Robust statistical reconstruction for charged particle tomography

• US 20130238291A1
• Filed: 10/24/2007
• Published: 09/12/2013
• Est. Priority Date: 10/27/2006
• Status: Active Grant

• Current Assignee: Los Alamos National Security LLC (Government of the United States of America)
• Original Assignee: Andrew Mcleod Fraser, Nicolas W. Hengartner
• Inventors: Schultz, Larry Joe, Klimenko, Alexei Vasilievich, Morris, Christopher, Borozdin, Konstantin N., Sossong, Michael James, Fraser, Andrew McLeod, Orum, John Christopher, Hengartner, NIcolas W.
• Granted Patent: US 8,552,370 B2
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: G01N 23/20 by using diffraction of the radiation by the materials, e.g. for investigating crystal structure; by using scattering of the radiation by the materials, e.g. for investigating non-crystalline materials; by using reflection of the radiation by the materials
• CPC Class Codes: G01N 23/207 Diffractometry using detectors, e.g. using a probe in a central position and one or more displaceable detectors in circumferential positions
• CPC Class Codes: G01V 5/222 measuring scattered radiation
• CPC Class Codes: G01V 5/26 Passive interrogation, i.e. by measuring radiation emitted by objects or goods
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04

Abstract

Systems and methods for charged particle detection including statistical reconstruction of object volume scattering density profiles from charged particle tomographic data to determine the probability distribution of charged particle scattering using a statistical multiple scattering model and determine a substantially maximum likelihood estimate of object volume scattering density using expectation maximization (ML/EM) algorithm to reconstruct the object volume scattering density. The presence of and/or type of object occupying the volume of interest can be identified from the reconstructed volume scattering density profile. The charged particle tomographic data can be cosmic ray muon tomographic data from a muon tracker for scanning packages, containers, vehicles or cargo. The method can be implemented using a computer program which is executable on a computer.

Claims

1. A method for detecting an object volume from charged particle tomographic data obtained from the object volume, said method comprising:

(a) obtaining predetermined charged particle tomographic data corresponding to scattering angles and estimated momenta of charged particles passing through an object volume;

(b) providing the probability distribution of a charged particle scattering for use in an expectation maximization (ML/EM) algorithm, said probability distribution being based on a statistical multiple scattering model;

(c) determining a substantially maximum likelihood estimate of the object volume scattering density using said expectation maximization (ML/EM) algorithm; and

(d) outputting a reconstructed object volume scattering density based on the substantially maximum likelihood estimate.

2. The method of claim 1, comprising:

making a decision on at least one of (1) a presence and (2) a type of a target object in the object volume based on said reconstructed object volume scattering density.

3. The method of claim 1, wherein providing the probability distribution of a charged particle scattering for use in an expectation maximization (ML/EM) algorithm comprises:

(g) obtaining a probability distribution in 2D for a charged particle based on a predefined scattering density of a homogenous object;

(h) obtaining a 3D probability distribution for said charged particle based on said 2D probability distribution;

(i) obtaining a probability distribution for scattering of multiple charged particles through a non-homogenous object volume characterized via basis functions; and

(j) obtaining a probability distribution for multiple scattering based on said definition thereof and scattering and momentum measurements of said charged particles.

4. The method of claim 3, wherein obtaining a probability distribution in 2D for a charged particle based on a predefined scattering density of an homogenous object comprises

(k) determining the scattering density of a material as the expected mean square scattering of said charged particles through a unit depth of said material;

(l) approximating the charged particle scattering distribution based on a Gaussian model; and

(m) approximating charged particle ray scattering and displacement based on a correlated 2D Gaussian distribution.

5. The method of claim 3, wherein obtaining a 3D probability distribution for said charged particle based on said 2D probability distribution comprises:

adding a coordinate and defining a three dimensional path length;

computing a 3D displacement; and

defining a 3D covariance matrix.

6. The method of claim 5, wherein obtaining a probability distribution for scattering of multiple charged particles through a non-homogenous object volume characterized via basis functions comprises

establishing a 3D grid of basis functions representing discrete scattering density estimates;

determining the scattering/displacement covariance matrix for each individual moon as a function of the ray path and scattering density estimates; and

determining a probability distribution for a plurality of charged particles as the product of individual charged particle probabilities.

7. The method of claim 1, wherein determining a substantially maximum likelihood estimate of the object volume scattering density using said expectation maximization (ML/EM) algorithm comprises

gathering measurements of scattering and momentum for each charged particle;

estimating geometry of interaction of each charged particle with each basis function of said statistical scattering model;

for each charged particle basis function pair, determining the weight matrix;

W_ij;

initializing scattering density in each basis function with a guess; and

iteratively solving for the approximate maximum likelihood solution for object volume contents;

wherein the iterative process is stopped at a predetermined number of iterations or when the solution is changing less than a predetermined tolerance value.

8. The method of claim 1, wherein determining a substantially maximum likelihood estimate of the object volume scattering density using said expectation maximization (ML/EM) algorithm comprises

gathering measurements of scattering and momentum for each charged particle i=1 to M (Δ

θ

_x,Δ

θ

_y,Δ

x,Δ

_y,p_r²)_i;

estimating the geometry of interaction of each moon with each voxel j=1 to N;

(L,T)_ij;

for each charged particle voxel pair, computing the weight matrix;

W_ij as

9. The method of claim 1, wherein said expectation maximization (ML/EM) algorithm includes a mean update rule or a median update rule.

10. The method of claim 1, wherein said charged particle tomographic data comprises cosmic ray muon tomographic data.

11. (canceled)

12. (canceled)

13. (canceled)

14. (canceled)

15. (canceled)

16. (canceled)

17. (canceled)

18. (canceled)

19. (canceled)

20. (canceled)

21. A computer program product comprising:

a computer-usable data carrier storing instructions that, when executed by a computer, cause the computer to perform a method for statistical reconstruction of object volume density profiles from charged particle tomographic data, the method comprising;

(a) obtaining a predetermined charged particle tomographic data corresponding to scattering angles and estimated momenta of charged particles passing through object volume;

(b) providing the probability distribution of a charged particle scattering for use in an expectation maximization (ML/EM) algorithm, said probability distribution being based on a statistical multiple scattering model;

(c) determining a substantially maximum likelihood estimate of object volume density using said expectation maximization (ML/EM) algorithm; and

(d) outputting a reconstructed object volume scattering density.

22. A detection system for detecting an object volume via charged particles passing through the object volume, comprising:

a first set of position sensitive detectors located on a first side of an object volume to measure positions and angles of incident charged particles towards the object volume;

a second set of position sensitive detectors located on a second side of the object volume opposite to the first side to measure positions and angles of outgoing charged particles exiting the object volume; and

a signal processing unit to receive data of measured signals from the first set of position sensitive detectors and measured signals from the second set of position sensitive detectors, wherein the signal processing unit processes the received data to produce a statistical reconstruction of a volume scattering density distribution within the object volume.

23. The system of claim 22, wherein the signal processing unit is configured to:

(a) obtain charged particle tomographic data corresponding to scattering angles and estimated momenta of charged particles passing through an object volume;

(b) provide a probability distribution of a charged particle scattering density based on a statistical multiple scattering model;

(c) determine a substantially maximum likelihood estimate of the object volume scattering density using an expectation maximization (ML/EM) algorithm; and

(d) output a reconstructed object volume scattering density based on the substantially maximum likelihood estimate.

25. The system of claim 23, wherein the charged particles are natural cosmic ray muons incident to the object volume and the signal processing unit is configured to indicate whether a target object is present in the object volume based on the statistical reconstruction of the volume scattering density distribution within the object volume.

26. The system of claim 23, wherein the signal processing unit is further configured to:

make a decision on at least one of (1) a presence and (2) a type of a target object in the volume based on said reconstructed object volume scattering density.

27. The system of claim 23, wherein:

said provide a probability distribution of a charged particle scattering density based on a statistical multiple scattering model; and

said determine a substantially maximum likelihood estimate of the object volume scattering density using an expectation maximization (ML/EM) algorithm, further comprise;

obtain a probability distribution in 2D for a charged particle based on a predefined scattering density of a homogenous object;

obtain a 3D probability distribution for said charged particle based on said 2D probability distribution;

obtain a probability distribution for scattering of multiple charged particles through a non-homogenous object volume characterized via basis functions; and

obtain a probability distribution for multiple scattering based on said definition thereof and scattering and momentum measurements of said charged particles.

28. The system of claim 27 wherein said obtain a 3D probability distribution for said charged particle based on said 2D probability distribution, further comprises:

add a coordinate and define a three dimensional path length;

compute a 3D displacement; and

define a 3D covariance matrix.

29. The system of claim 23 wherein the signal processing unit is further configured to:

establish a 3D grid of basis functions representing discrete scattering density estimates;

determine the scattering/displacement covariance matrix for each individual moon as a function of the ray path and scattering density estimates; and

determine a probability distribution for a plurality of charged particles as the product of individual charged particle probabilities.

30. The system of claim 23 wherein the signal processing unit is further configured to:

gather measurements of scattering and momentum for each cosmic ray charged particle;

estimate geometry of interaction of each charged particle with each basis function of said statistical multiple scattering model;

for each charged particle basis function pair, determine the weight matrix;

W_ij;

initialize scattering density in each basis function with a guess;

iteratively solve for the approximate maximum likelihood solution for object volume contents;

where the iterative process is stopped at a predetermined number of iterations or when the solution is changing less than a predetermined tolerance value.

31. The system of claim 23 wherein the signal processing unit is further configured to:

gather measurements of scattering and momentum for each charged particle i=1 to M (Δ

θ

_xΔ

θ

_y,Δ

x,Δ

_y,p_r²)_i;

estimate the geometry of interaction of each charged particle with each voxel j=1 to N;

(L,T)_ij;

for each charged particle voxel pair, computing the weight matrix;

W_ij as

32. The system of claim 31, wherein said stopping criteria process comprises

for each charged particle, computing Σ

_Di<sup>−

1</sup> using

33. The system of claim 32, wherein said charged particles comprise muons.

34. The system of claim 32, wherein said ML/EM algorithm includes a mean update rule defined as

35. The system of claim 25, wherein:

each of the first and second sets of particle detectors is arranged to allow at least three charged particle positional measurements in a first direction and at least three charged particle positional measurements in a second direction different from the first direction.

24. (canceled)