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Detection of Obscured Targets: Signal Processing
James McClellan and Waymond R. Scott, Jr. School of Electrical and Computer Engineering
Georgia Institute of TechnologyAtlanta, GA 30332-0250
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MURI Review 2-25-04 Scott/McClellan, Georgia Tech 2
Outline
IntroductionMulti-resolution & Multi-modal Signal Processing
Physical Basis for Multimodal Processing/InversionQuadtree Imaging
SP for Three Sensor ExperimentReverse-Time Processing
FocusingImaging
Accomplishments/Plans
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Three Sensor ExperimentA three sensor experiment has been developed to investigate the potential for multimodal processing
Electromagnetic Induction (EMI) SensorGround Penetrating Radar (GPR) SensorSeismic Sensor
Multiple Experimental ScenariosBuried LandminesBuried Clutter Objects Target Distribution
Properties
Physical Properties of TargetSensor
Yes
No
No
Mechanical Contrast
NoNoNoSeismic
Yes*YesYesGPR
YesWeakNoEMI
High Conductivity
(Metal)
Low Conductivity(Dielectric)
Permittivity Contrast
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Comparison of EMI, GPR and Seismic Response VS-50, 1 cm deep
EMI GPR Seismic
depth
x
ty
0.00
1,000 10,000Frequency (Hz)
RealImag.
-0.02
0.02
0.04
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Multi-Sensor Processing
GPR
EMI
Seismic
Imaging
SigProc
Imaging
Features
Features
Features
DecisionProcess
ExploitCorrelation
Training
Detect
Classify
ID
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Multi-Sensor Adaptation
GPR
EMI
Seismic
Imaging
SigProc
Imaging
Features
Features
Features
DecisionProcess
ExploitCorrelation & Sensitivity
Feedback
Feedback
Controls
Controls
Controls
Controls
Controls
Controls
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Three Sensor ExperimentSensor Adjustments and Features
Adjustable Parameters for all three sensors
Frequency rangeFrequency ResolutionSpatial ResolutionIntegration time/bandwidthHeight above ground
Possible Features for sensorsEMI
Relaxation frequencyRelaxation strengthRelaxation shapeSpatial response
GPRPrimary ReflectionsMultiple ReflectionsDepthSpatial Response
SeismicResonanceReflectionsDispersionSpatial response
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Multi-Resolution Processing
GPR
EMI
Seismic
Imaging
SigProc
Imaging
Features
Features
Features
DecisionProcess
ExploitCorrelation
Training
Detect
Classify
ID
Quadtree Imaging@ increasingResolution(Eliminate Areas)
Target Localization@ specific sites
Multi-band Imaging
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Outline
IntroductionMulti-resolution & Multi-modal Signal Processing
Physical Basis for Multimodal Processing/InversionQuadtree Imaging
SP for Three Sensor ExperimentReverse-Time Processing
FocusingImaging
Accomplishments/Plans
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Multi-Res Quadtree Algorithm
10
Standard BackprojectionSpace-Time Domain CorrelationSignificant amount of computations
Quadtree AlgorithmApproximates Standard BackprojectionConsists of many sub-aperture and sub-image operations:
beamforming over the sensors in sub-apertures with respect to the virtual sensor and sub-images.Significant amount of Time-Domain Interpolation required.
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Quadtree BackProjection
Sub-Aperture Formation
(Virtual Sensor)
Image Patch Dividing
(Sub-Patch )
Quadtree BackProjection
1st Stage
2nd Stage
3rd Stage
4th Stage
Space-Time Domain Decomposition Image Patch Dividing and Sub-Aperture Formation (Virtual Sensor)Divide and Conquer Strategy
Computational Complexity O(N2log2N)
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Quadtree PruningMultiresolution Imaging
Intermediate Data with Energy Functiond(u,t) ⇒ di(u,t,1,1) ⇒ … ⇒ di(u’,t’,ξ,η) ⇒ … ⇒ di(1,1,ξ,η) ⇒ f(x,y)
Intermediate Stage Data Pruning ⇒⇒⇒⇒ Early Detection
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Quadtree Equivalence
Quadtree BackProjection Imaging AlgorithmComputes sub-images with sub-aperturesUltra WideBand (UWB) SAR: FOPEN
Quadtree Tomographic BackProjectionTomographic ImagingMultiresolution Imaging
Quadtree Broadband BeamformerDelay-Sum BeamformerMulti-Angle Multiresolution Beamforming
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Outline
IntroductionMulti-resolution & Multi-modal Signal Processing
Physical Basis for Multimodal Processing/InversionQuadtree Imaging
SP for Three Sensor ExperimentReverse-Time Processing
FocusingImaging
Accomplishments/Plans
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Three Sensor Experiment
Experimental Scenario #16 Mines> 20 Clutter objectsRelatively uniform distribution
Experimental Scenario #27 Mines> 25 Clutter objectsNon-uniform distribution
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EMI Processing
Frequency Domain: 600 Hz to 60 KHz
Extract the break frequency via signal modeling & form an image
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Burial Scenario #1
1.8m by 1.8m Scan Region
Rocks (3 and4 cm deep)
Dry Sand(5cm deep)
MINESVS-2.2
(7cm deep)
TS-50(1.5cm deep)
w/ Nail
M-14(0.5cm deep)
VS-50(1cm deep)
EMF-1(1.5 cm deep)
VS-1.6(6.5cm deep)
SeismicSources
Cans (3 and2.5 cm deep)
AssortedMetal Clutter (2 to 4 cm deep)
Shells(4cm deep)
ThreadedRod(3.5cm deep)
Penny(5.5cm deep)
Nails(4cm deep)
Ball Bearing(3.5cm deep)
Shells(5.5cm deep)
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Energy Plot (db scale)Break Frequencies in Hz (linear scale)Frequency Range: 300-60,000 HzBurial Scenario-1
Energy Plot Break Frequencies
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Burial Scenario #2
1.8m by 1.8m Scan Region
SeismicSourcesMINES
VS-50(1.3cm deep)
VS-2.2(5.4cm deep)
M-14(1cm deep)
TS-50(1.3cm deep)
EMF-1(0.6cm deep)
VS-50(0.5cm deep)
VS-1.6(5.1cm deep)
Rocks(2, 2.2, 2.5,and 1.3cm deep)
Can(2.2cm deep)
AssortedMetalClutter(
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“QUADTREE” Burial Scenario-2
Energy Plot Break Frequencies
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GPR ProcessingData taken in frequency domain with network analyzer: 500 MHz to 8 GHzImaging
Backprojection does migration2-D, extend to 3-Dωωωω-k algorithmsExtend to Quadtree
Multi-resolution
y
x
2 =
4.5
"A
w = 3mm
2 =
62.
4mil
a
L = 6.75"Antenna Shape
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GPR Processing ExampleOriginal Data Cut Ground Reflection
Removed By CorrelationImage is formed by Back Projection Algorithm
VS-50
TS-50
VS-1.6
VS-2.2
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Total Energy Imaged(Burial #2 Quadtree)
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Energy in Different Depth Slices(Burial #2 Quadtree)
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Seismic Sensor
Radar:R.F. Source,Demodulator, andSignal Processsing
Signal Generator
Elastic WaveTransducer
ElasticSurfaceWave
Mine
E.M. Waves
AirSoil
S N S
Wav
egui
deDisplacements
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Seismic SensorImage 30 dB Scale
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Outline
IntroductionMulti-resolution & Multi-modal Signal Processing
Physical Basis for Multimodal Processing/InversionQuadtree Imaging
SP for Three Sensor ExperimentReverse-Time Processing
FocusingImaging
Accomplishments/Plans
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Time Reverse Imaging
Probe the medium containing targets with P sources and measure reflection on N sensors
P sources (p) and N Receivers (q), each source sends a pulse which is received by N sensors
Form the Response Matrix, P(t), ( P x N x T )
Process P(t) in frequency domainOne frequency at a time
• Borcea, Papanicolaou, Tsogka, Berryman, “Imaging and Time Reversal in Random Media,” Inverse Problems, 2002.
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Problem Definition
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Time Reversal MethodEach source (P) sends a pulse, then scattered waves are received by receivers (N) to build up a response matrixIf e(t) is the transmitted pulse, then the received signal at each receiver is
Frequency Domain
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Time Reversal MethodIn Frequency domain, time reversal is equivalent to phase conjugation, hence after one time reversal operation
This signal is linked to the transmitted signal through a phase conjugation and a matrix called Time-Reversal Matrix
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Response Matrix Response matrix is given in terms of Green’s function between sources and targets and receiver and targets
M = number of targets, G(y,x,ω) = Green’s functionEigenvalues and eigenvectors of response matrix are related to each target
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Time Reversal MatrixSVD of response matrix and time reversal matrix is related by
Time Reversal Matrix can be interpreted as covariance matrix used in standard array processing techniques*
Receivers correspond to sensorsSources correspond to snapshots
* Prada, JASA., Vol. 144, No1, July 2003
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SVD of response matrix in Imaging
Determine number of targets (by using significant eigenvalues)Localize by using the eigenvectors
MUSIC-like methods: null vs. the “Noise Subspace”
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Near Field DOA & Range Estimation
Time Reversal Matrix can be interpreted as covariance matrix
Images obtained from Time Reversal have poor range resolution.
Formulate new methods for high resolution Range and DOA estimates?
Detect the position of targets using near-field DOA and Range estimatesEstimate target location with “Spot-Forming”
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Signal Model For Near Field
n sources located at (Ri,θi)Array of m sensors, with spacing d, with aperture of (m-1)dRange Information is given in terms of reference sensor #1
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Time Reversal & Near Field Model
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Green’s Vector
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Method for estimating near field DOA and Range Estimates
Two Frequency-Domain methods have been studied:
Frequency-Domain Method based on WVD (Wigner-Ville Distribution) and Fresnel approximation2-D MUSIC based algorithm
Time-domain processing based on direct time-delay estimation between sensors from singular vectors is possible
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2D MUSIC approachn sources located at (Ri,θi)Array of m sensors, with spacing d, with aperture of (m-1)dRange Information is given in terms of reference sensor #1No Fresnel approximation
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2D MUSIC approach
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Processing for Near Field Data
Use Time-Reversal Matrix as a covariance matrix KH(ω)K(ω) Signal/Noise subspace is same for both response matrix and Time-Reversal MatrixProcessing is done for different freqs
Frequencies used: [932 — 1050 Hz]then mean is takenReceiver spacing: d = λ/2, where λ corresponds to highest frequency
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Single Target6 Sources, 9 cm apart
15 Receivers, 2 cm apart
Peak Values are picked
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Two Targets6 Sources,9 cm apart
15 Receivers, 4 cm apart
Peak Values are picked
Two targets of same size and symmetric w.r.t. array
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Two Targets15 Sources,6 cm apart
23 Receivers, 4 cm apart
Peak Values are picked
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Effect of Number of Receivers
15 Sources,6 cm apart23 Receivers, 4 cm apart
15 Sources,6 cm apart46 Receivers, 2 cm apart
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AccomplishmentsDeveloped three sensor experiment to study multimodal processing
Developed new metal detector and a radarInvestigated two burial scenariosShowed responses for all the sensors over a variety of targetsDemonstrated possible feature for multimodal/cooperative processing
Developed reverse-time experiments, models, and processingDemonstrated focusingDemonstrated enhancement of mine signatureDemonstrated reverse-time imaging on numerical and experimental data
Buried structuresDeveloped numerical model for a buried structureDemonstrated two possible configurations for a sensor
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PlansThree sensor experiment
Incorporate reverse-time focusing and imagingMore burial scenarios based on inputs from the signal processing.
More/Stronger clutterDistribution of targets and clutterClose proximity between clutter and targets
Look for more connections between the sensor responses that can be exploited for multimodal/cooperative imaging/inversion/detection algorithmsDevelop multimodal/cooperative imaging/inversion algorithms
Reverse-time processingImprove experiments (Characterize/improve seismic sources)Perform experiments to improve demonstration of reverse time imagingImprove reverse-time imaging algorithmsInvestigate the use of reverse-time ideas to characterize the inhomogeneity of the ground
Buried StructuresOther scenariosSignal Processing