SAR Tomography

Patrick McCormick

EECS 800

What is tomography?

• A type of imaging that compares intensity profiles of captured energy that penetrates a scene (or object) of interest from different aspect angles and heights.

• Tomography is used widely in medical sciences in the form of computed tomographic (CT) scans and magnetic resonance imaging (MRI).

• The terminology is adopted for SAR imaging where the synthetic aperture is extended in the direction orthogonal to the direction of flight and direction of propagation.

InSAR or SARTom?

[1]

InSAR or SARTom?

• Two passes with temporal and/or spatial baselines

• No information on distribution of scatterers in height

• Height associated with effective phase center

• N>2 passes with spatial baselines • Want to minimize temporal baseline • Retrieves information on distribution in

height using beamforming techniques (Fourier, Capon, MUSIC, CS)

Fig. 1. InSAR digital elevation map (DEM) of Nyamuragira volcano (Democratic Republic of Congo)

Fig. 2. (a) Slice of polarimetric tomographic profile (b) Full polarimetric tomographic scene

SAR Tomography - Basics • Tomographic resolution

𝛿𝑛 =𝜆𝑟0

2𝐿 (Fourier beamforming)

• Maximum allowable separation between passes to avoid ambiguities

𝑟0: minimum range distance 𝜆: operating wavelength 𝐿: synthetic aperture length in n-direction

𝑑 ≤𝜆𝑟0

2𝐻

𝑑: distance between passes 𝐻: total height of examined volume

Fig. 3. Simplified tomographic geometry [2]

Fig. 4. Tomogram from K SAR images [3]

Fig. 5. Height-Azimuth slice of tomogram using Fourier beamforming

Non-linear beamforming

Fig. 6. Height-Azimuth slice of tomogram using Capon beamforming

Fig. 7. Height-Azimuth slice of tomogram using MUSIC beamforming (parametric) [3]

SAR Tomography - Example

Polarimetric SARTom • German Aerospace Center (DLR) • Location: Dornstetten test site • L-band (𝜆 ≈ 30 cm) • No information on bandwidth • Tomographic resolution: 2 meters • Max volume height: 30 meters • 21 Tracks @ ~20 meters (max 26.6) • 𝐿 = 400 meters • 𝑟0 ≈ 5.3 km • Look angle 45°

Goal: To identify a truck covered by the forest canopy via the truck’s polarimetric signature

Fig. 8. Total PolSAR image of Dornstetten. Trucks oriented along (1)

Fig. 9. Perpendicular baselines for each track

[4]

SAR Tomography - Example VV

HV/VH

HH

Pauli basis Blue: HH+VV (single bounce) Red: HH-VV (double bounce) Green: 2HV (volumetric)

Beamforming method: Fourier

Fig. 10. Slice of tomogram for polarizations: VV, HV, and HH [4]

Fig. 11. Combined polarimetric components of tomogram using Pauli basis [4]

Holographic Tomography

[1]

Stripmap vs. Circular

Δ𝑥 ≈𝐷𝑎

2 Azimuth resolution: Δ𝑥 ≈

𝜆

4 Azimuth resolution:

[1]

SAR Holography – Example

SAR Holography • AFRL 2006 CSAR data collect • X-band (𝜆 ≈ 3 cm) • Bandwidth: 640 MHz • 100 𝑚 × 100 𝑚 spotlighted area • 8 Tracks @ ~no info on separation • Look angle 42° − 46°

Fig. 12. Single-pass CSAR image

Fig. 13. CSAR flight paths for each pass

Top-hat Camry

[5]

SAR Holography – Example

Fig. 14. 10 𝑚 × 10 𝑚 × 10 𝑚 cuts of (a) top-hat and (b) Camry responses [5]

SAR Holography – Example

Sparse - 𝑙1 regularized least squares

Compressive Sampling-based Matching Pursuit

Fig. 15. Estimate of top-hat response (VV) using l1-norm LS and CoSaMP [5]

SAR Holography – Example

Sparse - 𝑙1 regularized least squares

Compressive Sampling-based Matching Pursuit

Fig. 16. Estimate of Camry response (VV) using l1-norm LS and CoSaMP [5]

References 1. O. Ponce, A. Reigber and A. Moreira, “Airborne Holographic SAR

Tomography at L- and P-band,” Microwaves and Radar Institute (HR) and German Aerospace Center (DLR).

2. Reigber. A, Moreira. A. First Demonstration of Airborne SAR Tomography Using Multibaseline L-Band Data. IEEE Transactions on Geoscience and Remote Sensing. Vol.38, NO.5, September 2000.

3. Guillaso, S.; Reigber, A. Polarimetric SAR Tomography (POLTOMSAR). In Proceedings of POLINSAR'05; Frascati, Italy, 2005.

4. M. Nannini, R. Scheiber, R. Horn and A. Moreira "First 3-D reconstructions of targets hidden beneath foliage by means of polarimetric SAR tomography", IEEE Geosci. Remote Sens. Lett., vol. 9, no. 1, pp.60 -64 2012.

5. Ferrara, Matthew, Julie A. Jackson, and Christian Austin. "Enhancement of multi-pass 3D circular SAR images using sparse reconstruction techniques."SPIE Defense, Security, and Sensing. International Society for Optics and Photonics, 2009.