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Simulation Study of Muon Scattering For Tomography Reconstruction
Presented at NSS-MIC 2009 Orlando Florida Institute of Technology K. Gnanvo M. Hohlmann D. Mitra A. Banerjee 4/25/2017 Decision Sciences, San Diego, April 2010
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Decision Sciences, San Diego, April 2010
Muon Scattering Scattering angle Scattering function distribution: Approx. Normal (Bethe 1953) Heavy tail over Gaussian milirad 2 /cm 4/25/2017 Decision Sciences, San Diego, April 2010
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Decision Sciences, San Diego, April 2010
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 4/25/2017 Decision Sciences, San Diego, April 2010
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Decision 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 4/25/2017 Decision Sciences, San Diego, April 2010
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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 Introduced by Schultz et al. (at LANL) More physics based-model than POCA Estimates Scattering density (λ) per voxel 4/25/2017 Decision Sciences, San Diego, April 2010
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Decision Sciences, San Diego, April 2010
POCA Concept Incoming ray 3D POCA Emerging ray Three detector-array above and three below 4/25/2017 Decision Sciences, San Diego, April 2010
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POCA Result ≡ processed-Sinogram?
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U) Unit: mm Θ U W Pb Fe Al 4/25/2017 Decision Sciences, San Diego, April 2010
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Decision Sciences, San Diego, April 2010
POCA Pro’s Fast and efficient Accurate for simple scenario’s Con’s No Physics: multi- scattering ignored Deterministic Unscattered tracks are not used 4/25/2017 Decision Sciences, San Diego, April 2010
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Decision Sciences, San Diego, April 2010
ML-EM System Matrix L T Voxels following POCA track Dynamically built for each data set 4/25/2017 Decision Sciences, San Diego, April 2010
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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, momentum values estimate track-parameters (L, T) for all muons initialize λ (arbitrary small non-zero number, or…) 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 4/25/2017 Decision Sciences, San Diego, April 2010
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Decision Sciences, San Diego, April 2010
ML-EM Reconstruction [In ‘Next Generation Applied Intelligence’ (Springer Lecture Series in Computational Intelligence: 214), pp , June 2009.] Slow for complex scenario Our implementation used some smart data structure for speed and better memory usage 4/25/2017 Decision Sciences, San Diego, April 2010
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POCA Result for a vertical clutter
4/25/2017 Decision Sciences, San Diego, April 2010
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Decision Sciences, San Diego, April 2010
Slabbing Concept Slabbing Slice 3cm thick 4/25/2017 Decision Sciences, San Diego, April 2010
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Decision Sciences, San Diego, April 2010
“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 4/25/2017 Decision Sciences, San Diego, April 2010
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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 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) 4/25/2017 Decision Sciences, San Diego, April 2010
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Decision Sciences, San Diego, April 2010
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 4/25/2017 Decision Sciences, San Diego, April 2010
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Decision Sciences, San Diego, April 2010
POClust Results Medium: Air G4 Phantom U,W,Pb,Fe,Al Size: 40X40X20cm 4/25/2017 Decision Sciences, San Diego, April 2010
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Three target vertical clutter scenario
Fe W Al Fe Al-Fe-W: 40cm*40cm*20cm 100cm gap W 4/25/2017 Decision Sciences, San Diego, April 2010
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Three target vertical clutter scenario: Smaller gap
Al-Fe-W: 40cm*40cm*20cm 10cm gap Al Fe W 4/25/2017 Decision Sciences, San Diego, April 2010
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POClust Results: Reverse Vertical Clutter
Medium: Vacuum U Pb Al U-Pb-Al Size:40X40X20cm Gap:10cm 4/25/2017 Decision Sciences, San Diego, April 2010
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Decision Sciences, San Diego, April 2010
POClust Results Medium: Vacuum U inside Pb box U size: 10X10X10cm Pb Box: 200X200X200 cm Thickness(Pb box): 10cm 4/25/2017 Decision Sciences, San Diego, April 2010
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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 4/25/2017 Decision Sciences, San Diego, April 2010
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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) 4/25/2017 Decision Sciences, San Diego, April 2010
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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) 4/25/2017 Decision Sciences, San Diego, April 2010
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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 4/25/2017
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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 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 4/25/2017
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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 4/25/2017 Decision Sciences, San Diego, April 2010
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Department of Homeland Security National Science Foundation
Thanks! Acknowledgement: Department of Homeland Security National Science Foundation & many students at FIT Debasis Mitra 4/25/2017 Decision Sciences, San Diego, April 2010
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