Transcript Advances in Reconstruction Algorithms for Muon Tomography

Simulation Study of Muon Scattering
For Tomography Reconstruction
Florida Institute of Technology
D. Mitra, A. Banerjee, S. White,
M. Hohlmann
S. Waweru, R. Hoch
10/27/2009
K. Gnanvo
IEEE NSS-MIC 2009, Orlando, FL
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Co-ordinates
oWhere are we?
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Cosmic Ray-generated Muons
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more massive cousin of
electron
produced by cosmic ray
decay
arrives at sea-level @
1 /cm2/min
highly penetrating, long
half-life
affected by Coulomb
force
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Muon Tomography Concept
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Muon Scattering
Scattering angle
distribution: Approx. Normal
Scattering function
(Bethe 1953)
15MeV
 
cp
H
Lrad
2
 15  1
 Lrad    
 p 0  Lrad
Heavy tail over Gaussian
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milirad 2 /cm
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Cosmic-ray generated Muon
• Generated by proton and upper atmosphere’s interaction
• Median at about 3 Gev
• Peaks at about 30 degree
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Physics behind Models
• Emission tomography:
• SPECT
• PET
• MRI
• Transmission tomography
• X-ray
• Some Optical
• Reflection
• Ultra Sound
• Total Internal Reflection Fluoroscopy (TIRF)
• Scattering/ Diffusion
• Muon tomography
• Some Optical tomography
7/7/2015
CS Seminar, FIT
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Experiment
• GEANT4 simulation with partial physics for
scattering
• Large array of Gas Electron Multiplier (GEM)
detector is being built
• Poster# N13-246
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Reconstruction Algorithms
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Point of Closest Approach (POCA)
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Purely geometry based
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Estimates where each muon is scattered
Max-Likelihood Expectation Maximization for
Muon Tomography
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Introduced by Schultz et al. (at LANL)
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More physics based-model than POCA
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Estimates Scattering density (λ) per voxel
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POCA Concept
Incoming ray
3D
POCA
Emerging ray
Three GEM detector-array above and three below
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POCA Result ≡ processed-Sinogram
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)
Θ
Unit: mm
U
W
Pb
Fe
Al
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POCA Discussion
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Pro’s
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Fast and efficient
Accurate for simple
scenario’s
Con’s
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No Physics: multiscattering ignored
Deterministic
Unscattered tracks
are not used
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ML-EM System Matrix
L
T
Voxels following
POCA track
Dynamically built for each data set
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x
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ML-EM Algorithm
(adapted from Schultz et al., TNS 2007, & Tech Reports LANL)
(1)
gather data: (ΔΘ, Δ, p): scattering angles, linear displacements,
momentums
(2)
estimate track-parameters (L, T) for all muons
(3)
initialize λ (arbitrary small non-zero number)
(4)
for each iteration k=1 to I (or, until λ stabilizes)
(1) for each muon-track i=1 to M
Compute Cij
(2) for each voxel j=1 to N
j
new
 j
old
 ( j
old
1
)
Cij

Mj i:Lij 0
// Mj is # tracks
2
(5) return λ
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ML-EM Reconstruction
[In ‘Next Generation Applied Intelligence’ (Springer Lecture Series in Computational
Intelligence: 214), pp. 225-231, June 2009.]
• Very slow for complex scenario
• Reconstruction used smart data structure for
speed and better memory usage
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POCA Result ≡ processed-Sinogram
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Slabbing Concept
Slabbing Slice
3cm thick
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“Slabbing” studies with POCA:
Filtered tracks with DOCA (distance of closest approach)
Ev: 10Mil
Vertical stack: Al-Fe-W: 50cm50cm20cm, Vert. Sep: 10cm
Slab size: 3 cm
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POClust Algorithm: clustering POCA points
Input: Geant4 output (list of all muon tracks and associated parameters)
1. For each Muon track {
2. Calculate the POCA pt P and scattering-angle
3. if (P lies outside container) continue;
4. Normalize the scattering angle (angle*p/3GeV).
5. C = Find-nearest-cluster-to-the (POCA pt P);
6. Update-cluster C for the new pt P;
7. After a pre-fixed number of tracks remove sporadic-clusters;
8. Merge close clusters with each-other }
9. Update λ (scattering density) of each cluster C using straight
tracks passing through C
Output: A volume of interest (VOI)
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POClust essentials
• Not voxelized, uses raw POCA points
•Three types of parameters:
• Scattering angle of POCA point
• proximity of the point to a cluster
• how the “quality” of a cluster is affected
by the new poca point and
merger of points or clusters
• Real time algorithm: as data comes in
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POClust Results
G4 Phantom
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Three target vertical clutter scenario
Al
Fe
W
Al
Fe
Al-Fe-W: 40cm*40cm*20cm
100cm gap
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W
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Three target vertical clutter scenario:
Smaller gap
Al
Al-Fe-W: 40cm*40cm*20cm
10cm gap
Fe
W
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POClust Results: Reverse Vertical Clutter
U
Pb
Al
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POClust Results
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Why POClust &
Not just POCA visualization?
• Quantitate: ROC Analyses
• Improve other Reconstruction algorithms
with a Volume of Interest (VOI) or
Regions of Interest (ROI)
• Why any reconstruction at all?
POCA visualization is very noisy in a
complex realistic scenario
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Additional works with POClust
1. Clustering provides Volumes of Interest (VOI) inside the
container: Run ML-EM over only VOI for better
precision and efficiency
2. Slabbing, followed by Clustering
3. Clusters growing over variable-sized hierarchical voxel tree,
followed by ML-EM
4. Automated cluster-parameter
selection by optimization
5. Use cluster λ values in a Maximum
A Posteriori –EM, as priors (Wang
& Qi: N07-6)
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POClust as a pre-processor
Volume of Interest reduces
after Clustering:
A minimum bounding box
(235cm X 235cm X 45cm)
Initial Volume of Interest
(400cm X 400cm X 300cm)
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EM after pre-processing with POClust
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Scenario: 5 targets
VOI : 400X400X300 cm3
Iterations: 50
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Targets:
Uranium (100,100,0),
Tangsten (-100, 100, 0)
W
U
Results From EM over POClust generated VOI
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Scenario: U, W, Pb, Al, Fe placed horizontally
Important Points:
◦ IGNORE ALL VOXELS OUTSIDE ROI
◦ EM COMPUTATION DONE ONLY INSIDE ROI
Here, Total Volume = 400 X 400 X 300 cm
Voxel Size= 5 X 5 X 5 cm
#Voxels = 384000
Iterations
After Clustering, VOI reduces,
#Voxels = 18330
Actual Volume
(400 X 400 X 300 cm)
Clustered Volume
(235 X 235 X 45 cm )
Time taken (seconds)
Time taken (seconds)
100
113.5
21.5
60
99.54
20.2
50
95.6
19.5
30
84.48
17.4
10
79.27
16.0
A human in muon!
…not on moon,
again, yet …
Twenty million tracks
In air background
130cmx10cmx10cm Ca slab inside
150cmx30cmx30cm H2O slab
GEANT4 Phantom
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Thanks!
Debasis Mitra
[email protected]
Acknowledgement:
Department of Homeland Security
Domestic Nuclear Detection Office
Acknowledgement:
Patrick Ford
for single handed heroic effort in maintaining the cluster
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