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Simulation Study of Muon Scattering For Tomography Reconstruction. D. Mitra A. Banerjee. K. Gnanvo M. Hohlmann. Presented at NSS-MIC 2009 Orlando. Florida Institute of Technology. Muon Scattering. Scattering angleScattering function distribution: Approx. Normal(Bethe 1953). - PowerPoint PPT Presentation
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Simulation Study of Muon Scattering For Tomography Reconstruction
D. Mitra
A. Banerjee
K. Gnanvo
M. Hohlmann
Florida Institute of Technology
04/21/23 1Decision Sciences, San Diego, April 2010
Presented at NSS-MIC 2009 Orlando
Muon ScatteringMuon Scattering
Scattering angleScattering angle Scattering function Scattering function
distribution: Approx. Normaldistribution: Approx. Normal (Bethe 1953)(Bethe 1953)
Lrad
H
cp
MeV
15
rad
radLp
L115
2
0
Heavy tail over Gaussian
04/21/23 2Decision Sciences, San Diego, April 2010
milirad 2 /cm
Types of Tomography• Emission tomography:
• SPECT• PET• MRI
• Transmission tomography• X-ray• Some Optical
• Reflection• UltraSound• Total Internal Reflection Fluoroscopy (TIRF)
• Scattering/ DiffusionMuon tomography• Some Optical (IR) tomography
04/21/23 3Decision Sciences, San Diego, April 2010
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
04/21/23 4Decision Sciences, San Diego, April 2010
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 (λλ) per voxel
04/21/23 5Decision Sciences, San Diego, April 2010
POCA Concept
Incoming ray
Emerging ray
POCA
3D
Three detector-array above and three below
04/21/23 6Decision Sciences, San Diego, April 2010
POCA Result ≡ processed-Sinogram?
AlFe
Pb
UW
Θ
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)
Unit: mm
04/21/23 7Decision Sciences, San Diego, April 2010
POCAPOCA
Pro’sPro’s Fast and efficientFast and efficient Accurate for simple Accurate for simple
scenario’sscenario’s Con’sCon’s
No Physics: multi-No Physics: multi-scattering ignoredscattering ignored
DeterministicDeterministic
Unscattered tracks Unscattered tracks are not usedare not used
04/21/23 8Decision Sciences, San Diego, April 2010
ML-EM System MatrixML-EM System Matrix
Voxels following POCA track
x
L
T
Dynamically built for each data set
04/21/23 9Decision Sciences, San Diego, April 2010
ML-EM AlgorithmML-EM Algorithm(adapted from Schultz et al., TNS 2007, & Tech Reports LANL)(adapted from Schultz et al., TNS 2007, & Tech Reports LANL)
(1)(1) gather data: (gather data: (ΔΘΔΘ, , ΔΔ, p): scattering angles, linear displacements, , p): scattering angles, linear displacements, momentum valuesmomentum values
(2)(2) estimate track-parameters (L, T) for all muonsestimate track-parameters (L, T) for all muons
(3)(3) initialize initialize λλ (arbitrary small non-zero number, or…) (arbitrary small non-zero number, or…)
(4)(4) for each iteration k=1 to I (or, until for each iteration k=1 to I (or, until λλ stabilizes) stabilizes)
(1)(1) for each muon-track i=1 to Mfor each muon-track i=1 to M
Compute CCompute Cijij
(2) for each voxel j=1 to N(2) for each voxel j=1 to N
// M// Mjj is # tracks is # tracks
(5) return (5) return λλ
0:
2 1)(
ijLi
ijold
jold
jnew
j CMj
04/21/23 10Decision Sciences, San Diego, April 2010
ML-EM Reconstruction
• Slow for complex scenario
• Our implementation used some smart data structure for speed and better memory usage
[In ‘Next Generation Applied Intelligence’ (Springer Lecture Series in Computational Intelligence: 214), pp. 225-231, June 2009.]
04/21/23 11Decision Sciences, San Diego, April 2010
POCA Result for a vertical clutter
04/21/23 12Decision Sciences, San Diego, April 2010
Slabbing Concept
04/21/23 Decision Sciences, San Diego, April 2010 13
Slabbing Slice3cm thick
“Slabbing” studies with POCA: Filtered tracks with DOCA (distance of closest approach)
Ev: 10MilVertical stack: Al-Fe-W: 50cm50cm20cm, Vert. Sep: 10cm
Slab size: 3 cm
04/21/23 14Decision Sciences, San Diego, April 2010
POClust Algorithm: clustering POCA points
04/21/23 Decision Sciences, San Diego, April 2010 15
Input: Geant4 output (list of all muon tracks and associated parameters)
1. For each Muon track {1. For each Muon track { 2.2. Calculate the POCA pt Calculate the POCA pt P P and its scattering-angle and its scattering-angle 3. 3. if ( if (PP lies outside container) continue; lies outside container) continue; 4.4. Normalize the scattering angle (angle*p/3GeV). Normalize the scattering angle (angle*p/3GeV). 5.5. CC = Find-nearest-cluster-to-the (POCA pt = Find-nearest-cluster-to-the (POCA pt PP);); 6.6. Update-cluster Update-cluster CC for the new pt for the new pt PP; ; 7. After a pre-fixed number of tracks remove sporadic-clusters;7. After a pre-fixed number of tracks remove sporadic-clusters; 8. 8. Merge close clusters with each-other } Merge close clusters with each-other } 9. Update 9. Update λλ (scattering density) of each cluster (scattering density) of each cluster C C using straight using straight tracks passing through tracks passing through CC
Output: A volume of interest (VOI)
POClust essentials
04/21/23 Decision Sciences, San Diego, April 2010 16
• 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 andmerger of points or clusters
• Real time algorithm: as data comes in
POClust Results
04/21/23 17Decision Sciences, San Diego, April 2010
G4 Phantom
Three target vertical clutter scenario
04/21/23 Decision Sciences, San Diego, April 2010 18
Al-Fe-W: 40cm*40cm*20cm 100cm gap
Al
Fe
W
AlFe
W
Three target vertical clutter scenario:Smaller gap
04/21/23 Decision Sciences, San Diego, April 2010 19
Al-Fe-W: 40cm*40cm*20cm 10cm gap
Al
Fe
W
POClust Results: Reverse Vertical Clutter
04/21/23 20Decision Sciences, San Diego, April 2010
Al
U
Pb
POClust Results
04/21/23 21Decision Sciences, San Diego, April 2010
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
04/21/23 22Decision Sciences, San Diego, April 2010
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 λ values in a Maximum
A Posteriori –EM, as priors (Wang
& Qi: N07-6)
04/21/23 23Decision Sciences, San Diego, April 2010
POClust as a pre-processor
04/21/23 Decision Sciences, San Diego, April 2010 24
Volume of Interest reduces after Clustering:
A minimum bounding box(235cm X 235cm X 45cm)
Initial Volume of Interest (400cm X 400cm X 300cm)
Scenario: 5 targets VOI : 400X400X300 cm3
Iterations: 50
EM after pre-processing with POClust
Targets: Uranium (100,100,0), Tangsten (-100, 100, 0)
W
U
04/21/23 25
Scenario: U, W, Pb, Al, Fe placed horizontally Important Points:
◦ IGNORE ALL VOXELS OUTSIDE ROI◦ EM COMPUTATION DONE ONLY INSIDE ROI
Iterations
Actual Volume(400 X 400 X 300 cm)
Time taken (seconds)
Clustered Volume(235 X 235 X 45 cm )
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
Here, Total Volume = 400 X 400 X 300 cmVoxel Size= 5 X 5 X 5 cm#Voxels = 384000
After Clustering, VOI reduces, #Voxels = 18330
Results From EM over POClust generated VOI
04/21/23 26
A human in muon! …not on moon,
again, yet …
04/21/23 Decision Sciences, San Diego, April 2010 27
Twenty million tracksIn air background130cmx10cmx10cm Ca slab inside150cmx30cmx30cm H2O slab
GEANT4 Phantom
04/21/23 Decision Sciences, San Diego, April 2010 28
Thanks!
Debasis Mitra
Acknowledgement:Department of Homeland Security
National Science Foundation& many students at FIT