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

lcarin@ee.duke.eduwww.ee.duke.edu/~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

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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