Dr. Jacob Barhen

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Advances in Algorithms for Processing...
...CTIS Flash Hyperspectral Imagery
Deirdre' Johnson Research Alliance in Math and
Science Program Fisk University
Dr. Jacob Barhen Computer Science and
Mathematics Division
August 8, 2007 Oak Ridge, Tennessee
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OUTLINE

• MDA context for flash hyperspectral imaging
• Signal processing
• Approach
• CTIS information processing model and
  computational challenges
• Advances in algorithms
• Mixed expectation
• Asymptotic attractor dynamics
• Sparse conjugate gradient
• MART
• Conclusions and Future Work

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(No Transcript)
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Missile Defense Applications

• MDA Signal Processing and Computation
• MDAs objective is to detect, track and assess
  the killing of targets
• Target intercept generates spatially-distributed
  radiation
• Hyperspectral sensors collect spectrally-contiguou
  s images of the target intercept in 3D ( produces
  data cube x, y,
• Process collected data in shortest possible time
• The Approach
• Recover target information from data collected on
  FPA
• Solve very large scale system of noise-perturbed
  equations
• Analysis and identification based on spectral
  response to material content or temperature

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What is CTIS?

• Computed Tomography Imaging Spectrometer
• Sensor built by the University of Arizona
• Measures objects in a manner that requires
  complex post-processing
• Object cube projected on sensors focal plane
• Diffractive optics causes dispersion
• Images are blurred (noise)
• Requires solution of inverse problem

f
University of Arizona Computer Tomography Imaging
Spectrometer
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RESEARCH GOALS

• Develop , implement, and test
• innovative algorithms for CTIS
• image reconstruction
• Compare
• Speed of recovery
• Accuracy of reconstruction
• Identify a computer platform that
• would benefit this MDA application
• processing speed
• power required

Each blurred images represents a 2D recording of
a projection through the object cube at a
different angle
g?
g
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RECONSTRUCTION APPROACH

1. Mixed Expectation Maximization

• Costs and Challenges
• 3 matrix-vector multiplications per iteration
• results in about 2 m per iteration assuming some
  overlap can be achieved
• algorithm exhibits oscillatory behavior
• convergence requires over 100 iterations
  (typically, 500)
• UA stops at 10-20! ? ? 40 m / run

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2. Attractor Dynamics

• Benefits and Costs
• Limitations of conventional image inversion
• Conventional algorithms are too expensive because
  FPA is noisy
• optical system matrix H is non-square,
  non-symmetric, and singular
• Benefits of attractor dynamics paradigm
• no inversion of H required readily applies to
  non-square, non-symmetric, even singular matrices
• sparsity of H is fully exploited, and no
  transpose of H is used

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3. Conjugate Gradients

• Benefits and Costs
• Limitations of Conventional CG
• matrix A is assumed square, symmetric, and
  positive definite (SSPD)
• not the case for CTIS optical system matrix H
• For overdetermined systems, conventional CG
  considers the associated normal equations
• an SSPD matrix obtained by defining A HT H
• Benefits and costs of Sparse (NS)2 CG
• Sparsity of H is fully exploited, and no explicit
  transpose of H is required
• Readily applies to (NS)2 , i.e., non-square,
  non-symmetric matrices
• One additional (but sparse) matrix-vector
  multiplication needed per iteration
• Preconditioning required for large scale systems

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4. MULTIPLICATIVE ALGEBRAIC RECONSTRUCTION
TECHNIQUE (MART)

• Iterative algorithm proposed by UOA
• Much faster than MEM
• Assume noise was prefiltered

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Hyperspectral Object Reconstruction
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Hyperspectral Object Reconstruction
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Convergence to True Target Conjugate Gradient
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Convergence to True Target Conjugate Gradient
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Convergence to True Target Asymptotic Attractor
Dynamics
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Convergence to True Target Asymptotic Attractor
Dynamics
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Convergence to True Target Mixed Expectation
Maximization
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Convergence to True Target Mixed Expectation
Maximization
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Convergence to True Target MART
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Convergence to True Target MART
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Convergence to True Target Voxel Recovery Error
MART MEM
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Convergence to True Target Voxel Recovery Error
AA CG MART MEM
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CONCLUSIONS and FUTURE WORK

• Algorithms were implemented and tested
• Considerable speedup compared to previous methods
  were obtained
• Excellent accuracy in target acquisition
• Fastest algorithms will be implemented in IBM
  cell multi-core processor
• ORNL will support MDA on algorithms on real
  flight test missile experience
• CTIS will take measurements in real time
• Code will analyze data in real time

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Acknowledgements

• Department of Energy Office of Science/Advanced
  Scientific Computing Research (ASCR)
• Missile Defense Agency/Advanced Concepts
  Directorate
• Research Alliance in Math and Science (RAMS)
• ORNL
• Mrs. Debbie McCoy
• Dr. Jacob Barhen

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• ANY QUESTIONS?