Dr. Jacob Barhen Computer Science and Mathematics Division.

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



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


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


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


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


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


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


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


0

100

200

300

400

500

600

0 100 200 300 400 500 600

Iterations

Erro

r Mag

nitu

de

MART MEM

Hyperspectral Object Reconstruction


0

100

200

300

400

500

600

0 50 100 150 200 250 300 350

Iterations

Err

or

Mag

nit

ud

e

AA CG MART MEM

Hyperspectral Object Reconstruction


Convergence to True Target Conjugate Gradient

-0.2

0

0.2

0.4

0.6

0.8

1

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


Convergence to True Target: Conjugate Gradient

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120 140

Voxels

Valu

es o

f C

on

verg

en

ce

true value result value


Convergence to True TargetAsymptotic Attractor Dynamics

-0.2

0

0.2

0.4

0.6

0.8

1

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 initial guess


-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120 140

Voxels

Va

lue

s o

f C

on

ve

rge

nc

e


Convergence to True TargetAsymptotic Attractor Dynamics


Convergence to True TargetMixed Expectation Maximization

-1.5

-1

-0.5

0

0.5

1

1.5

0 5 10 15 20 25 30 35

Voxels

Val

ues

of C

on

verg

ence



-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120 140

Voxels

Val

ues

of C

on

verg

ence


Convergence to True TargetMixed Expectation Maximization


-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30 35

Voxels

Va

lue

s o

f C

on

ve

rge

nc

e


Convergence to True TargetMART


-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120 140

Voxels

Val

ues

of

Co

nve

rgen

ce


Convergence to True TargetMART


-350

-300

-250

-200

-150

-100

-50

0

50

100

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


-350

-300

-250

-200

-150

-100

-50

0

50

100

0 20 40 60 80 100 120 140

Voxels

Pe

rce

nta

ge

Re

co

ns

tru

cti

on

Err

or

AA CG MART MEM

Convergence to True TargetVoxel Recovery Error : AA – CG – MART –

MEM


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


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


ANY QUESTIONS?

Dr. Jacob Barhen Computer Science and Mathematics Division.

Documents

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department of energydevelop

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noisyoptical system

explicit transpose of

singular matricessparsity

d produces data cube