Inversion via Bayesian Adaptive Multi-Modality Processing (AMMP)

Transcription

1 Inversion via Bayesian Adaptive Multi-Modality Processing (AMMP) Leslie Collins Electrical and Computer Engineering Duke University Work supported by DARPA/ARO MURI

2 Outline Problem Background and Setup Adaptive Feature Selection AMMP HSTAMIDS results NIITEK/GEM-3 results Georgia Tech results Confidence-based Fusion

3 Adaptive Feature Selection

4 Subsurface Sensing (Landmines, UXO, Subsurface Structures) Simulate seismic, EMI, and MAG data Large number of features available Pre-screener needed based on RDOF feature set Issue: best features function of sensor implementation, test site, etc. In some scenarios, need to adaptively select features Ultimately: AMMP applied to results of prescreener

5 NIITEK Radar Results Features selected based on training from test lanes Variable performance on off-road scenarios

6 Manual Feature Selection

7 RDOF Feature Selection Guide initial selection of features Adaptively prune features based on input from multiple sensors Carin et al. proposed RDOF for induction sensing Induction, mag, seismic still produce many features JCFO verified by Carin on acoustic data not yet applied to EMI/MAG/Seismic data In year 2, evaluated JCFO/adaptive feature selection on: GPR and EMI for landmines EMI and MAG for UXO Next year: Simulated data for subsurface structures

8 JCFO Classification of a feature vector, x, performed using kernel-based technique N c( x) = wnk( x, xn) + w n= 1 For a binary classifier with labels, l, of +1 and 1, training data T and weights w 1 pl ( = 1/ xtw,, ) = ( ) 1 + c x e pl ( = 1/ xtw,, ) = 1 pl ( = 1/ xtw,, ) A Laplacian sparseness prior is placed on the weights of the training samples x n 0

9 JCFO, Cont. Associate each training sample with parameter Beta, and each feature with parameter Theta example: training data of 128 samples, 17 features for each sample Theta[1] Theta[2] Theta[3] Theta[4] Theta[17] Object1: Object2: feature1 feature2 feature3 feature4 feature17 feature1 feature2 feature3 feature4 feature17 Beta[1] Beta[2]. Object128: feature1 feature2 feature3 feature4 feature17 Beta[128] Training Objective : Estimating parameters of Theta and Beta Feature Selection: Sparsity in Theta implies that it finds only a few features highly relevant for classification. (making some Theta[i]=0) Kernel function selection: Sparsity in Beta implies that it finds a small subset of data highly representative of the different classes (making some Beta[i]=0) Find the maximum a posterior (MAP) estimate of Theta and Beta using EM algorithm

10 Manual Physics-Based versus Random Feature Selection (EMI+MAG)

11 Physics-Based versus JCFO for EMI and MAG (Area 2) JCFO picks 4 features and used 5 of 128 training vectors!

12 Physics-Based versus JCFO for EMI and MAG (Area 1)

13 AMMP

14 Traditional Versus Collaborative/AMMP Approach Traditional: Sensor Algorithm Threshold Sensor Algorithm Threshold Data or Feature Fusion Collaborative/AMMP: Sensor Sensor Algorithm Fusion Algorithm Algorithm Decision Fusion Adaptive Control

15 AMMP Bayesian Processing Λ ( r) = f ( r / Θ, H ) f ( Θ/ H ) dθ 1 1 f ( r / Ω, H ) f ( Ω/ H ) dω 0 0 Two modes of adaptation Statistical parameters tracked and updated (e.g. covariance matrix) Priors on uncertain parameters modified based on context (e.g. size, depth of of radar response indicates an anti-tank mine, EMI library modified accordingly)

16 AMMP for Landmine Detection Prior work suggests adaptively pruning EMI/MD library using signature magnitude improved processor performance: LM vs vs HM Multi-modality processing suggests adaptively pruning EMI/MD library using GPR magnitude: AP vs vs AT suggests adaptively pruning GPR library using EMI/MD discrimination algorithms: mine type New work: incorporate uncertainty in in pruning algorithm into processing algorithm Sensor fusion at at data level or or decision level

17 MD Signature Library AP Response Library 2 θ LM HM Sig 1 Sig 1 Sig 2 Sig 2 Sig 3 Sig 3 AP 1 θ AT Sig N-1 Sig N *Sources of uncertainty Sig M-1 Sig M 2 Nt ( θi ) 1 x 1 = θi rx θi, j 1 θi, j i= 1 j= 1 f( r / H ) p( )[ f( / t, H ) p( t )] 1 Nt( θ ) i AT θ = AP, θ = AT

18 Application to Field Data: HSTAMIDS (Handheld, co-located MD and GPR)

19 A B C D E F G H I J K L 1 PMD-6 CL-2 TAB-1 CL-5RP VAL-69 CL-5RW CL-5RW TM-46 CL-5RP CL-3 VS2.2 Blank 1.75" 2.5" 1.125" 3.875" 2.75" 3.25" 2.0" 3.5" 2.5" 3.375" 1.0" 1 2 CL-1 CL-3 CL-2 CL-5IP CL-5RS CL-5IP CL-5IS CL-5RS CL-5IP M-14 CL-1 CL-4 3.0".9375" 1.875" 0.5" 1.5" 2.125" 2.875" 0.5" 3.75" 1.0" " 0.875" 2 3 VS2.2 CL-2 CL-3 CL-4 CL-3 CL-3 Blank Blank CL-3 3.5" Blank CL-2 4.0" CL-3 2.0" 2.875" 1.625" 0.25" 1.875" 0.75" 2.25" 3 4 CL-2 CL-4 M409 CL-3 TS-50 CL-5IW M409 CL-1 CL-2 CL-4 Blank 0.75" 0.75" 2.375" 2.25" " 1.5" 2.5" 2.25" 1.875" 1.25" Blank 4 5 CL-1 1.5" CL-1 CL-4 CL-4 CL-1 M-14 CL-1 CL " 4.0" 2.25" 1.75" " 0.625" 3.75" CL-2 2.5" Blank CL-1 3.0" CL-4 3.0" 5 6 M-19 CL-1 TMA-4 CL-3 CL-4 TM-62P3 CL-2 CL-4 2.5" Blank Blank CL-1 4.0" CL-4 3.0" 1.25" 2.75" 2.125" 2.25" " " 6 7 CL-2 M-14 CL-5IS M409 CL-3 CL-2 TS-50 CL-3 Blank CL-4 0.5" CL-3 2.0" 2.25" 0.5" 2.5" " 2.25" 0.75" 2.25" 3.25" Blank 7 8 Blank CL-3 TS-50 CL-2 TM-62P3 CL-1 CL-3 M-19 CL-1 M409 CL-3 0.5" CL-4 0.5" 3.5" 1.25" 2.875" 2.125" 2.625" 3.25" " 1.375" 0.5" 8 9 CL-4 M-19 CL-1 CL-1 VS.50 CL-4 CL-2 CL-4 1.5" CL-2 0.5" CL-1 1.5" CL-3 2.5" Blank 0.625" " 0.5" 3.625" 2.125" 1.25" 0.875" 9 10 TM-62P3 CL-4 CL-5IW CL-5RP CL-5IS TMA-4 CL-4 M-14 CL-4 Blank " 3.25" 1.25" 1.375" 2.25" 1.25" 2.25" 1.625" 2.75" CL-3 0.5" CL-1 3.5" CL-2 CL-1 CL-5RW VAL-69 CL-5RS CL-1 M409 TMA-4 CL-1 2.5" Blank CL " CL-2 4.0" 1.625" 1.875" 2.5" 1.75" 1.875" 1.375" 1.5" 1.375" CL-5RP CL-5IP VS2.2 CL-5IW CL-5RW CL-5RW CL-5IS CL-5RW CL-5IS CL-2 CL-3 Blank 0.875" 3.625" 3.25" 0.75" 1.625" 3.5" " 2.5" 1.25" 3.25" 3.25" TM-46 CL-5RS CL-2 CL-2 CL-5RW TM-46 CL-5RP CL-3 CL-4 CL-3 1.0" CL-1 0.5" Blank " 0.75" 1.875" 1.875" 1.0" 2.25" 3.0" 1.25" 2.625" CL-5IP CL-5RS CL-5IP TAB-1 CL-3 CL-5IW CL-5RS CL-5IW TS-50 CL-2 M " 2.125" 2.875" " 0.875" 2.25" 1.5" 2.125" 1.375" 1.25" 1.25" Blank VAL-69 CL-5RP TS-50 CL-3 CL-4 CL-4 CL-4 VS-50 CL " 0.75" 1.25" 0.25" 2.375" 1.25" 3.125" 0.875" 1.875" CL-1 2.5" Blank CL5-IS CL-3 CL-4 CL-1 TAB-1 CL-3 CL-1 TAB-1 Blank 3.0" 1.75" 1.25" 2.625" 1.125" 3.375" 0.75" 2.25" Blank Blank CL-2 2.5" CL-2 0.5" PMD " CL-4 CL-3 3.0" CL-3 1.0" Blank 1.875" Blank CL-4 VS-50 CL-4 Blank Blank Blank 0.875" 0.5" 1.375" Blank 18 CL-2 CL-2 CL-1 CL-2 CL-3 19 Blank " 2.375" 1.625" 0.75" 2.25" 20 JUXOCO TMA-4 Blank CL-4 3.5" CL-1 4.0" Blank " CL-2 CL-4 CL-2 21 CL-1 1.0" 21 Version Cal Grid (AMD) 3.75" 0.875" 3.125" 22 Blank CL-3 2.0" TMA-4 CL " 2.75" 22 A B C D E F G H I J K L 12 Mine types (2-5 of each AT, AP, LM, HM) 4 types metallic clutter: - CL1: < 3g - CL2: 3 to 10g - CL3: 11 to 40g - CL4: > 40g Non-metallic clutter: - Wood - Plastic - Stone Blank Ground

20 HM/LM MD Energy Comparison Note difference in in downtrack/crosstrack extent, as as well as as level of of response

21 Example of One Feature from MD Mix of AT/AP, LM/HM

22 Performance of HSTAMIDS MD HSTAMIDS MD Algorithm Performance Energy Detector 100% Detection 73% False Alarm Pd Feature/Region Energy Feature Pfa Feature-Based Detector 100% Detection 76% False Alarm Feature-Based Detector w/region Processing 100% Detection 24% False Alarm Can reduction of AP/AT, HM/LM uncertainty improve performance?

23 AT/AP GPR Energy Comparison Note difference in in downtrack/crosstrack extent

24 AT/AP GPR Energy Comparison as as well as as level of of response

25 Performance with Bayesian AMMP HSTAMIDS MD Algorithm Performance Energy Detector 100% Detection 73% False Alarm Feature-Based Detector 100% Detection 76% False Alarm Pd Feature/Region Energy Feature AMMP Pfa Feature-Based Detector w/region Processing 100% Detection 24% False Alarm Feature-Based Detector w/ Bayesian AMMP 100% Detection 17% False Alarm

26 Application to Field Data: NIITEK GPR and Geophex s GEM-3 Metal Detector

27 NIITEK GPR Data

28 GEM-3 Data Frequency PPM A Frequency PPM A Frequency PPM A1 Clutter Frequency PPM B Frequency PPM B Frequency PPM B20 VAL69 PMA-3 Clutter Clutter Frequency B2 VS50

29 AMMP Processing Results

30 Application to Lab Data: Georgia Tech s EMI, GPR and Seismic Sensors

31 EMI/GPR/Seismic Processing Data collected by Georgia Tech Progress First, consider single sensor processing Compare AMMP to various fusion algorithms Conclude: need a more difficult test set for AMMP to show its worth!

32 Seismic Sources MINES VS-2.2 (7cm deep) TS-50 (1.5cm deep) w/ Nail M-14 (0.5cm deep) VS-50 (1cm deep) PFM-1 (1.5 cm deep) VS-1.6 (6.5cm deep) Assorted Metal Clutter (2 to 4 cm deep) Burial Scenario #1 1.8m by 1.8m Scan Region Shells (4cm deep) Threaded Rod (3.5cm deep) Dry Sand (5cm deep) Penny (5.5cm deep) Rocks (3 and 4 cm deep) Nails (4cm deep) Cans (3 and 2.5 cm deep) Ball Bearing (3.5cm deep) Shells (5.5cm deep)

33 Seismic Sources MINES VS-50 (1.3cm deep) VS-2.2 (5.4cm deep) Burial Scenario #2 Assorted Metal Clutter (<3cm deep) CD (29cm deep) M-14 (1cm deep) TS-50 (1.3cm deep) PFM-1 (0.6cm deep) VS-50 (0.5cm deep) VS-1.6 (5.1cm deep) 1.8m by 1.8m Scan Region Can (2.2cm deep) Rocks (2, 2.2, 2.5, and 1.3cm deep)

34 EMI Responses

35 EMI Processing Results

36 GPR Responses

37 GPR Responses

38 GPR Processing Results

39 Initial Seismic Data/Results

40 Fusion

41 Confidence Fusion

42 Traditional Sensor Fusion Voting, Bayesian Decision, Bayesian Decision Statistic, Bayesian Decision Confidence (e.g. Hoballah and Varshney, Krzystofowicz and Long, Dasarathy, Blum, Kassam, and Poor, Chen and Varshney, Hall and Llinas) Confidence useful because normalized Usually assume sensors/decisions are independent Have not found Bayesian confidence fusion for the correlated case so have developed this metric

43 Confidence Fusion Confidence = probability of correct decision c c d * * * d, d Kd Hd, d Kd λ1 λ2kλn 1 2 N 1 2 * Pr( λ / Hd) Pr( Hd) f( λ/ Hd) Pr( Hd) * * = Pr( Hd / λ ) = Pr( λ ) f ( λ) = Pr( /, ) N f ( λ / Hd)Pr( Hd) f ( λ) λ= λ Compare results when confidence obtained rigorously and when confidence is assigned using a sigmoid function λ= λ * *

44 1 Individual sensor performance P D Sensor fusion performance P FA Sensor 1 Sensor 1 Performance Point Sensor 2 Sensor 2 Performance Point Sensor 3 Sensor 3 Performance Point P D Majority Vote Fusion 0.1 Bayesian Decision Fusion Sigmoid Confidence Fusion Decision Statistic Confidence Fusion P FA

45 Accomplishments Adaptive Feature Selection (JCFO) applied to UXO problem AMMP successfully applied to two sets of field data (HSTAMIDS, NIITEK) Multi-sensor data from Georgia Tech processed traditional fusion to date

46 Future Work JCFO application to landmines JCFO application to subsurface structures Simulation Data? AMMP application to EMI+GPR+Seismic Adaptively modify sensor parameters AMMP application to subsurface structures