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

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

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

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

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

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

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

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

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

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

Decision Sciences, San Diego, April 2010 ML-EM Reconstruction [In ‘Next Generation Applied Intelligence’ (Springer Lecture Series in Computational Intelligence: 214), pp. 225-231, 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

POCA Result for a vertical clutter 4/25/2017 Decision Sciences, San Diego, April 2010

Decision Sciences, San Diego, April 2010 Slabbing Concept Slabbing Slice 3cm thick 4/25/2017 Decision Sciences, San Diego, April 2010

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

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 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) 4/25/2017 Decision Sciences, San Diego, April 2010

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

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

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

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

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

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

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

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

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

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

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 4/25/2017

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

Department of Homeland Security National Science Foundation Thanks! Acknowledgement: Department of Homeland Security National Science Foundation & many students at FIT Debasis Mitra dmitra@cs.fit.edu 4/25/2017 Decision Sciences, San Diego, April 2010