Advances in Reconstruction Algorithms for Muon Tomography

1. Advances in Reconstruction Algorithms for Muon Tomography • R. Hoch, M. Hohlmann, D. Mitra, K. Gnanvo

2. Tomography • Imaging by sections • Image different sides of a volume • Use reconstruction algorithms to combine 2D images into 3D • Used in many applications • Medical • Biological • Oceanography • Cargo Inspections?

3. Muons • Cosmic Ray Muons • More massive cousin of electron • Produced by cosmic ray decay • Sea level rate 1 per cm^2/min • Highly penetrating, but affected by Coulomb force

4. Previous Work • E.P George • Measured rock depth of a tunnel • Luis Alvarez • Imaged Pyramid of Cheops in search of hidden chambers • Nagamine • Mapped internal structures of volcanoes • Frlez • Tested efficiency of CsI crystals for calorimetry

5. Muon Tomography • Previous work imaged large structures using radiography • Not enough muon loss to image smaller containers • Use multiple coulomb scattering as main criteria

6. Why Muon Tomography? • Other ways to detect: • Gamma ray detectors (passive and active) • X-Rays • Manual search • Muon Tomography advantages: • Natural source of radiation • Less expensive and less dangerous • Decreased chance of human error • More probing i.e. tougher to shield against • Can detect non-radioactive materials • Potentially quicker searches

7. Computer Science Seminar Muon Detection • Drift tubes: • Low resolution • Proven technology • Gas Electron Multiplier • Higher resolution • A challenge is building a large detector array

8. Muon Tomography Concept

9. Reconstruction Algorithms • Point of Closest Approach (POCA) • Geometry based • Estimate where muon scattered • Expectation Maximization (EM) • Developed at Los Alamos National Laboratory • More physics based • Uses more information than POCA • Estimate what type of material is in a given sub-volume

10. Reconstruction Concerns • Accuracy • No false negatives with low false positives • Exposure time needed • Goal is one minute • Computation time • POCA and EM have wildly different run times • Online Algorithm • Continuously updating algorithm

11. Simulations • Geant4 - simulates the passage of particles through matter • CRY – generates cosmic ray shower distributions

12. POCA Concept Incoming ray 3D POCA Emerging ray

13. POCA Result 40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U) Unit: mm Θ U W Pb Fe Al

14. POCA Discussion • Pro’s • Fast and efficient • Can be updated continuously • Accurate for simple scenario’s • Con’s • Doesn’t use all available information • Unscattered tracks are useless • Breaks down for complex scenarios

15. Expectation Maximization • Explained in 1977 paper by Dempster, Laird and Rubin • Finds maximum likelihood estimates of parameters in probabilistic models using “hidden” data • Iteratively alternates between an Expectation (E) and Maximization (M) steps • E-Step computes an expectation of the log likelihood with respect to the current estimate of the distribution for the “hidden” data • M-Step computes the parameters which maximize the expected log likelihood found on the E step

16. EM Basis Scattering Angle Scattering function Distribution ~ Gaussian (Rossi)

17. EM Concept L T Voxels following POCA track

18. Algorithm • gather data: (ΔΘx, Δθy, Δx, Δy, pr^2) • estimate LT for all muon-tracks • initialize λ (small non-zero number) • for each iteration k=1 to I • for each muon-track i=1 to M • Compute Cij - E-Step • for each voxel j=1 to N M-Step • return λ

19. Implementation • One program coded in C • POCA and EM independent • Designed to make most efficient use of memory • Developed to facilitate easy testing of different parameters (config file) • Run on high performance computing cluster in HEP lab

20. EM Results 40cmx40cmx20cm U block centered at the origin Unit: mm z x y

21. EM Results 40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U) 10cmx10cmx10cm Blocks (Al, Fe, Pb, W, U) Unit: mm Unit: mm U U W W Pb Fe Pb Fe z z Al Al x x y y

22. Median Method • Rare large scattering events cause the average correction value to be too big • Instead, use median as opposed to average • Significant computational and storage issues • Use binning to get an approximate median

23. EM Median Results 40cmx40cmx20cm U block centered at the origin Unit: mm z x y

24. EM Results 40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U) Average Approximate Median Unit: mm Unit: mm U U W W Fe Pb Pb Fe z z Al Al x x y y

25. EM Median Results 40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U) Average Approximate Median U U Fe W Pb Fe W Pb z (λ) Al z (λ) Al x (mm) x (mm) y (mm) y (mm)

26. EM Voxel Size Effects Unit: mm Unit: mm Fe Fe z z x y x y Unit: mm Unit: mm Fe Fe z z x y x y

27. EM Target Size Effects Unit: mm Unit: mm U U z z x y x y Unit: mm Unit: mm z z x y x y

28. LANL Scenario • New standard scenario • Detector Geometry 2mX2mX1.1m • 3 10cmx10cmx10cm Targets • W (-300mm, -300mm, 300mm) • Fe (0mm, 0mm, 0mm) • Al (300mm, 300mm, -300mm) • Only run with 5cmX5cmX5cm voxels W Fe Al

29. Standard Scenario Average Results Unit: mm W W z (λ) Fe z Al x (mm) x y y (mm)

30. Standard Scenario Median Results Unit: mm Al z (λ) z x (mm) y (mm) x y Fe W z (λ) z (λ) x (mm) x (mm) y (mm) y (mm)

31. Online EM • Unlike POCA, EM needs all data at once, preventing continuous updates • Use multi-threading to collect data and run EM in parallel • Experimentally find thresholds to determine when to transfer new data • Simulate: • Only process arbitrary number of events and run EM for a set number of iterations • Process more events, run EM and repeat until all events are used

32. POCA Biased EM • EM makes assumptions about “hidden” data • Weight this data based on location to voxel containing POCA • Total POCA – Voxels containing POCA 1, others 0 • Linear – Voxel containing POCA 1, others (POCA-voxel - current-voxel) / total-voxels-on-track • Others – Experiment to figure out distribution of hidden data

33. Current Work • Stabilize EM convergence and lambda values • Create and analyze correction value distributions • Some correction values very large or small and cause wild changes in lambda • Determine why these values are so large or small • Experiment with different parameters • Alter initial lambda value • Cut off large angles

34. Future Work • Improvement of lambda values/convergence • Online (Incremental) EM • Combination between EM and POCA • Analysis of complex scenarios

35. Who we are? Team @ PSS department: Dr. Marcus Hohlmann Dr. Kondo Gnanvo Patrcik Ford Ben Storch Judson Locke Xenia Fave Amilkar Segovia Nick Leioatts Team @ CS department: Dr. Debasis Mitra Richard Hoch Scott White Sammy Waweru Acknowledgement: Domestic Nuclear Detection Office of Department of Homeland Security Past Students: Jennifer Helsby, David Pena

36. Thanks!