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

2. Muon Tomography Cosmic Ray Muons Tomography
More massive cousin of electron, produced by cosmic ray decay at rate 1 per cm^2/min
Highly penetrating, but affected by Coulomb force
Tomography
Imaging by sections
CT, SPECT, PET scans

3. Muon Tomography Concept

4. 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

5. POCA Concept
Incoming ray 3D
POCA
Emerging ray

6. 40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)
POCA Result
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)
Unit: mm Θ U W Pb Fe Al

7. POCA Discussion Pro’s Con’s Fast and efficient
Accurate for simple scenario’s
Con’s
Doesn’t use all available information
Unscattered tracks are useless

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

9. EM Concept L T
Voxels following
POCA track

10. 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
for each voxel j=1 to N
return λ

11. 40cmx40cmx20cm U block centered at the origin
EM Results
40cmx40cmx20cm U block centered at the origin
Unit: mm z x y

12. EM Results Unit: mm Unit: mm z z x y x y U U W W Pb Fe Pb Fe Al Al
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 Al z z Al x y x y

13. 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

14. 40cmx40cmx20cm U block centered at the origin
EM Median Results
40cmx40cmx20cm U block centered at the origin
Unit: mm z x y

15. 40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U) Average Approximate Median
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

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