Model-Based Imaging and Feature Extraction for Synthetic Aperture Radar

Transcription

1 Model-Based Imaging and Feature Extraction for Synthetic Aperture Radar Randy Moses Department of Electrical and Computer Engineering The Ohio State University with lots of help from Lee Potter, Mujdat Cetin, Yeliz Akyildiz, Christian Austin, Hung-Chih Chiang, Mike Gerry, Mike Koets, and Brian Rigling

2 Outline Framing the problem: a research perspective Synthetic Aperture Radar: A quick tutorial Parametric Models for Radar Scattering Wide Angle SAR 3D SAR reconstructions Feature-Based Target Recognition

3 Outline Framing the problem: a research perspective Synthetic Aperture Radar: A quick tutorial Parametric Models for Radar Scattering Wide Angle SAR 3D SAR reconstructions Feature-Based Target Recognition

4 Image Exploitation In many applications, the image is not the end goal. Images are further processed in some way Extract features Make inferences A key assumption: a low dimensional representation describes (part of) the image. Sparsity? Modeling!

5 Model-based Imaging and Inferencing Parametric models encode prior information about scattering physics Scattering physics informs about new directions to take wide-angle imaging 3D reconstructions x=35.2 m y=46.3 m A=9.43 db α = 0.5 L=0.34 m X = X1 X2 X3 K X m [,,,, ] Γ Y = Y1 Y2 Y3 K Y n [,,,, ] Estimation theory gives predictions and fundamental limits on feature accuracy Classify by feature matching: Feature uncertainty integrates to recognition confidence.

6 Outline Framing the problem: a research perspective Synthetic Aperture Radar: A quick tutorial Parametric Models for Radar Scattering Wide Angle SAR 3D SAR reconstructions Feature-Based Target Recognition

7 SAR Data Collection θ φ Frequency Space

8 SAR - Data Collection Range Downrange resolution Crossrange resolution

9 SAR Resolution (Filled Aperture) E(x,y) Response to an ideal point scatterer: Crossrange Downrange Resolution is determined by, e.g., 3 db width of peaks.

10 SAR - Image Formation E(f x,f y ) SAR Imager E(x,y) Window, Zero Pad 2-D IFFT Resampled data SAR image

11 Image Formation Comments Conventional image formation Assumes isotropic point scatterer: scattering points on the object have zero extent and constant response A as a function of frequency, angle: Image formation is adjoint operator (not inverse) Interpretation: I(x,y)= matched filter output to an isotropic point scattering center at assumed location (x,y). Resolution and sidelobes: trade off with windowing.

12 Outline Framing the problem: a research perspective Synthetic Aperture Radar: A quick tutorial Parametric Models for Radar Scattering Wide Angle SAR 3D SAR reconstructions Feature-Based Target Recognition

13 Scattering Physics At sufficiently high resolution, individual scattering centers are isolated. versus Phase, amplitude, polarization characteristics of isolated scattering centers are stable and relate to object shape Viable features for recognition/visualization

14 SLICY Test Target SLICY Test Target Frequency Domain Data SAR Image

15 Modeling Radar Scattering Centers Develop parsimonious parametric scattering models: -data reduction - (almost) sufficient statistics Encode prior information about scattering physics Geometric Theory of Diffraction Physical Optics Estimate physically meaningful parameters 1 ft MSTAR image Dihedral, L=1.10m SLICY target Dihedral, L=1.16m

16 Attributed Scattering Center Model E ( f, φ ) = n k = 1 Polarization Dependence A x α L φ γ A k j f f c α e Frequency Dependence 2πfγ Scattering Attributes k k k k k k, y k = = = = = = amplitude k location k sin φ frequency type length pose angle sinc [H, V, X] angle response 2πf c L Aspect Dependence k sin( φ φ k ) exp Extract x=35.2 m y=46.3 m A=9.43 db α = 0.5 L=1.33 m 4πf j c [ x cos φ + y sin φ ] k Location Dependence T72-sn132 AZ=249.79, EL=17.18 k

17 Scattering Primitives Frequency Dependence α=1 α=1/2 α=0 Aspect Dependence L=0 L>0 Corner Reflector L Dihedral Top Hat L Cylinder Sphere L Edge Polarization Dependence Scattering dependence across frequency, angle, and polarization parameters permit discrimination among target primitives using radar measurements.

18 Localized vs. Distributed Scatterers Exy (, ) : image domain E( f, f ) : freq. domain x y

19 Simulation and Field Measurements: Aspect Behavior EM Models: Dihedral Field measurement

20 Parameter Estimation Approaches Directly from measured data High-dimensional models High data dimension Complex optimization problem E(f,φ) From formed (complex) image 1-1 transform (no information loss) Partition into smaller problems Lower complexity; better conditioned E(x,y)

21 Approximate Maximum Likelihood Parameter Estimation Recursively model for computational efficiency Image Estimate ML model fitting on small regions; Nonlinear Least squares Scattering Center Removal Original complex SAR Image Watershed Segmentation Image domain concentrates scattering information to a few pixels

22 Parameter Uncertainty Variance : Theoretical Bounds x: Algorithm Performance A r, A i α γ x, y Estimation Theory is used to compute attribute uncertainty and uncertainty bounds statistical estimation error Cramer-Rao bounds SAR image resolution (inches) SNR = 20 db

23 Structure Selection x, i A y i i i : amplitude : location α : frequency dependence Model Parameters L i i i : length of scatterer φ :tilt angle γ :angle response H d H l Scattering Center Structure H l Localized S. C. : Distributed S. C. :H d θi, l = [ xi, yi, Ai, αi, γi] θ, = [ x, y, A, α, φ, L] id i i i i i i Problem: given SAR data, determine H l : localized scatterer H d : distributed scatterer

24 Structure Selection : GLRT Generalized Likelihood Ratio Test: d : vector of image pixels in a region GLRT Detector: SNR=20 db L c =2 L c = Example: Dihedral Detector P D : correctly detect a dihedral P FA : incorrectly declare a trihedral as a dihedral P D L c =1 L c =0.5 L c = Dihedral length in crossrange resolution units P FA

25 Outline Framing the problem: a research perspective Synthetic Aperture Radar: A quick tutorial Parametric Models for Radar Scattering Wide Angle SAR 3D SAR reconstructions Feature-Based Target Recognition

26 Motivation for Wide Angle Emerging technologies enable collection of radar backscatter data over wide angular apertures Better INS UAV, possibly multiple UAVs working in tandem Bistatic radar with close-in passive receiver Investigate SAR processing of wide angle apertures Resolution and image properties Impact of scattering persistence

27 Wide Angle Image Response Wide angle aperture, narrow bandwidth aperture sparse; high sidelobes -3 db image resolution ~ excribed rectangle -24 db image resolution area ~ 1/(aperture area) 1 ft circle 0.3 meter resolution, Hamming Crossrange, meters Range, meters 0.4

28 Image Response vs. Aperture Frequency Support Image meter resolution, Hamming Crossrange, meters Range, meters

29 Backhoe Data Dome Xpatch synthetic backscatter data Publicly released 7-13 GHz frequency band az, 0-90 elev 0.07 angle spacing 1 x 1 x 1 resolution Full polarization ~300 Gbyte of data

30 Wide-Angle Imaging 110 azimuth aperture, MHz (1ft); 4GHz (1.5in) 30 elevation at center

31 Coherent SAR 110 Image 4 GHz Bandwidth 500 MHz Bandwidth Coherent wide-angle image is not well-matched to limited persistence scattering behavior

32 Scattering Aspect Dependence Most target scattering has limited response persistence 20 or less [Dudgeon et al, 1994] Downrange resolution 1/BW Crossrange resolution depends on scattering persistence Image response is no longer characterized by a single impulse response shape. φ c = 40 φ c = 20 φ c =0 φ c =20 Frequency Support Image φ c =40

33 GLRT Image Formation SAR Image: Image I(x,y) is a matched filter output to an isotropic point scattering center at (projected) location (x,y). GLRT Image: Image I(x,y) is GLRT output to a limitedpersistence scattering center at (projected) location (x,y). I( x, R( x, y) = y, φ, α) c arg max R( x, φ, α c = y, φ, α) std image with center φ, width α For fixed α(=20 ) and sampled φ=k φ ( φ=5 ), the GLRT image is approximately max over subimages: GLRT Image: c c

34 Composite GLRT Image 4 GHz Bandwidth 500 MHz Bandwidth

35 Coherent SAR 110 Image 4 GHz Bandwidth 500 MHz Bandwidth

36 GLRT Image with Angle Encoding Color Denotes angle at which GLRT test is maximum 4 GHz Bandwidth 500 MHz Bandwidth

37 Scattering Physics At sufficiently high resolution, individual scattering centers are isolated. versus Phase, amplitude, polarization characteristics of isolated scattering centers are stable and relate to object shape Viable features for recognition/visualization Resolution enhancement (bandwidth extrapolation) becomes much less ill-posed.

38 Resolution Enhanced; Color-Encoded 500 MHz Bandwidth Res. Enhanced, p=0.8 Cetin p=1 Joint work with Mujdat Cetin

39 Outline Framing the problem: a research perspective Synthetic Aperture Radar: A quick tutorial Parametric Models for Radar Scattering Wide Angle SAR 3D SAR reconstructions Feature-Based Target Recognition

40 Reconstruction Challenges Enormous data size and processing requirements 300 GBytes of data Filled aperture is very difficult to measure Understanding highdimensional data Each (x,y,z) point is characterized by: Amplitude Scattering response vs. azimuth, elevation Polarization features (6 real-valued parameters)

41 Scattering Physics At sufficiently high resolution, individual scattering centers are isolated. versus Phase, amplitude, polarization characteristics of isolated scattering centers are stable and relate to object shape Viable features for recognition/visualization Resolution enhancement (bandwidth extrapolation) becomes much less ill-posed. Phase stability leads to height estimation using interferometry.

42 IFSAR: Uses two apertures closely spaced in elevation to estimate height from the image plane. Interferometric SAR elev elev This only works if response is dominated by a single scattering center. Need isolated scattering centers 30

43 Wide-Angle IFSAR Processing IFSAR processing: Form coherent image pairs from subapertures Select high amplitude pixels with a single dominant scatterer: Height z in slant plane for each image pixel estimated from relative phase between the two images Noncoherently combine points with GLRT approach.

44 IFSAR Reconstruction Color encodes azimuth angle

45 IFSAR Pairs Coherent IFSAR image pairs 1.5 x1.5 resolution 8-12 GHz 24 aperture Every 5 elevation θ=0.05 elevation spacing 1296 total image pairs 1/50 of data dome data used

46 Attributed Point Features From each pair of IFSAR images centered at (φ k,ψ k ) extract high amplitude points. Point features are: Slant-plane (x,y) location and height Polarization features from HH, HV, VH, VV pixel values Trihedral-dihedral mix parameter α Dihedral orientation angle θ Antenna pattern peak (φ k,ψ k ) for each point Translate points to target-centered reference frame. Noncoherently combine points from different IFSAR image pairs Total Feature Set: ~2.2 x10 6 points, 240Mbytes Matlab file. (Compare with 300 Gbyte data dome)

47 RCS Only

48 Color Encodes Azimuth Angle

49 Polarization

50 ±20º displayed Odd-bounce Even-bounce

51 Outline Framing the problem: a research perspective Synthetic Aperture Radar: A quick tutorial Parametric Models for Radar Scattering Wide Angle SAR 3D SAR reconstructions Feature-Based Target Recognition

52 From Features to Target Recognition Recognize objects from a collection of attributed scattering features Attributes: location; orientation; extent Much lower dimension than image pixels Physical basis for hypothesis refinement Target pose and articulation manifests in much simpler ways Simpler statistical relationships on nonlinear manifolds Feature uncertainty and uncertainty bounds Aggregate information to recognition uncertainty Performance prediction in new operating regimes E.g. greater bandwidth; wide aperture angles

53 Feature Matching Extracted Features + Feature Uncertainty Y j Rx j Ry j = A j α j L j Target/Pose Hypothesis + Hypothesis Uncertainty X i Rx i Ry i = A i α i L i Integrate feature match scored to determine target recognition confidence

54 Classification Performance Estimation Model-based Classification Performance Estimation Image data Feature extraction [,,, ] Y1 Y2 L Y n Indexing Matching Hypo 1 M Hypo N Predictor X X X M , 2, K, m X X X N N N 1, 2, K, m Feature Uncertainty 1 N MSTAR Public Targets: 10 tgts x ~275 aspects = 2747 image chips Class (and pose) means: A, x, y from 10 largest peaks; α, L from Bayes probabilistic model Monte-Carlo: 10 realizations /chip = 27,470 realizations ATR Performance Predictions Variance : Theoretical Bounds x: Algorithm Performance x, y SAR image resolution (inches) α γ A r, A i Estimation Theory is used to compute attribute uncertainty as a function of radar system parameters Parameter uncertainty is used to predict ATR performance. 10 log 10 (Pe) db Baseline 2 1 1/2 1/4 SAR Rayleigh Resolution in ft

55 Research Perspective Use parametric models encode prior information about scattering physics Physics-guided sparse representations. New imaging directions and processing strategies. Physically-meaningful features Use statistical signal processing to understand fundamental limits on feature accuracy Resolution of scattering centers Discrimination among primitive types Use estimated parameters for higher-level reasoning Hypothesis testing Feature uncertainties integrate to recognition confidence