Simulation Study of Muon Scattering For Tomography Reconstruction D. Mitra A. Banerjee K. Gnanvo M....

Simulation Study of Muon Scattering For Tomography Reconstruction

D. Mitra

A. Banerjee

K. Gnanvo

M. Hohlmann

Florida Institute of Technology

04/21/23 1Decision Sciences, San Diego, April 2010

Presented at NSS-MIC 2009 Orlando

Muon ScatteringMuon Scattering

Scattering angleScattering angle Scattering function Scattering function

distribution: Approx. Normaldistribution: Approx. Normal (Bethe 1953)(Bethe 1953)

Lrad

H

cp

MeV

15

rad

radLp

L115

2

0

Heavy tail over Gaussian


milirad 2 /cm

Types of Tomography• Emission tomography:

• SPECT• PET• MRI

• Transmission tomography• X-ray• Some Optical

• Reflection• UltraSound• Total Internal Reflection Fluoroscopy (TIRF)

• Scattering/ DiffusionMuon tomography• Some Optical (IR) tomography


Experiment

• GEANT4 simulation with partial physics for scattering

• Large array of Gas Electron Multiplier (GEM)

detector is being built • IEEE NSS-MIC’09 Orlando Poster# N13-246


Reconstruction Algorithms

Point of Closest Approach (POCA) Purely geometry based Estimates where each muon is scattered

Max-Likelihood Expectation Maximization for Muon Tomography

Introduced by Schultz et al. (at LANL) More physics based-model than POCA Estimates Scattering density (λλ) per voxel


POCA Concept

Incoming ray

Emerging ray

POCA

3D

Three detector-array above and three below


POCA Result ≡ processed-Sinogram?

AlFe

Pb

UW

Θ

40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)

Unit: mm


POCAPOCA

Pro’sPro’s Fast and efficientFast and efficient Accurate for simple Accurate for simple

scenario’sscenario’s Con’sCon’s

No Physics: multi-No Physics: multi-scattering ignoredscattering ignored

DeterministicDeterministic

Unscattered tracks Unscattered tracks are not usedare not used


ML-EM System MatrixML-EM System Matrix

Voxels following POCA track

x

L

T

Dynamically built for each data set


ML-EM AlgorithmML-EM Algorithm(adapted from Schultz et al., TNS 2007, & Tech Reports LANL)(adapted from Schultz et al., TNS 2007, & Tech Reports LANL)

(1)(1) gather data: (gather data: (ΔΘΔΘ, , ΔΔ, p): scattering angles, linear displacements, , p): scattering angles, linear displacements, momentum valuesmomentum values

(2)(2) estimate track-parameters (L, T) for all muonsestimate track-parameters (L, T) for all muons

(3)(3) initialize initialize λλ (arbitrary small non-zero number, or…) (arbitrary small non-zero number, or…)

(4)(4) for each iteration k=1 to I (or, until for each iteration k=1 to I (or, until λλ stabilizes) stabilizes)

(1)(1) for each muon-track i=1 to Mfor each muon-track i=1 to M

Compute CCompute Cijij

(2) for each voxel j=1 to N(2) for each voxel j=1 to N

// M// Mjj is # tracks is # tracks

(5) return (5) return λλ

0:

2 1)(

ijLi

ijold

jold

jnew

j CMj


ML-EM Reconstruction

• Slow for complex scenario

• Our implementation used some smart data structure for speed and better memory usage

[In ‘Next Generation Applied Intelligence’ (Springer Lecture Series in Computational Intelligence: 214), pp. 225-231, June 2009.]


POCA Result for a vertical clutter


Slabbing Concept

04/21/23 Decision Sciences, San Diego, April 2010 13

Slabbing Slice3cm thick

“Slabbing” studies with POCA: Filtered tracks with DOCA (distance of closest approach)

Ev: 10MilVertical stack: Al-Fe-W: 50cm50cm20cm, Vert. Sep: 10cm

Slab size: 3 cm


POClust Algorithm: clustering POCA points


Input: Geant4 output (list of all muon tracks and associated parameters)

1. For each Muon track {1. For each Muon track { 2.2. Calculate the POCA pt Calculate the POCA pt P P and its scattering-angle and its scattering-angle 3. 3. if ( if (PP lies outside container) continue; lies outside container) continue; 4.4. Normalize the scattering angle (angle*p/3GeV). Normalize the scattering angle (angle*p/3GeV). 5.5. CC = Find-nearest-cluster-to-the (POCA pt = Find-nearest-cluster-to-the (POCA pt PP);); 6.6. Update-cluster Update-cluster CC for the new pt for the new pt PP; ; 7. After a pre-fixed number of tracks remove sporadic-clusters;7. After a pre-fixed number of tracks remove sporadic-clusters; 8. 8. Merge close clusters with each-other } Merge close clusters with each-other } 9. Update 9. Update λλ (scattering density) of each cluster (scattering density) of each cluster C C using straight using straight tracks passing through tracks passing through CC

Output: A volume of interest (VOI)

POClust essentials


• Not voxelized, uses raw POCA points

•Three types of parameters:• Scattering angle of POCA point

• Normalized “proximity” of the point to a cluster

• how the “quality” of a cluster is affected by the new poca point andmerger of points or clusters

• Real time algorithm: as data comes in

POClust Results


G4 Phantom

Three target vertical clutter scenario


Al-Fe-W: 40cm*40cm*20cm 100cm gap

Al

Fe

W

AlFe

W

Three target vertical clutter scenario:Smaller gap


Al-Fe-W: 40cm*40cm*20cm 10cm gap

Al

Fe

W

POClust Results: Reverse Vertical Clutter


Al

U

Pb

POClust Results


Why POClust & Not just POCA visualization?

• Quantitate: ROC Analyses

• Improve other Reconstruction algorithms with a Volume of Interest (VOI) or

Regions of Interest (ROI)

• Why any reconstruction at all?POCA visualization is very noisy in a

complex realistic scenario


Additional works with POClust

1. Clustering provides Volumes of Interest (VOI) inside the container: Run ML-EM over only VOI for better precision and efficiency

2. Slabbing, followed by Clustering

3. Clusters growing over variable-sized hierarchical voxel tree, followed by ML-EM

4. Automated cluster-parameter

selection by optimization

5. Use cluster λ λ values in a Maximum

A Posteriori –EM, as priors (Wang

& Qi: N07-6)


POClust as a pre-processor


Volume of Interest reduces after Clustering:

A minimum bounding box(235cm X 235cm X 45cm)

Initial Volume of Interest (400cm X 400cm X 300cm)

Scenario: 5 targets VOI : 400X400X300 cm3

Iterations: 50

EM after pre-processing with POClust

Targets: Uranium (100,100,0), Tangsten (-100, 100, 0)

W

U

04/21/23 25

Scenario: U, W, Pb, Al, Fe placed horizontally Important Points:

◦ IGNORE ALL VOXELS OUTSIDE ROI◦ EM COMPUTATION DONE ONLY INSIDE ROI

Iterations

Actual Volume(400 X 400 X 300 cm)

Time taken (seconds)

Clustered Volume(235 X 235 X 45 cm )

Time taken (seconds)

100 113.5 21.5

60 99.54 20.2

50 95.6 19.5

30 84.48 17.4

10 79.27 16.0

Here, Total Volume = 400 X 400 X 300 cmVoxel Size= 5 X 5 X 5 cm#Voxels = 384000

After Clustering, VOI reduces, #Voxels = 18330

Results From EM over POClust generated VOI

04/21/23 26

A human in muon! …not on moon,

again, yet …


Twenty million tracksIn air background130cmx10cmx10cm Ca slab inside150cmx30cmx30cm H2O slab

GEANT4 Phantom


Thanks!

Debasis Mitra

[email protected]

Acknowledgement:Department of Homeland Security

National Science Foundation& many students at FIT

mailto:[email protected]

Simulation Study of Muon Scattering For Tomography Reconstruction D. Mitra A. Banerjee K. Gnanvo M....

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