muon tomography algorithms for nuclear threat detection r. hoch, d. mitra, m. hohlmann, k. gnanvo
TRANSCRIPT
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