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Physics-Based Adaptive Multi-Modal Inverse Scattering and Sensing
Lawrence Carin, Xuejun Liao, Yanting Dong, Shaorong Chang, Zhijun Lu and Yijun YuDepartment of Electrical and Computer Engineering
Duke UniversityDurham, NC 27708-0291
[email protected]/~lcarin
Outline
• Reduced-degrees-of-freedom (RDOF) representations and feature optimization
- Simple physical models for inductive sensing- Bayesian sparse feature optimization
• Use of rigorous electromagnetic models (MLFMM) to validate simpler, more-efficient representations (ray models)
• Development of physics-based coding algorithms which adaptively capture thephysical information most important for inversion
• Bayesian adaptive inversion via an autonomous sensor
- Example results for inductive sensing of underground structures
• Future work
Physical RDOF for Induction Sensing
• Have demonstrated previously development of a simple model for induction sensing, which will play an important role in sensing mines, UXO and underground structures
zx , y
][])[()(2
o21
o1 ∑∑ −++
−++=
i ii
i ii j
bMj
aMωω
ωωω
ωω zzyyxxM
• Underground structure may be modeled as a summation of subsurface EMI dipoles
Solid: Measured Dotted: Model Fit (2 offset dipoles)
Dipole1 (2 poles)Resonant frequencies: f1 = 193 Hzf2 = 5613 Hz
Dipole2 (2 poles)Resonant frequencies: f1 = 104 Hzf2 = 654 Hz
Frequency (Hz)
Nor
mal
Mag
netic
Fie
ldRod and Ring Composite
Measurements: Y. Dalichaouch, Quantum Magnetics
Frequency (Hz)
Nor
mal
Mag
netic
Fie
ld
Rod and Ring Composite
Measurements: Y. Dalichaouch, Quantum Magnetics
RDOF for Feature Selection and Classification
• Classification effected via a kernel-based model
∑=
+=N
nnn wKwc
10),()( fff
where f is a feature vector and K(f,fn) is a measure of similarity between featurevector f and training example fn
• For a binary classifier, for which the label l is +1 or -1, we have the probability
)](exp[11),,1(
fwTf
clp
−+≡+=
),,1(1),,1( wTfwTf +=−=−= lplp
where T represents the training data and w the weights
• A Laplacian sparseness prior is employed for the weights wn, whereby we select themost “relevant” training examples fn
RDOF for Feature Selection and Classification
• The final Bayesian classifier is defined by
αwααTwwTfTf ddpplplp ∫∫ +==+= )(),(),,1(),1(
Kernel Model Laplacian Sparseness Prior
• Integrals evaluated efficiently via iterative procedure, with most weights wn going to zero
RDOF for Feature Selection and Classification
• The sparseness invoked above was in selecting a small number of representativeexamples from the training set
• We may also place weights on the individual feature components, by which weobtain sparseness in feature space as well
• We have termed this Joint Classification and Feature Optimization (JCFO)
• Used to process NSWC acoustic data for mines
1. Npix_nor: Number of normalized image pixels in the window that exceed a threshold2. Npix_mf: Number of matched-filter pixels in the window that exceed a threshold3. Max_pix_nor: Maximum normalized image pixel intensity in the window4. Max_pix_mf: Maximum matched-filter pixel intensity in the window5. HiLite_str_nor: Average highlight strength computed from the normalized image6. HiLite_str_mf: Average highlight strength computed from the matched-filter image7. Max_eig_nor: Length of major axis of an ellipse fit to highlight region of the normalized image8. Min_eig_nor: Width of minor axis of an ellipse fit to highlight region of the normalized image9. Max_eig_mf: Length of major axis of an ellipse fit to bright region of the matched-filter image10. Min_eig_mf: Width of minor axis of an ellipse fit to bright region of the matched-filter image11. Shadow_len: Shadow length12. Shadow_str: Shadow strength13. Max_pix_clu_mf: Maximum matched-filter intensity over the pixels in the detection cluster14. Npix_clu: Number of pixels in the detection cluster15. Nclusters: Number of detected clusters in the image (measure of clutter density)16 - 25. Nnor(i): Number of normalized pixels above threshold(i) in the window26 - 35. Nmf(i): Number of matched-filter pixels above threshold(i) in the window
36 - 45. Nnor_diff(i): Number of normalized pixels above threshold(i) in the window minus the number ofnormalized pixels above threshold(i) in the region that locally surrounds the window
46 - 55. Nmf_diff(i): Number of matched-filter pixels above threshold(i) in the window minus the number ofmatched-filter pixels above threshold(i) in the region that locally surrounds the window
56 - 58. Avg_nor(i) Average pixel intensity of normalized image over i-th window59 - 61. Avg_mf(i) Average pixel intensity of matched-filter image over i-th window
Classification Features for CSS CAD/CAC AlgorithmCoastal Systems Station
Classification and Feature Pruning
0 10 20 30 40 50 60 70-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Feature Number
Feat
ure
We i
ght
0 100 200 300 400 500 6000
5
10
15
20
25
30
35
40
45
Number of False Alarms
Num
ber o
f Tar
gets
Dec
lare
d C
orre
ctly
Outline
• Reduced-degrees-of-freedom (RDOF) representations and feature optimization
- Simple physical models for inductive sensing- Bayesian sparse feature optimization
• Use of rigorous electromagnetic models (MLFMM) to validate simpler, more-efficient representations (ray models)
• Development of physics-based coding algorithms which adaptively capture thephysical information most important for inversion
• Bayesian adaptive inversion via an autonomous sensor
- Example results for inductive sensing of underground structures
• Future work
1
2Z[m
]
-4
-2
0
2
4
6
X [m]-4
-2
0
2
Y [m]
X Y
Z
Tank with 7 trees in half spaceDiameter of the tree trunk: 30cm, Height: 5mIncident angle: phi = 90o, theta = 45o
X Y
Z|Re(<Js>*exp(jwt)/H0)| (v)4.003.713.433.142.862.572.292.001.711.431.140.860.570.290.00
Current distribution, with trees around - Vpol
shadows
shadows
X Y
Z|Re(<Js>*exp(jwt)/H0)| (v)2.001.861.711.571.431.291.141.000.860.710.570.430.290.140.00
Current distribution on trees - Vpol
1.5 cm
25 cm
VS2.2
Sandy soil
wood
Sensor 7. 5cm Above Ground
23 cm
15 cm
5 cm
0 1 2 3 4 5 6 7 8 9 10-7
-6
-5
-4
-3
-2
-1
0center position
time(ns)
ampl
itude
wood mine mine and wood
Top of wood Bottom of wood
Ground bounce
0 1 2 3 4 5 6 7 8 9 10-11
-10
-9
-8
-7
-6
-5
-4 the response from the mine with the wood
time(ns)
ampl
itude
center5cm 10cm
Note: Response from top of wood changes a lot as a function of sensor position, while mine signature is relatively stable
Mostly mine signature
Outline
• Reduced-degrees-of-freedom (RDOF) representations and feature optimization
- Simple physical models for inductive sensing- Bayesian sparse feature optimization
• Use of rigorous electromagnetic models (MLFMM) to validate simpler, more-efficient representations (ray models)
• Development of physics-based coding algorithms which adaptively capture thephysical information most important for inversion
• Bayesian adaptive inversion via an autonomous sensor
- Example results for inductive sensing of underground structures
• Future work
Multiple UAV Sensor Platforms
Flight Paths and Sensor Parameters Refined as Inversion Undertaken
Concealed Ground Target
UndergroundFacility
Conduit/Tunnel
Landmines
Multiple Robotic Sensor Platforms
Robot Positions & Sensor Parameters Refined as Inversion Undertaken
Physics-Based Importance Coding for Remote Inversion
• Have extended Bayes-VQ to the problem of remote-sensing importanceencoding, wherein the encoder accounts for the ultimate classification goal
• Define a hybrid distortion measure, which takes into account conventionalEuclidian distortion, as well as the affects of encoding on Bayes classification error
Targetp(y)
y Sensor Physics)( yxp
x, observed data Source Coding)( xxp ˆ
Remote Sensor(s)
Entropy Channel Coding/DecodingxxClassifier
)( xyp ˆˆy
Distortion Measure Accounting for Inversion Goals
Classifier
Physics-Based Statistical Modelof Sensor Physics
• Bayes-VQ employed to design codebook, encoder and decoder to optimize the composite distortion, which accounts for both reconstruction error and classification error
• Reconstruction error important because decoded data may be observed by human
• Phenomenology exploited in density function
• Amenable to a rate-distortion analysis, via extension of Blahut-Arimoto algorithm
)( xyp
)(])([1)(),( 2 xypyxCxxxxdy y
yy, ˆˆˆˆˆ
ˆ =+−= ∑ ∑ δλ
Example: Multi-Aspect Acoustic Sensing of Target
Target
0 0.5 1 1.5 2 2.50.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6La
gran
gian
Dis
tort
ion
Rate (Bits)
Rate-Distortion AnalysisHMM LloydHMM Bayes-VQ B = 2HMM Bayes-VQ B = 3TS Bayes-VQ B = 2TS Bayes-VQ B = 3
Sensor motion
Outline
• Reduced-degrees-of-freedom (RDOF) representations and feature optimization
- Simple physical models for inductive sensing- Bayesian sparse feature optimization
• Use of rigorous electromagnetic models (MLFMM) to validate simpler, more-efficient representations (ray models)
• Development of physics-based coding algorithms which adaptively capture thephysical information most important for inversion
• Bayesian adaptive inversion via an autonomous sensor
- Example results for inductive sensing of underground structures
• Future work
Multiple UAV Sensor Platforms
Flight Paths and Sensor Parameters Refined as Inversion Undertaken
Concealed Ground Target
UndergroundFacility
Conduit/Tunnel
Landmines
Multiple Robotic Sensor Platforms
Robot Positions & Sensor Parameters Refined as Inversion Undertaken
Bayesian Interpolation and Optimal Experiments
• Assume that data is collected as a function of the parameters x, and that we have aninterpolant modal y(x;w), where y represents the (scalar) measured data and w the modelparameters
• The measured data t(x) may be represented as t(x)=y(x;w)+n(x)
• After taking N measurements {tn,xn}n=1,N , the question is what should be the measurementparameters xN+1 for measurement N+1 that are most informative about the unknown target,reflected in the weights w
• After N measurements, we estimate most-probable parameters wMP, and perform a locally Gaussian approximation to pN(w)=exp[-M(w)]/ZM
wAwww ∆∆+≈ TMP 2
1)()( MM
Bayesian Interpolation and Optimal Experiments
• The regression model is linearized about the most-probable parameters wMP
where
• If the new observation xN+1 occurs within domain for which linear approximation isvalid, then the new Hessian is
• After simple manipulations, one can show that the most informative measurement, inthe sense of minimizing the average entropy of the parameters w, reduces to choosingxN+1 that maximizes
wxgwxx ∆⋅+≈ )();()( MPyy
jj wyg ∂∂= /
T21
1 ggAAσ
+≈+ NN
)()( 11T
1 +−
+ NNN gg xAx
Geometry of EMI Data Collecting System
…
…
…
… …
x
z
rn−rs
The y axis pointing out of the page
Source dipole at rnrn
rn
Moving Sensor dipole at rs
Target consisting of Ndipoles
Results of EMI Active Data Selection
-20 -15 -10 -5 0 5 10 15 20-20
-15
-10
-5
0
5
10
15
20
1
2 34
5
6
7
8
9
10
11 12
13
14
15
16
17
18
19
20
21
2223
24
25
digits=sensor positions,diamond=dipole position,angles=[45.0 45.0]
x dimension z=0 for sensor and 10 for dipoles
y di
men
sion
• Planar positions in (x,y) of the source dipole and sensor measurements.
Diomand: the source dipole
the digits are the positions rs where the data were measured, and the data are selected in the increasing order of the digits . The frequency ωs’s are fixed.
x position
0 5 10 15 20 250
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018MSE of EMI responses as a function of number of data used
number of data used in model fitting
mea
n sq
uare
d er
rors
(MS
E)
with data selectionwithout data selection
The data at r2, r3 , and r4 reduce the error bars effectively
Number of Points Used in Data Fitting
-30 -20 -10 0 10 20 30
-30
-20
-10
0
10
20
30
40
50
1
23
4
5
67
89
1011121314
15
161718192021222324
digits=sensor positions,diamond=dipole position,angles=[63.6 146.9] Deg.
xdimension z=0 for sensor and 10 for dipoles
y di
men
sion
testing gridsource dipoleinitial sensor position
0 5 10 15 20 2550
100
150
200
250
300
350
400
450
500
550optimal frequency in the same order as the optimal sensing positions
indexoftheoptimalsensing(positionsfrequency)op
timal
freq
uenc
y in
Hz
x position Position Index
Optimize Sensor Position and Active EMI Frequency
0 5 10 15 20 250
0.5
1
1.5
2
2.5
3
3.5MSE of EMI responses as a function of number of data used
number of data used in model fitting
mea
n sq
uare
d er
rors
(MS
E)
using data at optimal positionsusing data at initial positions
The data at r2 , r3 , and r4 reduce the error bars effectively
Number of Points in Model Fitting
Future Work
• Continue advanced forward-model development, with transition to simple RDOF representations
• Continue development of Bayesian joint classification and feature optimization (JCFO) algorithms
• Extend Bayes-VQ coding, with account for classification goal, to the case of multiplesensors on multiple platforms, accounting for information acquired by all
• Extend Bayesian optimal experiments to the case of sensors on multiple platforms (robots)wherein they operate as a team
• Extend optimal experiment design to vector sensor data