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

04/21/23 2Decision Sciences, San Diego, April 2010

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

04/21/23 3Decision Sciences, San Diego, April 2010

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

04/21/23 4Decision Sciences, San Diego, April 2010

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

04/21/23 5Decision Sciences, San Diego, April 2010

POCA Concept

Incoming ray

Emerging ray

POCA

3D

Three detector-array above and three below

04/21/23 6Decision Sciences, San Diego, April 2010

POCA Result ≡ processed-Sinogram?

AlFe

Pb

UW

Θ

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

Unit: mm

04/21/23 7Decision Sciences, San Diego, April 2010

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

04/21/23 8Decision Sciences, San Diego, April 2010

ML-EM System MatrixML-EM System Matrix

Voxels following POCA track

x

L

T

Dynamically built for each data set

04/21/23 9Decision Sciences, San Diego, April 2010

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

04/21/23 10Decision Sciences, San Diego, April 2010

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.]

04/21/23 11Decision Sciences, San Diego, April 2010

POCA Result for a vertical clutter

04/21/23 12Decision Sciences, San Diego, April 2010

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

04/21/23 14Decision Sciences, San Diego, April 2010

POClust Algorithm: clustering POCA points

04/21/23 Decision Sciences, San Diego, April 2010 15

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

04/21/23 Decision Sciences, San Diego, April 2010 16

• 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

04/21/23 17Decision Sciences, San Diego, April 2010

G4 Phantom

Three target vertical clutter scenario

04/21/23 Decision Sciences, San Diego, April 2010 18

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

Al

Fe

W

AlFe

W

Three target vertical clutter scenario:Smaller gap

04/21/23 Decision Sciences, San Diego, April 2010 19

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

Al

Fe

W

POClust Results: Reverse Vertical Clutter

04/21/23 20Decision Sciences, San Diego, April 2010

Al

U

Pb

POClust Results

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

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

04/21/23 22Decision Sciences, San Diego, April 2010

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)

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

POClust as a pre-processor

04/21/23 Decision Sciences, San Diego, April 2010 24

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 …

04/21/23 Decision Sciences, San Diego, April 2010 27

Twenty million tracksIn air background130cmx10cmx10cm Ca slab inside150cmx30cmx30cm H2O slab

GEANT4 Phantom

04/21/23 Decision Sciences, San Diego, April 2010 28

Thanks!

Debasis Mitra

dmitra@cs.fit.edu

Acknowledgement:Department of Homeland Security

National Science Foundation& many students at FIT