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

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

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

POCA Concept Incoming ray 3D POCA Emerging ray

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

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

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

EM Concept L T Voxels following POCA track

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

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

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

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

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

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

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