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 at rate 1 /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
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
11/10/2018
CS Seminar, FIT

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

9. 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

10. 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

11. 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

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

13. 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

14. IEEE NSS-MIC 2009, Orlando, FL
Experiment
GEANT4 simulation with partial physics for
scattering
(Gas Electron Multiplier detector is
being built)
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

15. IEEE NSS-MIC 2009, Orlando, FL
MLEM Reconstruction
[In ‘Next Generation Applied Intelligence’ (Springer Lecture Series in Computational
Intelligence: 214), pp , June 2009.]
Very slow for complex scenario
A computing cluster (Grid Tier 3) is available,
but our programs run on a single node
Reconstruction used smart data structure for
speed and better memory usage
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

16. IEEE NSS-MIC 2009, Orlando, FL
Slabbing Concept
Slabbing Slice
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

17. IEEE NSS-MIC 2009, Orlando, FL
“Slabbing” studies with POCA: Filtered tracks 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

18. 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 (Vossman/3-D regression).
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

19. IEEE NSS-MIC 2009, Orlando, FL
Scenario 1 Geometry
Five 40cmx40xcmx20cm Boxes
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

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

21. Three target scenario geometriesAl
Al-Fe-W: 40cm*40cm*20cm 10cm separation gap Fe W Al Fe
Al-Fe-W: 40cm*40cm*20cm 1m separation gap W
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

22. POClust Results: vertical clutter
Medium: Vacuum
POClust Results: vertical clutter
Al-Fe-W: 100cm vertical gap
Al-Fe-W
Size: 50X50X20cm
Separation: 10cm
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

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

24. 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

25. 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

26. Additional works with POClust
Clustering provides Volumes of Interest (VOI) inside the container: Run MLEM over only VOI’s for better precision and efficiency
Slabbing, followed by Clustering
Clustering first, and then sub-dividing regions into variable-sized hierarchical voxel tree, followed by MLEM
Clusters expanded over voxels
Automated cluster-parameter
selection by optimization
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL

27. 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

29. 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

30. 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

31. 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

32. Department of Homeland Security Domestic Nuclear Detection Office
Thanks!
Debasis Mitra
Acknowledgement:
Department of Homeland Security
Domestic Nuclear Detection Office
10/27/2009
IEEE NSS-MIC 2009, Orlando, FL