Sequential Adaptive Multi-Modality Target Detec-tion and Classification using Physics-Based Models

1. Sequential Adaptive Multi-Modality Target Detec-tion and Classification using Physics-Based Models • Professor Andrew E. Yagle (PI) (EECS) Signal and image processing, inverse scattering • Professor Alfred O. Hero III (EECS) Statistics, signal and image processing • Professor Kamal Sarabandi (Director, Rad Lab) Scattering, inverse scattering, remote sensing • Assistant Professor Marcin Bownik (Mathematics) Wavelets, functional analysis and approximation

2. Sequential Adaptive Multi-Modality Target Detec-tion and Classification using Physics-Based Models PROJECT SUPERVISION: • Dr. Douglas Cochran (DARPA) • Dr. Russell Harmon (ARO) INDUSTRY COLLABORATION: • Veridian (formerly ERIM) of Ann Arbor

3. Research Project Objectives • Develop overall algorithm for sequential detection, sensor management & selection • Develop physics-based models • Simplify physics-based models using functional-analysis-based approximation • Evaluate the resulting procedure on realistic models (statistical simulations) and real data

4. Issues: Overall Algorithm • How to select sensing modalities? • What is value-added for combining other modalities? Is it worth additional cost? • How do we implement data-adaptive configu-rations, e.g., selection of sources/receivers, based on scattering of targets and propagation in medium? • What are the figures of merit? • How to select decision thresholds?

5. Practical Applications Develop a set of signal processing/statistics al-gorithms to solve multi-modal sensing problems Examples: • Detection of “tanks under trees”: vehicles under canopy of tree foliage • Detection of buried objects (land mines)

6. Issues: Physics-Based Models • Scattering models • Hard targets of different types (vehicle, mines, etc.) • Clutter of different types (trees, rough surfaces, etc.) • Propagation models, e.g., tree canopies (attenuation, phase deformation, dispersion, etc.) • Sensor models • Radar, SAR, IR, etc. • Frequency, polarization, incidence angle, etc. • Model order reduction • Using function approximation, e.g., wavelets

7. Issues: Evaluation of Results • Behavior of algorithm on realistic models (UM Radiation Lab). • Benchmarking against physics-based models. • Figures-of-merit for evaluation of algorithm • Behavior of algorithm on real data

8. Overall Algorithm: Overview Sequential feedback structure: Detectibility for given sensor waveform/source/receiver used to guide future sensor selection Possible targets organized into tree structure leading to sequence of binary classifications Inverse filter based on physics-based model used to improve performance of the above

9. Target detector/ classifier Overall Algorithm: Overview

10. Target Detector/Classifier Hybrid hypothesis tests (majority rules): • Bayes optimal test: Optimal, but requires Bayesian priors for unknown parameters • GLRT: Use maximum likelihood estimates (MLE) for unknown parameters • Maximal Invariant: Project data onto subspace on which density functions are independent of unknown parameters

11. Target Detector/Classifier • EXAMPLE: ATR • 1 of 9 images~below hidden in image above (forest-grassy plain) • Location: column 305 at the A/B boundary • Clutter: #clutter-only reference chips used A B

12. Target Detector/Classifier • RESULTS: ATR • “Structured Kelly”: standard ATR GLRT • Figure-of-merit: min. detectable target amp. • MI best with 200 chips • GLR best with 250 • Hence need hybrid test

13. Target Detector/Classifier • SAR imaging: none of these 3 better than rest • We propose to use all 3 and let majority rule • Apply log(P) times to distinguish P possible target types (different models of tanks, mines) organized into a tree structure (known models) • Conditional pdf unknown parameters: Orientation, location, reflectivity of target Propagation characteristics of the medium

14. Target Detector/Classifier Vehicle type HMMWV Tank T72 Orientation

15. Physics based models

16. Physics-Based Models • Need models to develop conditional pdfs • Fast; include target, medium, sensor characteristics, with unknown parameters • Evaluation of integrals in Bayes optimal test: Monte Carlo marginalization too slow for us. • Sequential Importance Sampling: Denumerable-source blind deconvolution; Digital multi-user communications (real-time)

17. Physics-Based Models • Models needed for propagation and targets • Models include: unknown random parameters (e.g., wavelet coefficients-see the following) • Use Monte-Carlo-type simulations to obtain non-parametric estimates of pdfs for these • Validate these with real data for targets/clutter • Result: statistical models of targets and clutter

18. Physics-Based Models SAR image of tree stand using VV polarization Fractal generated tree stand

19. Physics-Based Models • Problem: Both the propagation and vehicle models are very complicated mathematically • Too complicated to be used as is in algorithm • Need: To simplify models so they can be used • How: Expand Green’s functions in efficient basis functions. Wavelets have proven to be very useful in electromagnetic modeling

20. Physics-Based Models • Solution: Need data-adaptive basis functions (precludes multipole expansions) • Adaptive anisotropic wavelet basis functions which are non-separable are more general and allow direction-dependent resolutions • Precomputed basis functions for different physical situations (e.g., forest types, season) • Try: “Best Basis” algorithm, “Basis Pursuit”

21. Detectibility Computer

22. Detectibility Computer • Issue : Should we use/deploy another sensor? • “Sensor”:Radar, acoustic, infrared and different frequencies & polarizations of radar (Both type and waveform of various sources) • Need: To compute value-added for another sensor: Improvement in E[detectibility - cost]. Choose the “sensor” which maximizes this. • Formulation: Dynamic stochastic scheduling

23. Detectibility Computer • “Cost”: Penalty for deploying another sensor: • Dollar cost of a UAV or other sensor times Pr[interception and destruction of new sensor] • Time cost in switching antennae types • Power cost in operating power and weight

24. Detectibility Computer • “Detectibility”: What does this mean? • Optimal: Use min Pr[detection] as criterion. • But: Too difficult to compute in real-time: Unknown target, unknown medium, etc. • Hence: Use easier-to-compute detectibility as a surrogate function for Pr[detection]. • Then: Choose “sensor” that maximizes E[detectibility-cost]based on previous data.

25. Detectibility Computer • “Detectibility”: What do we use for this? • Renyi information divergence: This is: • Much easier to compute (see next slide); • Related to Pr[detection] by error exponent; • Equals Kullback-Liebler distance between null model and most-likely target model for the special case a ~ 1. Choose 0 < a < 1.

26. Detectibility Computer • Renyi Information Divergence:RID • Log Pr[error] < (1-a)RID; so figure-of-merit. • Y = past data; N = Nth model; 0 = null model. • Conditional densities computed quickly with sequential importance sampling (see previous) Also may use particle filtering.

27. Mine Detection: Acoustic+Radar • One possible scenario of combining modalities • Acoustic source vibrates buried objects • Vibration significant at resonant frequencies • Radar source images vibrating objects • Doppler radar spectrum exhibits sharp peaks at resonant acoustic frequencies of objects • Use to identify shape and material of objects • Use this information in turn to detect mines

28. Mine Detection: Acoustic+Radar

29. Mine Detection: Multiple Sensors • Problem: False alarms time-consuming: Must treat each as if it is a real mine • Problem: Failure-to-detects disastrous! • Single-sensor technology is insufficient • Hybrid sensor modalities seem necessary to attain both very low Pr[F] and high Pr[D] • Multi-modal approach seems promising

30. Tanks Under Trees: Radar Sensor • Present work with ARL: Tanks Under Trees • 3-D MMW (millimeter wave) radar image: • Ka-band image of HMMWV on platform; • HMMWV parked under deciduous canopy • (UM/ARL field experiment in July 2000) • We are equipped for realistic work on this

31. Tanks Under Trees: Radar Sensor

32. Tanks Under Trees: Radar Sensor • Problems: Multiple scattering off of the: ground, trunk, leaves, branches, vehicle • Unknown presence and type of vehicles • Unknown orientation, location, reflectivity of vehicles (unknown parameters in models) • Unknown radar propagation characteristics through the atmosphere

33. Tanks Under Trees: Radar Sensor

34. Tanks Under Trees: Radar Sensor • Solutions: UM Radiation Lab has basic models for radar scattering off of vehicles • Parametrized by a few unknown parameters (position, orientation, reflectivity, etc.) • UM Radiation Lab also has good models for radar scattering off of tree canopies • Parametrized by a few unknown parameters (average leaf area, branch and trunk size)

35. Tanks Under Trees: Radar Sensor • Concept: Use radar at different frequencies and polarizations as multiple modalities • For each modality, already have good para- metrized models for vehicles and canopies • Combine these using previous sequential detection and sensor management algorithm to be developed as part of this research

36. Evaluation of Resulting Algorithms • UM Radiation Lab has a number of scattering models for vehicles and canopies • Permits realistic testing of algorithms • Compute ROC curves for various choices of: #sensors, sensor type, model dimension, noise • Figures-of-merit: power=Pr[detection] at fixed level of significance; area under ROC curve

37. Summary • Sequential detection and classification • Sensor scheduling and management • Physics-based models with dimensionality reduced using functional analysis • Vehicle and canopy scattering models already at UM permit test evaluations