Muon Tomography Algorithms for Nuclear Threat Detection

R. Hoch, D. Mitra, M. Hohlmann, K. Gnanvo

Tomography

• Imaging by sections Image different sides of a volume Use reconstruction algorithms to

combine 2D images into 3D Used in many applications

Medical Biological Oceanography Cargo Inspections?

Muons

Cosmic Ray Muons More massive cousin of

electron Produced by cosmic ray

decay Sea level rate 1 per

cm^2/min Highly penetrating, but

affected by Coulomb force

Muon Tomography

• Previous work imaged large structures using radiography

• Not enough muon loss to image smaller containers

• Use multiple coulomb scattering as main criteria

Muon Tomography Concept

Reconstruction Algorithms

Point of Closest Approach (POCA) Geometry based Estimate where muon scattered

Expectation Maximization (EM) Developed at Los Alamos National Laboratory More physics based Uses more information than POCA Estimate what type of material is in a given

sub-volume

Simulations

• Geant4 - simulates the passage of particles through matter

• CRY – generates cosmic ray shower distributions

POCA Concept

Incoming ray

Emerging ray

POCA

3D

POCA Result

AlFe

PbU

W

Θ (degrees)

40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)

Unit: mm

YX

Z

POCA DiscussionPOCA Discussion

Pro’sPro’sFast and efficientFast and efficientCan be updated continuouslyCan be updated continuouslyAccurate for simple scenario’sAccurate for simple scenario’s

Con’sCon’sDoesn’t use all available informationDoesn’t use all available informationUnscattered tracks are uselesUnscattered tracks are uselesssPerformance decreases for complex Performance decreases for complex

scenariosscenarios

Expectation Maximization

• Explained in 1977 paper by Dempster, Laird and Rubin

• Finds maximum likelihood estimates of parameters in probabilistic models using “hidden” data

• Iteratively alternates between an Expectation (E) and Maximization (M) steps

• E-Step computes an expectation of the log likelihood with respect to the current estimate of the distribution for the “hidden” data

• M-Step computes the parameters which maximize the expected log likelihood found on the E step

Basic PhysicsBasic Physics

Scattering AngleScattering Angle Scattering function Scattering function

Distribution ~ GaussianDistribution ~ Gaussian Non-deterministic (Rossi)Non-deterministic (Rossi)

Lrad

H

cp

MeV

15

rad

radLp

L115

2

0

20

2 )/( ppH

EM ConceptEM Concept

Voxels following POCA track

x

L

T

AlgorithmAlgorithm

(1)(1) gather data: (gather data: (ΔΘΔΘx, x, ΔθΔθy, y, ΔΔx, x, ΔΔy, pr^2)y, pr^2)

(2)(2) estimate LT for all muon-tracksestimate LT for all muon-tracks

(3)(3) initialize initialize λλ (small non-zero number) (small non-zero number)

(4)(4) for each iteration k=1 to Ifor each iteration k=1 to Ifor each muon-track i=1 to Mfor each muon-track i=1 to M

Compute Cij - Compute Cij - E-StepE-Step

for each voxel j=1 to Nfor each voxel j=1 to N

M-StepM-Step

(1)(1) return return λλ

0:

2 1)(

ijLi

ijold

jold

jnew

j CMj

Scenario 1 Geometry

5 40cmx40xcmx20cm Boxes

Scenario 1 Results10 minutes exposure

10cmx10cmx10cm voxels

X

Z

Y

Λ (mrad^2/cm)Axis in mm

Scenario 1 ResultsAccuracy Test

48000 total voxels, 32 Uranium

Threshhold: 1000

True Positives: 25False Negatives: 7True Positive Rate: 78.1%

False Positives: 119False Positive Rate: 0.0025%

Scenario 2 GeometrySimulated Truck

Red Boxes are UraniumBlue are Lower Z Materials

10 minutes exposure5cmx5cmx5cm voxels

Scenario 2 Results

X

Z

Y

Λ (mrad^2/cm)Axis in mm

Scenario 2 ResultsAccuracy Test

9704448 total voxels, 106 Uranium

Threshhold: 1000

True Positives: 90False Negatives: 16True Positive Rate: 85%

False Positives: 62False Positive Rate: 0.000006%

Median Method

Rare large scattering events cause the average correction value to be too big Instead, use median as opposed to average

Significant computational and storage issues Use binning to get an approximate median

))(( 2ij

oldj

oldj

newj Cmedian

Aproximate Median

Bin Size = 100,000

0 100,000 200,000 300,000 400,000+-100,000-200,000-300,000-400,000-

Cij = -357,000 Cij = -45,000 Cij = 25,000

Cij = 986,000

5 10 20 18 9 11 15 21 23 7

Total Tracks = 139 Median Track at 70 Track 70 in Bin 6

5 15 35 53 62 73 88 109 132 139

Take Average of Bin 6 (Total Value of Cij's / 11)

X

Z

Y

Λ (mrad^2/cm)Axis in mm

Scenario 1 Results10 minutes exposure5cmx5cmx5cm voxels

Scenario 1 ResultsAccuracy Test

48000 total voxels, 32 Uranium

Threshhold: 500

True Positives: 26False Negatives: 6True Positive Rate: 81.1%

False Positives: 31False Positive Rate: 0.000625%

X

Z

Y

Λ (mrad^2/cm)Axis in mm

10 minutes exposure5cmx5cmx5cm voxels

Scenario 2 Results

Scenario 2 ResultsAccuracy Test

9704448 total voxels, 106 Uranium

Threshhold: 500

True Positives: 97False Negatives: 9True Positive Rate: 91.5%

False Positives: 5False Positive Rate: 0.000001%

Future Work

Improvement of absolute lambda values

Real-time EM

Analysis of complex scenarios

Thanks!

Timing

Scenario 1:Average Method: 316sApproximate Median Method: 1533sMedian Method: ~12hrs

Scenario 2:Average Method: 1573sApproximate Median Method: 7953sMedian Method: +30hrs

Why Muon Tomography?

• Other ways to detect:– Gamma ray detectors (passive and active)

– X-Rays

– Manual search

• Muon Tomography advantages:– Natural source of radiation

• Less expensive and less dangerous

– Decreased chance of human error

– More probing i.e. tougher to shield against

– Can detect non-radioactive materials

– Potentially quicker searches