Transcript Advances in Reconstruction Algorithms for Muon Tomography

Simulation Study of Muon Scattering
For Tomography Reconstruction
Presented at
NSS-MIC 2009 Orlando
Florida Institute of Technology
K. Gnanvo
D. Mitra
M. Hohlmann
A. Banerjee
7/7/2015
Decision Sciences, San Diego, April 2010
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Muon Scattering
Scattering angle
distribution: Approx. Normal
Scattering function
(Bethe 1953)
15
MeV
H




cp Lrad
2
15
 1


L


rad
p
L
0
  rad
Heavy tail over Gaussian
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milirad 2 /cm
2
Types of Tomography
• Emission tomography:
• SPECT
• PET
• MRI
• Transmission tomography
• X-ray
• Some Optical
• Reflection
• UltraSound
• Total Internal Reflection Fluoroscopy (TIRF)
• Scattering/ Diffusion
 Muon tomography
• Some Optical (IR) tomography
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Experiment
• GEANT4 simulation with partial physics for
scattering
• Large array of Gas Electron Multiplier (GEM)
detector is being built
• IEEE NSS-MIC’09 Orlando Poster# N13-246
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Reconstruction Algorithms

Point of Closest Approach (POCA)

Purely geometry based

Estimates where each muon is scattered
Max-Likelihood Expectation Maximization for
Muon Tomography

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
Introduced by Schultz et al. (at LANL)

More physics based-model than POCA

Estimates Scattering density (λ) per voxel
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POCA Concept
Incoming ray
3D
POCA
Emerging ray
Three 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

Pro’s



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)
gather data: (ΔΘ, Δ, p): scattering angles, linear displacements,
momentum values
(1)
(2)
estimate track-parameters (L, T) for all muons
(3)
initialize λ (arbitrary small non-zero number, or…)
(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
 
// Mj is # tracks
1
 
( )
C
ij

Mj
i
:
L
ij

0
new
oldold
2
j
j
j
(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.]
• Slow for complex scenario
• Our implementation used some smart
data structure for speed and better
memory usage
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POCA Result for a vertical clutter
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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 its 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
• Normalized “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



Scenario: 5 targets
VOI : 400X400X300 cm3
Iterations: 50

Targets:
Uranium (100,100,0),
Tangsten (-100, 100, 0)
W
U
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Results From EM over POClust generated VOI


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
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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!
Acknowledgement:
Department of Homeland Security
National Science Foundation
& many students at FIT
Debasis Mitra
[email protected]
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