Advances in Reconstruction Algorithms for Muon Tomography

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

Tomography

• Imaging by sections Image different sides of a volume Use reconstruction algorithms to

combine 2D images into 3D Used in many applications

Medical Biological Oceanography Cargo Inspections?

Muons

Cosmic Ray Muons More massive cousin of

electron Produced by cosmic ray

decay Sea level rate 1 per

cm^2/min Highly penetrating, but

affected by Coulomb force

Previous Work

E.P George Measured rock depth of a tunnel

Luis Alvarez Imaged Pyramid of Cheops in

search of hidden chambers

Nagamine Mapped internal structures of

volcanoes

Frlez Tested efficiency of CsI crystals for calorimetry

Muon Tomography

• Previous work imaged large structures using radiography

• Not enough muon loss to image smaller containers

• Use multiple coulomb scattering as main criteria

Why Muon Tomography?

• Other ways to detect:– Gamma ray detectors (passive and active)

– X-Rays

– Manual search

• Muon Tomography advantages:– Natural source of radiation

• Less expensive and less dangerous

– Decreased chance of human error

– More probing i.e. tougher to shield against

– Can detect non-radioactive materials

– Potentially quicker searches

February 20, 2009 Computer Science Seminar 7

Muon Detection

• Drift tubes: Drift tubes: • Low resolutionLow resolution• Proven technologyProven technology

• Gas Electron MultiplierGas Electron Multiplier• Higher resolutionHigher resolution• A challenge is buildingA challenge is building a large detector arraya large detector array

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

Reconstruction Concerns

• Accuracy

– No false negatives with low false positives

• Exposure time needed

– Goal is one minute

• Computation time

– POCA and EM have wildly different run times

• Online Algorithm

– Continuously updating algorithm

Simulations

• Geant4 - simulates the passage of particles through matter

• CRY – generates cosmic ray shower distributions

POCA Concept

Incoming ray

Emerging ray

POCA

3D

POCA Result

AlFe

Pb

UW

Θ

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

Unit: mm

POCA DiscussionPOCA Discussion

Pro’sPro’s Fast and efficientFast and efficient Can be updated continuouslyCan be updated continuously Accurate for simple scenario’sAccurate for simple scenario’s

Con’sCon’s Doesn’t use all available informationDoesn’t use all available information Unscattered tracks are uselesUnscattered tracks are uselesss Breaks down for complex scenariosBreaks down for complex scenarios

Expectation Maximization

• Explained in 1977 paper by Dempster, Laird and Rubin

• Finds maximum likelihood estimates of parameters in probabilistic models using “hidden” data

• Iteratively alternates between an Expectation (E) and Maximization (M) steps

• E-Step computes an expectation of the log likelihood with respect to the current estimate of the distribution for the “hidden” data

• M-Step computes the parameters which maximize the expected log likelihood found on the E step

EM BasisEM Basis

Scattering AngleScattering Angle Scattering function Scattering function

Distribution ~ GaussianDistribution ~ Gaussian (Rossi)(Rossi)

Lrad

H

cp

MeV

15

rad

radLp

L115

2

0

20

2 )/( ppH

EM ConceptEM Concept

Voxels following POCA track

x

L

T

AlgorithmAlgorithm

(1)(1) gather data: (gather data: (ΔΘΔΘx, x, ΔθΔθy, y, ΔΔx, x, ΔΔy, pr^2)y, pr^2)

(2)(2) estimate LT for all muon-tracksestimate LT for all muon-tracks

(3)(3) initialize initialize λλ (small non-zero number) (small non-zero number)

(4)(4) for each iteration k=1 to Ifor each iteration k=1 to I(1)(1) for each muon-track i=1 to Mfor each muon-track i=1 to M

(1)(1) Compute Cij - Compute Cij - E-StepE-Step

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

M-StepM-Step

(1)(1) return return λλ

0:

2 1)(

ijLi

ijold

jold

jnew

j CMj

Implementation

• One program coded in C

– POCA and EM independent

– Designed to make most efficient use of memory

– Developed to facilitate easy testing of different parameters (config file)

• Run on high performance computing cluster in HEP lab

EM ResultsEM Results

40cmx40cmx20cm U block centered at the origin40cmx40cmx20cm U block centered at the origin

xy

z

Unit: mm

EM ResultsEM Results

xy

z

x y

z

Unit: mm Unit: mm

40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U) 10cmx10cmx10cm Blocks (Al, Fe, Pb, W, U)

Al

FePb

UW

Al

FePb

UW

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

))(( 2ij

oldj

oldj

newj Cmedian

EM Median ResultsEM Median Results

40cmx40cmx20cm U block centered at the origin40cmx40cmx20cm U block centered at the origin

x

y

z

Unit: mm

EM ResultsEM Results

x y

z

x y

z

Unit: mm Unit: mm

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

Al

FePb

UW

Al

FePb

U

W

EM Median ResultsEM Median Results

x (mm)

y (mm)

z(λ)

x (mm)

y (mm)

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

Al

FePb

U

W

Al

FePb

U

W

z(λ)

EM Voxel Size Effects

x y

z

Unit: mm

Fe

x y

z

Fe

x y

z

Fe

x y

z

Fe

Unit: mm

Unit: mm

Unit: mm

EM Target Size Effects

x y

z

Unit: mm

x y

z

x y

z

x y

z

Unit: mm

Unit: mm

Unit: mm

U U

LANL Scenario

New standard scenario Detector Geometry

2mX2mX1.1m

3 10cmx10cmx10cm Targets W (-300mm, -300mm,

300mm) Fe (0mm, 0mm, 0mm) Al (300mm, 300mm, -300mm)

Only run with 5cmX5cmX5cm voxels

W

Fe

Al

Standard Scenario Average Results

xy

z

Unit: mm

Al

Fe

W

x (mm)

z(λ)

W

y (mm)

Standard Scenario Median Results

x y

z

Unit: mm

x (mm) y (mm)

z(λ)

x (mm) y (mm)

z(λ)

x (mm) y (mm)

z(λ)

Al

W

Fe

Online EM

• Unlike POCA, EM needs all data at once, preventing continuous updates

• Use multi-threading to collect data and run EM in parallel

– Experimentally find thresholds to determine when to transfer new data

• Simulate:

– Only process arbitrary number of events and run EM for a set number of iterations

– Process more events, run EM and repeat until all events are used

POCA Biased EM

• EM makes assumptions about “hidden” data

• Weight this data based on location to voxel containing POCA

– Total POCA – Voxels containing POCA 1, others 0

– Linear – Voxel containing POCA 1, others (POCA-voxel - current-voxel) / total-voxels-on-track

– Others – Experiment to figure out distribution of hidden data

Current Work

• Stabilize EM convergence and lambda values

• Create and analyze correction value distributions

– Some correction values very large or small and cause wild changes in lambda

– Determine why these values are so large or small

• Experiment with different parameters

– Alter initial lambda value

– Cut off large angles

Future Work

Improvement of lambda values/convergence

Online (Incremental) EM

Combination between EM and POCA

Analysis of complex scenarios

Who we are?

Team @ PSS department:Dr. Marcus HohlmannDr. Kondo GnanvoPatrcik Ford Ben StorchJudson LockeXenia FaveAmilkar SegoviaNick Leioatts

Team @ CS department:Dr. Debasis Mitra

Richard HochScott White

Sammy Waweru

Acknowledgement:Domestic Nuclear Detection Office of

Department of Homeland SecurityPast Students:

Jennifer Helsby, David Pena

Thanks!