1088/1361-6420/ab1c80. |
[15] |
J. W. Goodman, Statistical properties of laser speckle patterns, Topics in Applied Physics: Laser Speckle and Related Phenomena (ed. J. C. Dainty, ), Vol. 9, Springer-Verlag, Berlin, 1984, 9–75. Google Scholar |
[16] |
T. Hastie, R. Tibshirani and J. Friedman, The Elements Of Statistical Learning. Data Mining, Inference, and Prediction, 2$^nd$ edition, Springer Series in Statistics, Springer, New York, 2009.
doi: 10.1007/978-0-387-84858-7. |
[17] |
A. Krizhevsky, I. Sutskever and G. E. Hinton, ImageNet classification with deep convolutional neural networks, Advances in Neural Information Processing Systems 25, Curran Associates, Inc., 2012, 1097–1105. Google Scholar |
[18] |
D. Marr and E. Hildreth,
Theory of edge detection, Proc. R. Soc. Lond. B, 207 (1980), 187-217.
doi: 10.1098/rspb.1980.0020. |
[19] |
W. Mendenhall and R. L. Scheaffer, Mathematical Statistics with Applications, Duxbury Press, North Scituate, Mass., 1973.
![]() |
[20] |
F. J. Meyer, K. Chotoo, S. D. Chotoo, B. D. Huxtable and C. S. Carrano,
The influence of equatorial scintillation on L-band SAR image quality and phase, IEEE Trans. Geoscience and Remote Sensing, 54 (2016), 869-880.
doi: 10.1109/TGRS.2015.2468573. |
[21] |
D. Mishkin, N. Sergievskiy and J. Matas,
Systematic evaluation of convolution neural network advances on the Imagenet, Computer Vision and Image Understanding, 161 (2017), 11-19.
doi: 10.1016/j.cviu.2017.05.007. |
[22] |
A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Dover Publications, Inc., Mineola, NY, 2007. |
[23] |
C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images, Artech House Remote Sensing Library, Artech House, Boston, 1988. Google Scholar |
[24] |
S. M. Rytov, Y. A. Kravtsov and V. I. Tatarskii, Principles of Statistical Radiophysics, Volume 4. Wave Propagation Through Random Media, Springer-Verlag, Berlin, 1989. |
[25] |
T. Scarnati and B. Lewis, A deep learning approach to the synthetic and measured paired and labeled experiment (SAMPLE) challenge problem, Algorithms for Synthetic Aperture Radar Imagery XXVI, 10987 (2019), 109870G.
doi: 10.1117/12.2523458. |
[26] |
F. T. Ulaby and M. C. Dobson, Handbook of Radar Scattering Statistics for Terrain, Artech House Remote Sensing Library, Artech House, Norwood, MA, USA, 1989. Google Scholar |
[27] |
X. X. Zhu, D. Tuia, L. Mou, G.-S. Xia, L. Zhang, F. Xu and F. Fraundorfer,
Deep learning in remote sensing: A comprehensive review and list of resources, IEEE Geoscience and Remote Sensing Magazine, 5 (2017), 8-36.
doi: 10.1109/MGRS.2017.2762307. |
[28] |
D. Ziou and S. Tabbone, et al., Edge detection techniques-an overview, Pattern Recognition and Image Analysis C/C of Raspoznavaniye Obrazov I Analiz Izobrazhenii, 8 (1998), 537-559. Google Scholar |
show all references
References:
[1] |
J. C. Allen and S. L. Hobbs,
Spectral estimation of non-stationary white noise, J. Franklin Inst. B, 334 (1997), 99-116.
doi: 10.1016/S0016-0032(96)00060-9. |
[2] |
M. Basu,
Gaussian-based edge-detection methods–a survey, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 32 (2002), 252-260.
doi: 10.1109/TSMCC.2002.804448. |
[3] |
C. M. Bishop, Pattern Recognition and Machine Learning, Information Science and Statistics, Springer, New York, 2006. |
[4] |
B. Borden, Dispersive scattering for radar-based target classification and duct-induced image artifact mitigation, NATO Symposium on Non-Cooperative Air Target Identfication Using Radar, Mannheim, Germany, 1998, 14.1–14.7. Google Scholar |
[5] |
J. Canny,
A computational approach to edge detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-8 (1986), 679-698.
doi: 10.1109/TPAMI.1986.4767851. |
[6] |
S. Chen and H. Wang, SAR target recognition based on deep learning, 2014 International Conference on Data Science and Advanced Analytics (DSAA), IEEE, Shanghai, China, 2014, 541–547.
doi: 10.1109/DSAA.2014.7058124. |
[7] |
V. C. Chen and H. Ling, Time-Frequency Transforms for Radar Imaging and Signal Analysis, Artech House Radar Library, Artech House, Norwood, MA, 2002. |
[8] |
M. Cheney and B. Borden, Fundamentals of Radar Imaging, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 79, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2009.
doi: 10.1137/1.9780898719291. |
[9] |
F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, (eds.). NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/, Release 1.0.24 of 2019-09-15. Google Scholar |
[10] |
M. Ferrara, A. Homan and M. Cheney, Hyperspectral SAR, IEEE Trans. Geoscience and Remote Sensing, 55 (2017), 1682–1695.
doi: 10.1109/TGRS.2016.2629265. |
[11] |
J. Garnier and K. Sølna, A multiscale approach to synthetic aperture radar in dispersive random media, Inverse Problems, 29 (2013), 054006, (18pp).
doi: 10.1088/0266-5611/29/5/054006. |
[12] |
M. Gilman and S. Tsynkov, Mathematical analysis of SAR imaging through a turbulent ionosphere, Application of Mathematics in Technical and Natural Sciences: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences– AMiTaNS'17, Vol. 1895, AIP Conference Proceedings, Albena, Bulgaria, 2017, 020003 (23pp).
doi: 10.1063/1.5007357. |
[13] |
M. Gilman, E. Smith and S. Tsynkov, Transionospheric Synthetic Aperture Imaging, Applied and Numerical Harmonic Analysis, Birkhäuser/Springer, Cham, Switzerland, 2017.
doi: 10.1007/978-3-319-52127-5. |
[14] |
M. Gilman and S. Tsynkov, Detection of delayed target response in SAR, Inverse Problems, 35 (2019), 085005, (38pp).
doi: 10.1088/1361-6420/ab1c80. |
[15] |
J. W. Goodman, Statistical properties of laser speckle patterns, Topics in Applied Physics: Laser Speckle and Related Phenomena (ed. J. C. Dainty, ), Vol. 9, Springer-Verlag, Berlin, 1984, 9–75. Google Scholar |
[16] |
T. Hastie, R. Tibshirani and J. Friedman, The Elements Of Statistical Learning. Data Mining, Inference, and Prediction, 2$^nd$ edition, Springer Series in Statistics, Springer, New York, 2009.
doi: 10.1007/978-0-387-84858-7. |
[17] |
A. Krizhevsky, I. Sutskever and G. E. Hinton, ImageNet classification with deep convolutional neural networks, Advances in Neural Information Processing Systems 25, Curran Associates, Inc., 2012, 1097–1105. Google Scholar |
[18] |
D. Marr and E. Hildreth,
Theory of edge detection, Proc. R. Soc. Lond. B, 207 (1980), 187-217.
doi: 10.1098/rspb.1980.0020. |
[19] |
W. Mendenhall and R. L. Scheaffer, Mathematical Statistics with Applications, Duxbury Press, North Scituate, Mass., 1973.
![]() |
[20] |
F. J. Meyer, K. Chotoo, S. D. Chotoo, B. D. Huxtable and C. S. Carrano,
The influence of equatorial scintillation on L-band SAR image quality and phase, IEEE Trans. Geoscience and Remote Sensing, 54 (2016), 869-880.
doi: 10.1109/TGRS.2015.2468573. |
[21] |
D. Mishkin, N. Sergievskiy and J. Matas,
Systematic evaluation of convolution neural network advances on the Imagenet, Computer Vision and Image Understanding, 161 (2017), 11-19.
doi: 10.1016/j.cviu.2017.05.007. |
[22] |
A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Dover Publications, Inc., Mineola, NY, 2007. |
[23] |
C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images, Artech House Remote Sensing Library, Artech House, Boston, 1988. Google Scholar |
[24] |
S. M. Rytov, Y. A. Kravtsov and V. I. Tatarskii, Principles of Statistical Radiophysics, Volume 4. Wave Propagation Through Random Media, Springer-Verlag, Berlin, 1989. |
[25] |
T. Scarnati and B. Lewis, A deep learning approach to the synthetic and measured paired and labeled experiment (SAMPLE) challenge problem, Algorithms for Synthetic Aperture Radar Imagery XXVI, 10987 (2019), 109870G.
doi: 10.1117/12.2523458. |
[26] |
F. T. Ulaby and M. C. Dobson, Handbook of Radar Scattering Statistics for Terrain, Artech House Remote Sensing Library, Artech House, Norwood, MA, USA, 1989. Google Scholar |
[27] |
X. X. Zhu, D. Tuia, L. Mou, G.-S. Xia, L. Zhang, F. Xu and F. Fraundorfer,
Deep learning in remote sensing: A comprehensive review and list of resources, IEEE Geoscience and Remote Sensing Magazine, 5 (2017), 8-36.
doi: 10.1109/MGRS.2017.2762307. |
[28] |
D. Ziou and S. Tabbone, et al., Edge detection techniques-an overview, Pattern Recognition and Image Analysis C/C of Raspoznavaniye Obrazov I Analiz Izobrazhenii, 8 (1998), 537-559. Google Scholar |





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