SAR correlation imaging and anisotropic scattering

Kaitlyn (Voccola) Muller

doi:10.3934/ipi.2018030

Article Contents

2018, Volume 12, Issue 3: 697-731. Doi: 10.3934/ipi.2018030

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SAR correlation imaging and anisotropic scattering

Kaitlyn (Voccola) Muller^,

Department of Mathematics and Statistics, Villanova University, Villanova, PA 19085, USA

Corresponding author: k.muller@villanova.edu
Corresponding author: k.muller@villanova.edu

Received: July 31, 2017

Revised: November 30, 2017

Published: March 2018

The author was supported by AFOSR grant FA9550-14-1-0124.

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Abstract

In this paper we investigate the ability of correlation synthetic-aperture radar (SAR) imaging to reconstruct isotropic and anisotropic scatterers. SAR correlation imaging was suggested by the author previously in [34]. Correlation imaging algorithms produce an image of a second-order quantity describing an object an interest, for example, the reflectivity function squared. In the previous work [34] it was argued that the effects of volume scattering clutter on the image can be minimized by choosing which pairs of collected data to correlate prior to applying a backprojection-type reconstruction algorithm. This choice of pairs for the correlation process is determined by what is known as the memory effect of scattering of waves by random scatterers [42,43,40,41,7,14]. It is the goal of this current work to determine the different imaging outcomes for an isotropic or point scatterer versus an anisotropic or dipole scatterer. In addition we aim to determine if removing contributions to the image due to the memory effect is necessary for diminishing the contributions of anisotropic or clutter scatterers to the scene of interest. Finally we extend the analysis of [34] to the polarimetric SAR case to determine whether the additional data provided by this modality contributes to decreasing the effects of clutter on the SAR image.

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Mathematics Subject Classification: Primary: 78A46, 94A13; Secondary: 35Q60.

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Figure 1. Single point; standard reconstruction, correlation reconstruction with memory directions

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Figure 2. Single point; correlation reconstruction without memory directions with $\tilde{s} = 1, 25, 75$ slow-time steps (recall $\tilde{s} = s-s'$)

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Figure 3. Single dipole, orientation $\pi/4$, length$ = .3\lambda$; standard reconstruction, correlation reconstruction with memory directions

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Figure 4. Single dipole, orientation $\pi/4$, length$ = .3\lambda$; correlation reconstruction without memory directions with $\tilde{s} = 1, 25, 75$ slow-time steps (recall $\tilde{s} = s-s'$)

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Figure 5. Single dipole, orientation $\pi/4$, length$ = 3\lambda$; standard reconstruction, correlation reconstruction with memory directions

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Figure 6. Single dipole, orientation $\pi/4$, length$ = 3\lambda$; correlation reconstruction without memory directions with $\tilde{s} = 1, 25, 75$ slow-time steps (recall $\tilde{s} = s-s'$)

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Figure 8. Single dipole, orientation $\pi/4$, length$ = 30\lambda$; standard reconstruction, correlation reconstruction with memory directions

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Figure 9. Single dipole, orientation $\pi/4$, length$ = 30\lambda$; correlation reconstruction without memory directions with $\tilde{s} = 1, 25, 75$ slow-time steps (recall $\tilde{s} = s-s'$)

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Figure 7. Single dipole, orientation $\pi/4$, length$ = 3\lambda$; correlation reconstruction without memory directions with $\tilde{s} = 1, 25, 75$ slow-time steps (recall $\tilde{s} = s-s'$), second flight path

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Figure 10. Single dipole, orientation $\pi/4$, length$ = 30\lambda$; correlation reconstruction without memory directions with $\tilde{s} = 1, 25, 75$ slow-time steps (recall $\tilde{s} = s-s'$), second flight path

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Figure 11. Two point targets, dipole clutter, each dipole with orientation $\pi/4$, length$ = \lambda$, and Gaussian reflectivity; standard polarimetric reconstruction, HH, HV, VV images respectively

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Figure 12. Two point targets, dipole clutter, each dipole with orientation $\pi/4$, length$ = \lambda$, and Gaussian reflectivity; correlation polarimetric reconstruction $\tilde{s} = 1$ (recall $\tilde{s} = s-s'$), HH-HH, HV-HV, VV-VV images respectively

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Figure 13. Two point targets, dipole clutter, each dipole with orientation $\pi/4$, length$ = \lambda$, and Gaussian reflectivity; correlation polarimetric reconstruction $\tilde{s} = 50$ (recall $\tilde{s} = s-s'$), HH-HH, HV-HV, VV-VV images respectively

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Table 1. Single point; peak image value at center pixel

Standard BP		1.7158 - 0.2106i
Correlation BP with memory directions		1.5112 - 0.0000i
Correlation BP with $\tilde{s}=1$		1.4772 - 0.0000i
Correlation BP with $\tilde{s}=25$		1.1470 - 0.0000i
Correlation BP with $\tilde{s}=50$		0.8461 + 0.0000i
Correlation BP with $\tilde{s}=75$		0.5869 + 0.0000i

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Table 2. Peak Image Value at center pixel, single dipole target, orientation $\pi/4$, length$ = .3\lambda$

Standard BP		1.1491e-04 - 6.2788e-06i
Correlation BP with memory directions		0.6668e-08 - 0.0410e-08i
Correlation BP with $\tilde{s}=1$		0.6575e-08 - 0.0410e-08i
Correlation BP with $\tilde{s}=25$		0.5030e-08 - 0.0377e-08i
Correlation BP with $\tilde{s}=50$		0.3642e-08 - 0.0290e-08i
Correlation BP with $\tilde{s}=75$		0.2490e-08 - 0.0208e-08i

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Table 4. Peak Image Value at center pixel, single dipole target, orientation $\pi/4$, length$ = 3\lambda$, second flight path

Standard BP		0.0090 + 0.0004i
Correlation BP with memory directions		0.4206e-04 + 0.0014e-04i
Correlation BP with $\tilde{s}=1$		0.4072e-04 + 0.0014e-04i
Correlation BP with $\tilde{s}=25$		0.2535e-04 + 0.0049e-04i
Correlation BP with $\tilde{s}=50$		0.1363e-04 - 0.0087e-04i
Correlation BP with $\tilde{s}=75$		0.0592e-04 - 0.0021e-04i

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Table 3. Peak Image Value at center pixel, single dipole target, orientation $\pi/4$, length$ = 3\lambda$

Standard BP		0.0012 - 0.0002i
Correlation BP with memory directions		0.7152e-06 - 0.1448e-06i
Correlation BP with $\tilde{s}=1$		0.6983e-06 - 0.1448e-06i
Correlation BP with $\tilde{s}=25$		0.3869e-06 - 0.1183e-06i
Correlation BP with $\tilde{s}=50$		0.2159e-06 + 0.0199e-06i
Correlation BP with $\tilde{s}=75$		0.1153e-06 + 0.0139e-06i

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Table 5. Peak Image Value at center pixel, single dipole target, orientation $\pi/4$, length$ = 30\lambda$

Standard BP		0.0010 - 0.0023i
Correlation BP with memory directions		0.3106e-05 - 0.0308e-05i
Correlation BP with $\tilde{s}=1$		0.3053e-05 - 0.0308e-05i
Correlation BP with $\tilde{s}=25$		0.2214e-05 - 0.0087e-05i
Correlation BP with $\tilde{s}=50$		0.1554e-05 - 0.0159e-05i
Correlation BP with $\tilde{s}=75$		0.1115e-05 - 0.0061e-05i

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Table 6. Peak Image Value at center pixel, single dipole target, orientation $\pi/4$, length$ = 30\lambda$, second flight path

Standard BP		1.7528 + 0.2160i
Correlation BP with memory directions		1.6668 - 0.3576i
Correlation BP with $\tilde{s}=1$		1.5072 - 0.3576i
Correlation BP with $\tilde{s}=25$		0.1084 - 0.1624i
Correlation BP with $\tilde{s}=50$		0.0157 - 0.0024i
Correlation BP with $\tilde{s}=75$		0.0045 - 0.0001i

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Table 7. Input vs. ouput SCR in dB, scalar SAR, two point targets in dipole clutter

Input SCR	Output SCR Standard BP	Output SCR Correlation BP $\tilde{s}=1$	Output SCR Correlation $\tilde{s}=10$	Output SCR Correlation $\tilde{s}=50$
20	17.3087	51.3593	52.0820	51.9498
10	7.3087	31.3593	32.0820	31.9498
0	-2.6913	11.3593	12.0820	11.9498
-10	-12.6913	-8.6407	-7.9180	-8.0502
-20	-22.6913	-28.6407	-27.9180	-28.0502

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Table 8. Input vs. ouput SCR in dB, pol SAR standard BP, two point targets in dipole clutter

Input SCR	Output SCR HH	Output SCR HV	Output SCR VV
20	18.0264	18.8373	18.9482
10	8.0264	8.8373	8.9482
0	-1.9736	-1.1627	-1.0518
-10	-11.9736	-11.1627	-11.0518
-20	-21.9736	-21.1627	-21.0518

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Table 9. Input vs. ouput SCR in dB, pol SAR correlation BP, two point targets in dipole clutter, $\tilde{s} = 1$

Input SCR	Output SCR HH-HH	Output SCR HV-HV	Output SCR VV-VV
20	51.1293	54.0229	53.9465
10	31.1293	34.0229	33.9465
0	11.1293	14.0229	13.9465
-10	-8.8707	-5.9771	-6.0535
-20	-28.8707	-25.9771	-26.0535

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Table 10. Input vs. ouput SCR in dB, pol SAR correlation BP, two point targets in dipole clutter, $\tilde{s} = 10$

Input SCR	Output SCR HH-HH	Output SCR HV-HV	Output SCR VV-VV
20	51.3130	54.0887	53.9973
10	31.3130	34.0887	33.9973
0	11.3130	14.0887	13.9973
-10	-8.6870	-5.9113	-6.0027
-20	-28.6870	-25.9113	-26.0027

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Table 11. Input vs. ouput SCR in dB, pol SAR correlation BP, two point targets in dipole clutter, $\tilde{s} = 50$

Input SCR	Output SCR HH-HH	Output SCR HV-HV	Output SCR VV-VV
20	51.4206	53.9605	53.7934
10	31.4206	33.9605	33.7934
0	11.4206	13.9605	13.7934
-10	-8.5794	-6.0395	-6.2066
-20	-28.5794	-26.0395	-26.2066

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