Dr. Jacob Barhen Computer Science and Mathematics Division.
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Dr. Jacob BarhenComputer Science and Mathematics Division
2OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
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
3OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
4OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
MDA Signal Processing and Computation
MDA’s objective is to detect, track and assess the “killing” of targets
Target intercept generates spatially-distributed radiation
Hyperspectral sensors collect spectrally-contiguous 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
Missile Defense Applications
5OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
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
sensor’s focal plane Diffractive optics causes
dispersion Images are blurred
(noise)
• Requires solution of inverse problem
University of ArizonaComputer Tomography Imaging Spectrometer
s g Hf
FPAObjectiveField stop
Disperser
Reimaginglens
Collimator
f gH s
f
6OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Develop , implement, and test innovative algorithms for CTISimage reconstruction
Compare
Speed of recovery
Accuracy of reconstruction
Identify a computer platform thatwould benefit this MDA application
processing speedpower required
Raw CTIS images on FPA
Each blurred images represents a 2D recording of a projection through the object cube at a different angle
g Hfg
gλ
RESEARCH GOALS
7OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
2 2 2 21
2 2 2 21 1
( 2 ) [( ) 2( ) ]{ }/{ }
[( ) ] [( ) ]
m M m Mm m s mn m m s mnn n m m
m s m s
gf f
H Hg
fH f
f
H
H fH
1.Mixed Expectation Maximization
Costs and Challenges3 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
RECONSTRUCTION APPROACH
8OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
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
1 2 ( )Tt
f f H g Hf
9OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
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
10OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
4. MULTIPLICATIVE ALGEBRAIC RECONSTRUCTION TECHNIQUE (MART)
Iterative algorithm proposed by UOA
Much faster than MEM
Assume noise was prefiltered
1 ( )
( )
Tn
n nn
Tf f
g
Hf
H
H
11OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
0
100
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0 100 200 300 400 500 600
Iterations
Erro
r Mag
nitu
de
MART MEM
Hyperspectral Object Reconstruction
12OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
0
100
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0 50 100 150 200 250 300 350
Iterations
Err
or
Mag
nit
ud
e
AA CG MART MEM
Hyperspectral Object Reconstruction
13OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Convergence to True Target Conjugate Gradient
-0.2
0
0.2
0.4
0.6
0.8
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1.2
0 5 10 15 20 25 30 35
Voxels
Va
lue
s o
f C
on
ve
rge
nc
e
true value result value intial guess
14OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Convergence to True Target: Conjugate Gradient
-0.2
0
0.2
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0 20 40 60 80 100 120 140
Voxels
Valu
es o
f C
on
verg
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ce
true value result value
15OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Convergence to True TargetAsymptotic Attractor Dynamics
-0.2
0
0.2
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0 5 10 15 20 25 30 35
Voxels
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lue
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f C
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rge
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e
true value result value initial guess
16OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
-0.2
0
0.2
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1
1.2
0 20 40 60 80 100 120 140
Voxels
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lue
s o
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nc
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true value result value
Convergence to True TargetAsymptotic Attractor Dynamics
17OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Convergence to True TargetMixed Expectation Maximization
-1.5
-1
-0.5
0
0.5
1
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0 5 10 15 20 25 30 35
Voxels
Val
ues
of C
on
verg
ence
true value result value initial guess
18OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
-0.2
0
0.2
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0.6
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1
1.2
0 20 40 60 80 100 120 140
Voxels
Val
ues
of C
on
verg
ence
true value result value
Convergence to True TargetMixed Expectation Maximization
19OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
-0.2
0
0.2
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0.6
0.8
1
1.2
0 5 10 15 20 25 30 35
Voxels
Va
lue
s o
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rge
nc
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true value result value initial guess
Convergence to True TargetMART
20OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
-0.2
0
0.2
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1
1.2
0 20 40 60 80 100 120 140
Voxels
Val
ues
of
Co
nve
rgen
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true value result value
Convergence to True TargetMART
21OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
-350
-300
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-50
0
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0 20 40 60 80 100 120 140
Voxels
Pe
rce
nta
ge
Err
or
MART MEM
Convergence to True TargetVoxel Recovery Error : MART – MEM
22OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
-350
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0
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0 20 40 60 80 100 120 140
Voxels
Pe
rce
nta
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ns
tru
cti
on
Err
or
AA CG MART MEM
Convergence to True TargetVoxel Recovery Error : AA – CG – MART –
MEM
23OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
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
24OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
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
25OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
ANY QUESTIONS?
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