1. Simulation Study of Muon Scattering For Tomography Reconstruction
Florida Institute of Technology
K. Gnanvo
M. Hohlmann
D. Mitra, A. Banerjee, S. White,
S. Waweru, R. Hoch
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

2. IEEE NSS-MIC 2009, Orlando, FL
Co-ordinates
Where are we?
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

3. Cosmic Ray-generated Muons
more massive cousin of electron
produced by cosmic ray decay
arrives at /cm2/min
highly penetrating, long half-life
affected by Coulomb force
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

4. Muon Tomography Concept
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

5. IEEE NSS-MIC 2009, Orlando, FL
Muon Scattering
Scattering angle Scattering function
distribution: Approx. Normal (Bethe 1953)
Heavy tail over Gaussian
milirad 2 /cm
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

6. Cosmic-ray generated Muon
Generated by proton and upper atmosphere’s interaction
Median at about 3 Gev
Peaks at about 30 degree
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

7. Physics behind Models Emission tomography: Transmission 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
11/28/2018
CS Seminar, FIT

8. IEEE NSS-MIC 2009, Orlando, FL
Experiment
GEANT4 simulation with partial physics for
scattering
Large array of Gas Electron Multiplier (GEM)
detector is being built
Poster# N13-246
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

9. Reconstruction Algorithms
Point of Closest Approach (POCA)
Purely geometry based
Estimates where each muon is scattered
Max-Likelihood Expectation Maximization for Muon Tomography
Introduced by Schultz et al. (at LANL)
More physics based-model than POCA
Estimates Scattering density (λ) per voxel
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

10. IEEE NSS-MIC 2009, Orlando, FL
POCA Concept
Incoming ray 3D
POCA
Emerging ray
Three GEM detector-array above and three below
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

11. POCA Result ≡ processed-Sinogram
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)
Unit: mm Θ U W Pb Fe Al
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

12. IEEE NSS-MIC 2009, Orlando, FL
POCA Discussion
Pro’s
Fast and efficient
Accurate for simple scenario’s
Con’s
No Physics: multi- scattering ignored
Deterministic
Unscattered tracks are not used
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

13. IEEE NSS-MIC 2009, Orlando, FL
ML-EM System Matrix L T
Voxels following
POCA track
Dynamically built for each data set
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

14. ML-EM Algorithm // Mj is # tracks
(adapted from Schultz et al., TNS 2007, & Tech Reports LANL)
gather data: (ΔΘ, Δ, p): scattering angles, linear displacements, momentums
estimate track-parameters (L, T) for all muons
initialize λ (arbitrary small non-zero number)
for each iteration k=1 to I (or, until λ stabilizes)
for each muon-track i=1 to M
Compute Cij
(2) for each voxel j=1 to N
// Mj is # tracks
(5) return λ
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

15. IEEE NSS-MIC 2009, Orlando, FL
ML-EM Reconstruction
[In ‘Next Generation Applied Intelligence’ (Springer Lecture Series in Computational
Intelligence: 214), pp , June 2009.]
Very slow for complex scenario
Reconstruction used smart data structure for
speed and better memory usage
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

16. POCA Result ≡ processed-Sinogram
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

17. IEEE NSS-MIC 2009, Orlando, FL
Slabbing Concept
Slabbing Slice
3cm thick
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

18. IEEE NSS-MIC 2009, Orlando, FL
“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
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

19. 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
if (P lies outside container) continue;
4. Normalize the scattering angle (angle*p/3GeV).
5. C = Find-nearest-cluster-to-the (POCA pt P);
Update-cluster C for the new pt P;
After a pre-fixed number of tracks remove sporadic-clusters;
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)
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

20. IEEE NSS-MIC 2009, Orlando, FL
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
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

21. IEEE NSS-MIC 2009, Orlando, FL
POClust Results
Medium: Air
G4 Phantom
U,W,Pb,Fe,Al
Size: 40X40X20cm
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

22. Three target vertical clutter scenarioFe W Al Fe
Al-Fe-W: 40cm*40cm*20cm 100cm gap W
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

23. Three target vertical clutter scenario: Smaller gap
Al-Fe-W: 40cm*40cm*20cm
10cm gap Al Fe W
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

24. POClust Results: Reverse Vertical Clutter
Medium: Vacuum U Pb Al
U-Pb-Al
Size:40X40X20cm
Gap:10cm
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

25. IEEE NSS-MIC 2009, Orlando, FL
POClust Results
Medium: Vacuum
U inside Pb box
U size: 10X10X10cm
Pb Box: 200X200X200 cm
Thickness(Pb box): 10cm
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

26. 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
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

27. Additional works with POClust
Clustering provides Volumes of Interest (VOI) inside the container: Run ML-EM over only VOI for better precision and efficiency
Slabbing, followed by Clustering
Clusters growing over variable-sized hierarchical voxel tree, followed by ML-EM
Automated cluster-parameter
selection by optimization
5. Use cluster λ values in a Maximum
A Posteriori –EM, as priors (Wang
& Qi: N07-6)
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

28. 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)
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

30. 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

31. 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
After Clustering, VOI reduces,
#Voxels = 18330
Here, Total Volume = 400 X 400 X 300 cm
Voxel Size= 5 X 5 X 5 cm
#Voxels =
Iterations
Actual Volume
(400 X 400 X 300 cm)
Time taken (seconds)
Clustered Volume
(235 X 235 X 45 cm )
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

32. A human in muon! …not on moon, again, yet …
Twenty million tracks
In air background
130cmx10cmx10cm Ca slab inside
150cmx30cmx30cm H2O slab
GEANT4 Phantom
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

33. Thanks! Debasis Mitra dmitra@cs.fit.edu
Acknowledgement:
Department of Homeland Security
Domestic Nuclear Detection Office
Acknowledgement:
Patrick Ford
for single handed heroic effort in maintaining the cluster
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL