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

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

Cosmic Ray-generated Muons more massive cousin of electron produced by cosmic ray decay arrives at sea-level @ 1 /cm2/min highly penetrating, long half-life affected by Coulomb force 10/27/2009 IEEE NSS-MIC 2009, Orlando, FL

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

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

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

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

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

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

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

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

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

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

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

IEEE NSS-MIC 2009, Orlando, FL ML-EM Reconstruction [In ‘Next Generation Applied Intelligence’ (Springer Lecture Series in Computational Intelligence: 214), pp. 225-231, 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 = 384000 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

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

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