Advances in Reconstruction Algorithms for Muon Tomography

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Advances in Reconstruction Algorithms for Muon
Tomography

• R. Hoch, M. Hohlmann, D. Mitra, K. Gnanvo

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Muon Tomography

• Cosmic Ray Muons
• More massive cousin of electron, produced by
  cosmic ray decay at rate 1 per cm2/min
• Highly penetrating, but affected by Coulomb force
• Tomography
• Imaging by sections
• CT, SPECT, PET scans

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Muon Tomography Concept
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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

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POCA Concept
Incoming ray
3D
POCA
Emerging ray
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POCA Result
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)
T
Unit mm
U
W
Pb
Fe
Al
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POCA Discussion

• Pros
• Fast and efficient
• Accurate for simple scenarios
• Cons
• Doesnt use all available information
• Unscattered tracks are useless

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EM Basis
Scattering Angle Scattering function
Distribution Gaussian (Rossi)
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EM Concept
L
T
Voxels following POCA track
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Algorithm

• gather data (?Tx, ??y, ?x, ?y, pr2)
• estimate LT for all muon-tracks
• initialize ? (small non-zero number)
• for each iteration k1 to I
• for each muon-track i1 to M
• Compute Cij
• for each voxel j1 to N
• return ?

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EM Results
40cmx40cmx20cm U block centered at the origin
Unit mm
z
x
y
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EM Results
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)
10cmx10cmx10cm Blocks (Al, Fe, Pb, W, U)
Unit mm
Unit mm
U
U
W
W
Fe
Pb
Fe
Pb
z
z
Al
Al
x
x
y
y
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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

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

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