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

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?

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

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

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

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

February 20, 2009Computer Science Seminar7 Muon Detection Drift tubes: Drift tubes: Low resolution Low resolution Proven technology Proven technology Gas Electron Multiplier Gas Electron Multiplier Higher resolution Higher resolution A challenge is building A challenge is building a large detector array a large detector array

Muon Tomography Concept

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

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

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

POCA Concept Incoming ray Emerging ray POCA 3D

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

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

Expectation Maximization Explained in 1977 paper by Dempster, Laird and Rubin 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

EM Basis Scattering AngleScattering function Scattering AngleScattering function Distribution ~ Gaussian(Rossi)

EM Concept Voxels following POCA track L T

Algorithm (1) gather data: (ΔΘx, Δθy, Δx, Δy, pr^2) (2) estimate LT for all muon-tracks (3) initialize λ (small non-zero number) (4) for each iteration k=1 to I (1)for each muon-track i=1 to M (1) Compute Cij - E-Step (2)for each voxel j=1 to N M-Step M-Step (1) return λ

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

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

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

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

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

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

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

EM Voxel Size Effects xy z Unit: mm Fe xy z xy z xy z Unit: mm

EM Target Size Effects xy z Unit: mm xy z xy z xy z UU

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

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

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

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

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

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

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

Who we are? PSS department: Dr. Marcus Hohlmann Dr. Kondo Gnanvo Patrcik Ford Ben Storch Judson Locke Xenia Fave Amilkar Segovia Nick Leioatts 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

Thanks!