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

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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
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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.
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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
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Iterative Adaptive Approach (IAA)

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

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IAA-R (IAA with Regularization)

• Noise effect taken into account explicitly
• Still user parameter free!

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Active Sensing Example

• Active sensing (radar, sonar, etc.)

• Received signal decomposition

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Range-Doppler Imaging
Matched Filter Initialization
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Movies Are Nice
Local Quadratic Convergence of IAA Proven.
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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.
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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)
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Adaptive Processing

• Space-Time Adaptive Processor

(Guerci et al. 06)
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Angle-Doppler Imaging in STAP
Clutter power distribution over angle-Doppler for
a fixed range
dB
IAA
DAS
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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 by x
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Range-Doppler Images
dB
Ideal (total knowledge)
IAA
Prior (wrong knowledge)
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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

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KASSPER DataSet
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ROC Curves (KASSPER Data)

• Median CFAR algorithm applied for target
  detection

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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.
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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.


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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

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SLIM Iterations

• SLIM Iterates the Following Steps (Starting with
  DAS)

Given q, SLIM is User Parameter Free Easy to
Use!
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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.

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FFT for GOTCHA
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SLIM for GOTCHA
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SLIM for GOTCHA
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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.
• IAAs fast implementation is trickier, especially
  for non-uniformly sampled data SLIM is faster
  and its fast implementation is more
  straightforward.

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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.

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• Thank you!