Inversion via Bayesian Multimodal Iterative Adaptive Processing (MIAP)

Transcription

1 Inversion via Bayesian Multimodal Iterative Adaptive Processing (MIAP) Leslie Collins, Yongli Yu, Peter Torrione, and Mark Kolba Electrical and Computer Engineering Duke University Work supported by DARPA/ARO MURI

2 Outline RDOF Feature Selection Adaptive Uncertainty Processing Tracking/Classification Sensor Management Processing Georgia Tech Data

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 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 previously applied to EMI/MAG/Seismic data Evaluated JCFO/adaptive feature selection on: EMI and MAG for UXO EMI and GPR for landmines

6 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

7 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

8 EMI Results FPDS System

9 MIAP

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

11 MIAP 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)

12 MIAP 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

13 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

14 Simulations: Proof of Concept MIAP can reduce P f by ΦΦ + ΦΦ ( ( Pd) d) ( ( Pd) d0) d ( µ ) ( µ ) = < d 2 0 = 2 2 ( µ ) δ 0 δ Experimental gains mimic these (2 test cases)

15 Follow-on Developments Theoretical treatment of imperfect class decision algorithms (assuming perfect performance hurts performance!) Theoretical proof of performance gain (previous page) Derivation of weight parameters for the multi- Gaussian case Determination of the optimal threshold (operating point) of individual classifiers Consider uncertainty in imperfect class decision algorithms

16 Substantial differences in pdfs of sensor outputs between testing and training sets (data from old JUXOCO grid)

17 PD training testing Fusion GPR test Processed MD test GPR training Processed MD training PF Resulting ROCs are quite different, and threshold settings do not translate. Need to consider uncertainty in threshold settings and performance metrics of individual sensors across testing and training sets (f)

18 Full uncertainty case

19 Even when not considering testing/training feature uncertainty, MIAP is more robust than full uncertainty case

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21 Uncertainty in Feature Distributions Assume the mean of the test data is a variable which has a uniform distribution centered at the training value. To incorporate this uncertainty into the MIAP algorithm use λ( c% ) = = c c c c max µ min µ max µ min µ c µ c c µ c c c P( x µ, c,mine) P( µ ) dµ w c c c c P( x µ, c, clutter) P( µ ) dµ w c c c c Px ( µ, c,mine) dµ w c c c Px ( µ, c,clutter) dµ w c c c

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24 Tracking

25 Adaptive Prescreening Previously used adaptive prescreener in depth bins (LMS) Extended subsurface anomalies across depth bins cause false alarms First approach: SSAD Second approach: target tracking

26 Segmented Shifting And Differencing Multiple Anomalies may move in opposite time/depth directions simultaneously Need to cancel all anomalies using nearby shifted versions of them if available

27 SSAD

28 Results of SSAD Processing Mode1 and Mode 2 Data Pre-SSAD Processing Post-SSAD Processing

29 Tracking/Discrimination Based on JMPD formulation developed by Kastella and colleagues and others using information-based metrics Can track unknown # of targets using Bayesian precepts Targets can be born and can die Well suited to GPR subsurface structure tracking.. Will evaluate extensions using particle filtering and alternative information metrics Must extend to consider coincident targets

30 Off-road NIITEK GPR processing

31 Sensor Management

32 Discrimination-Based Sensor Management Initial algorithm based on Kastella et al. S DPQ (, ) = Ps ( )ln( Ps ( )/ Qs ( )) s= 1 Select a cell which maximizes D Can be calculated recursively Initial simulations manage sensor threshold, cell sampling

33 Preliminary Results Error probability vs. number of measurements for 1 sensor and 1 target disc: 0 db direct: 0 db direct: 3 db direct: 6 db Pe Measurements

34 Work in Progress Extend to multiple sensors Consider unknown Pd, Pf for each sensor Constrained search (for ground based sensing as opposed to airborne) Overlapping targets Alternative measures of D (may not allow recursive formulation)

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

36 R31 CD D E A C AP2 S2 G R4 F S1 AP3 C2 B H I L N M K AP4 S3 S5 S4 Y AT2 X W V U AP1 TR T J DS AT1 S Stick O R C1 P Q AP5 19 Rocks Burial Scenario #3

37 This photograph shows the locations and orientations of the rocks, the aluminum can, and the VS-50 AP mine buried in the boxed region shown on the layout (previous slide). The corners of the region are indicated by the red and green markers. (90,0) (180,0) (90,-90) (180,-90)

38 EMI Energy

39 EMI Q-MSD (Train 3, Test 4)

40 Seismic Pre-processed Energy

41 GPR Pre-screener and Matched (Train 3, Test 4)

42 EMI Train & Test

43 GPR LMS & Energy

44 Seismic Results

45 Simple Fusion Results (Train 3, Test 4)

46 MIAP Processing Split data according to AP/AT classification Can utilize GPR pre-screener decision statistics to accomplish this Estimate Gaussian PDFs for other features for both AP and AT targets Utilize a-priori information from GPR (AP or AT) before calculating likelihood ratio based on Gaussian PDFs

47 Decision Statistics By Target Type AT DSs AP DSs

48 MIAP Results with Perfect AP/AT Classification

49 MIAP Results with Gaussian AP/AT Classification Only Change

50 MIAP and Fusion (Train 3, Test 4)

51 ICA Results (VS50 & Metal Clutter)

52 Accomplishments Adaptive Feature Selection (JCFO) successfully applied to landmine problem Uncertainties incorporated into MIAP processor improve robustness Adaptive tracking technique improves GPR detection performance Encouraging sensor management results Multi-sensor data from Georgia Tech processed using adaptive fusion