Easy Does It: User Parameter Free Dense and Sparse Methods for Spectral Estimation

1. Easy Does It: User Parameter FreeDense and Sparse Methods for Spectral Estimation Jian Li Department of Electrical and Computer Engineering University of Florida Gainesville, Florida USA

2. Spectral Estimation • The goal of spectral estimation is to determine how power distributes over frequency from a finite number of data samples. • Diverse Applications • For example: synthetic aperture radar (SAR) imaging. • Data-Independent Approaches • FFT, Matched Filter, Delay-and-Sum (DAS) • Poor resolution • High sidelobe levels, especially with missing data. A SAR imaging example using FFT.

3. Data-Adaptive Spectral Estimation • Data-Adaptive Approaches • Examples: APES, Capon • Multiple snapshots needed to form reliable sample covariance matrices – fails for single or few snapshots, irregularly sampled data • High computational complexities • High resolution • Low sidelobe levels • Recent Development • Iterative Adaptive Approach (IAA) • Applicable to single snapshot scenario • High computational complexities • High resolution • Low sidelobe levels • Dense and accurate WFFT IAA

4. IterativeAdaptiveApproach (IAA) • Each iteration of IAA includes two steps (user parameter free): • Estimate coefficients: • Update covariance matrix estimate

5. IAA-R (IAA with Regularization) • Noise effect taken into account explicitly: • Still user parameter free!

6. Active Sensing Example • Active sensing (radar, sonar, etc.) • Received signal decomposition: 6

7. Range-Doppler Imaging Matched Filter Initialization

8. Movies Are Nice Local Quadratic Convergence of IAA Proven.

9. Radar GMTI Example Terrain map yellow or green dots: moving vehicles The goal of ground moving target indication (GMTI) is to detect slow moving targets in the stationary background.

10. STAP • STAP: space-time adaptive processing • Datacube: MN samples for fixed range bin Antenna Elements N Range bins fasttime 1 1 M Pulses slowtime (J. Ward ’94)

11. Adaptive Processing • Space-Time Adaptive Processor (Guerci et al. ’06)

12. Angle-Doppler Imaging in STAP Clutter power distribution over angle-Doppler for a fixed range dB IAA DAS

13. Target Detection for Fixed Angle Simulated Ground Truth • Target angle: 195 • A total of 200 targets with constant power • Average SCNR over range:-18.94 dB o Ground truth denoted byx

14. GLC (partial knowledge) Range-Doppler Images dB Ideal (total knowledge) IAA Prior (wrong knowledge)

15. ROC Curves • Median CFAR algorithm • applied to target detection • GLC detector • Automatic diagonal loading • Sample Number N = 20 • Prior detector • Wrong prior knowledge of the clutter-and-noise covariance matrix

16. Main-beam width: 5 target angles: 190 - 200 • (3-D target detection) • A total of 246 targets with varying power • Slow-movingtargets and/or weak targets present o o o azimuth = KASSPER DataSet

17. ROC Curves (KASSPER Data) • Median CFAR algorithm applied for target detection

18. Sparse Approaches • Related work: • is replaced by to yield a convex optimization problem. • LASSO: The least absolute shrinkage and selection operator. • BP: Basis pursuit, very similar to LASSO • FOCUSS: Focal underdetermined system solution • SBL: Sparse Bayesian learning • L1-SVD: L1 – singular value decomposition, similar to BP • CoSaMP: Compressive Sampling Matching Pursuit • Most existing algorithms require • Large computation times • User parameters • Hard to decide • Performance sensitive to choice of user parameter Minimize such that is satisfied.

19. Kragh et al. Approach • Kragh et al. uses optimization transfer technique to obtain an iterative procedure: • A recent paper on SAR imaging states: This is FOCUSS. “ ’’

20. SLIM • Sparse Learning via Iterative Minimization (SLIM) Solves the User Parameter Problem!(Tan, Roberts, Li, and Stoica, 2010) • SLIM Assumes the Following Hierarchical Bayesian Model: • SLIM is a MAP Approach:

21. SLIM Iterations • SLIM Iterates the Following Steps (Starting with DAS): Given q, SLIM is User Parameter Free – Easy to Use!

22. Regularized Minimization in SLIM • Cyclic approach with majorization minimization employed to minimize cost function. • Conjugate gradient + FFT can be used for efficient implementation of SLIM. • For fixed noise variance (i.e., making it a user parameter), SLIM becomes FOCUSS/Kragh et al. Approach.

23. FFT for GOTCHA

24. SLIM for GOTCHA

25. SLIM for GOTCHA

26. IAA (Dense) vs. SLIM (Sparse) • IAA is dense; SLIM is sparse. • IAA is more accurate; SLIM tends to bias downward. • IAA has high resolution; SLIM has higher resolution. • IAA’s fast implementation is trickier, especially for non-uniformly sampled data; SLIM is faster and its fast implementation is more straightforward.

27. Concluding Remarks • We need to devise dense and sparse methods that are user parameter free – easy to use in practice, • And accurate, • And with high resolution, • And computationally efficient.

28. Thank you!