Marcus Hohlmann with help from Ashraf Farahat Cosmic Rays and Air Showers.
Advances in Reconstruction Algorithms for Muon Tomography R. Hoch, M. Hohlmann, D. Mitra, K. Gnanvo.
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Transcript of 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, 2009 Computer Science Seminar 7
Muon Detection
• Drift tubes: Drift tubes: • Low resolutionLow resolution• Proven technologyProven technology
• Gas Electron MultiplierGas Electron Multiplier• Higher resolutionHigher resolution• A challenge is buildingA challenge is building a large detector arraya large detector array
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 DiscussionPOCA Discussion
Pro’sPro’s Fast and efficientFast and efficient Can be updated continuouslyCan be updated continuously Accurate for simple scenario’sAccurate for simple scenario’s
Con’sCon’s Doesn’t use all available informationDoesn’t use all available information Unscattered tracks are uselesUnscattered tracks are uselesss Breaks down for complex scenariosBreaks down for complex scenarios
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
EM BasisEM Basis
Scattering AngleScattering Angle Scattering function Scattering function
Distribution ~ GaussianDistribution ~ Gaussian (Rossi)(Rossi)
Lrad
H
cp
MeV
15
rad
radLp
L115
2
0
20
2 )/( ppH
AlgorithmAlgorithm
(1)(1) gather data: (gather data: (ΔΘΔΘx, x, ΔθΔθy, y, ΔΔx, x, ΔΔy, pr^2)y, pr^2)
(2)(2) estimate LT for all muon-tracksestimate LT for all muon-tracks
(3)(3) initialize initialize λλ (small non-zero number) (small non-zero number)
(4)(4) for each iteration k=1 to Ifor each iteration k=1 to I(1)(1) for each muon-track i=1 to Mfor each muon-track i=1 to M
(1)(1) Compute Cij - Compute Cij - E-StepE-Step
(2)(2) for each voxel j=1 to Nfor each voxel j=1 to N
M-StepM-Step
(1)(1) return return λλ
0:
2 1)(
ijLi
ijold
jold
jnew
j CMj
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 ResultsEM Results
40cmx40cmx20cm U block centered at the origin40cmx40cmx20cm U block centered at the origin
xy
z
Unit: mm
EM ResultsEM Results
xy
z
x y
z
Unit: mm Unit: mm
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U) 10cmx10cmx10cm Blocks (Al, Fe, Pb, W, U)
Al
FePb
UW
Al
FePb
UW
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
))(( 2ij
oldj
oldj
newj Cmedian
EM Median ResultsEM Median Results
40cmx40cmx20cm U block centered at the origin40cmx40cmx20cm U block centered at the origin
x
y
z
Unit: mm
EM ResultsEM Results
x y
z
x y
z
Unit: mm Unit: mm
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U) Average Approximate Median
Al
FePb
UW
Al
FePb
U
W
EM Median ResultsEM Median Results
x (mm)
y (mm)
z(λ)
x (mm)
y (mm)
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U) Average Approximate Median
Al
FePb
U
W
Al
FePb
U
W
z(λ)
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 Median Results
x y
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?
Team @ PSS department:Dr. Marcus HohlmannDr. Kondo GnanvoPatrcik Ford Ben StorchJudson LockeXenia FaveAmilkar SegoviaNick Leioatts
Team @ CS department:Dr. Debasis Mitra
Richard HochScott White
Sammy Waweru
Acknowledgement:Domestic Nuclear Detection Office of
Department of Homeland SecurityPast Students:
Jennifer Helsby, David Pena