Modification of the normalized difference method for real-time optical tomography

• US 20040010397A1
• Filed: 04/07/2003
• Published: 01/15/2004
• Est. Priority Date: 04/06/2002
• Status: Active Grant

• Current Assignee: Randall L. Barbour, Yaling Pei
• Original Assignee: Randall L. Barbour, Yaling Pei
• Inventors: Barbour, Randall L., Pei, Yaling
• Granted Patent: US 7,616,984 B2
• Time in Patent Office: Days
• US Class Current: 702/189
• CPC Class Codes: A61B 5/0073 by tomography, i.e. reconstruction of 3D images from 2D projections A61B5/0066 takes precedence
• CPC Class Codes: A61B 5/0091 for mammography
• CPC Class Codes: A61B 5/4312 Breast evaluation or disorder diagnosis A61B5/0091 takes precedence
• CPC Class Codes: G01N 2021/1787 Tomographic, i.e. computerised reconstruction from projective measurements
• CPC Class Codes: G01N 2021/475 Bifurcated bundle
• CPC Class Codes: G01N 21/359 using near infrared light
• CPC Class Codes: G01N 21/4795 spatially resolved investigating of object in scattering medium in vivo A61B
• CPC Class Codes: G01N 21/49 within a body or fluid
• CPC Class Codes: G01N 2201/0826 Fibre array at source, distributing
• CPC Class Codes: G01N 2201/0833 Fibre array at detector, resolving
• CPC Class Codes: G06T 11/006 Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods

Abstract

Computation-saving techniques and stability-adding techniques provide for fast, accurate reconstructions of a time series of images involving large-scale 3D problems, such as real-time image recovery in an optical tomography imaging system. A system equation for a target medium (116) such as tissue is solved using a Normalized Difference Method (NDM) (250). Because of the inherent stability of the NDM solutions, a weight matrix (W) of the system equation can be provided for a given point in a time series (220), then reused without recalculation at subsequent points. Further savings are achieved by decomposing W using singular value decomposition or direct matrix decomposition, transforming it to reduce its dimensions, and/or scaling it to achieve a more stable numerical solution. Values of measured energy (112) emerging from the target medium are back-substituted into the system equation for the different points to obtain the target medium properties.

Claims

1. A method for obtaining a time series of tomographic images of a target medium, wherein source-detector pairs are positioned about a boundary of the target medium, and, in each source-detector pair, for different points in the time series, the source emits energy into the target medium and the detector measures the energy emerging from the target medium after passage therethrough, comprising:

selecting a reference medium;

providing a weight matrix describing an influence that volume elements of the reference medium have on energy traveling from sources to detectors in source-detector pairs of the reference medium; and

for the different points in the time series, solving a system equation for the target medium to determine properties of volume elements of the target medium that correspond to the volume elements of the reference medium based on the weight matrix and the energy emerging at the detectors of the target medium.

2. The method of claim 1, wherein:

the system equation is solved for at least some of the different points in the time series without repeatedly calculating the weight matrix.

3. The method of claim 1, further comprising:

storing the weight matrix in memory for use in solving the system equation for at least some of the different points in the time series.

4. The method of claim 1, wherein:

solving the system equation comprises decomposing the weight matrix, and back-substituting values of the measured energy emerging from the target medium into the system equation for the different points in the time series.

5. The method of claim 1, wherein:

solving the system equation comprises decomposing the weight matrix using at least one of singular value decomposition and direct matrix decomposition.

6. The method of claim 1, wherein:

solving the system equation comprises transforming the weight matrix to reduce its dimensions.

7. The method of claim 1, wherein:

solving the system equation comprises scaling row vectors of the weight matrix.

8. The method of claim 1, wherein:

the properties of the volume elements of the target medium comprise at least one of scattering and absorption properties.

9. The method of claim 1, wherein:

the reference medium has at least one of scattering and absorption properties substantially similar to the properties of the target medium.

10. The method of claim 1, wherein:

the reference medium has a boundary with boundary conditions that are substantially similar to boundary conditions of the boundary of the target medium.

11. The method of claim 1, wherein:

the volume elements of the reference medium are formed by dividing the reference medium into a grid of contiguous, non-overlapping sections.

12. The method of claim 1, wherein:

the system equation of the reference medium comprises a perturbation equation.

13. The method of claim 1, wherein:

the target medium and reference medium comprise analogous tissue regions in an animal.

14. The method of claim 1, wherein:

the determined properties of the volume element of the target medium are used to provide the time series of tomography images substantially in real-time.

15. The method of claim 1, wherein:

the target medium comprises a turbid, scattering medium.

16. The method of claim 1, wherein:

the energy comprises near infrared light.

17. The method of claim 1, wherein:

the weight matrix is estimated.

18. The method of claim 1, wherein:

the weight matrix is obtained from a storage area of weight matrices that are correlated with different reference media.

19. The method of claim 1, wherein:

the source-detector pairs of the reference medium are positioned about a boundary of the reference medium in correspondence with the source-detector pairs positioned about the boundary of the target medium.

20. A method for obtaining a time series of tomographic images of a target medium, wherein source-detector pairs are positioned about a boundary of the target medium, and, in each source-detector pair, for different points in the time series, the source emits energy into the target medium and the detector measures the energy emerging from the target medium after passage therethrough, comprising:

selecting a reference medium;

providing a weight matrix describing an influence that volume elements of the reference medium have on energy traveling from sources to detectors in source-detector pairs of the reference medium; and

for the different points in the time series, solving a system equation for the target medium to determine properties of volume elements of the target medium corresponding to the volume elements of the reference medium by;

decomposing the weight matrix using at least one of singular value decomposition and direct matrix decomposition;

transforming the weight matrix to reduce its dimensions; and

back-substituting values of the measured energy emerging from the target medium into the system equation for the different points in the time series;

wherein the system equation is solved for at least some of the different points in the time series without repeatedly calculating the weight matrix.

21. A method for obtaining a time series of images of a target medium, comprising:

positioning detectors about a boundary of the target medium for measuring energy that emerges from the target medium at different points in the time series, wherein the energy originates within the target medium;

selecting a reference medium;

providing a weight matrix describing an influence that volume elements of the reference medium have on energy originating within the reference medium and emerging from the reference medium at detectors positioned about a boundary of the reference medium; and

for the different points in the time series, solving a system equation for the target medium to determine properties of volume elements of the target medium corresponding to the volume elements of the reference medium based on the weight matrix and the energy emerging at the detectors of the target medium.

22. The method of claim 21, wherein:

the energy emerging from the target medium comprises at least one of fluorescence, bioluminescence, chemiluminescence, and thermal energy.

23. The method of claim 21, wherein:

the system equation is solved for at least some of the different points in the time series without repeatedly calculating the weight matrix.

24. The method of claim 21, wherein:

solving the system equation comprises decomposing the weight matrix, and back-substituting values of the measured energy emerging from the target medium into the system equation for the different points in the time series.

25. The method of claim 21, wherein:

solving the system equation comprises decomposing the weight matrix using at least one of singular value decomposition and direct matrix decomposition.

26. The method of claim 21, wherein:

solving the system equation comprises transforming the weight matrix to reduce its dimensions.

27. The method of claim 21, wherein:

solving the system equation comprises scaling row vectors of the weight matrix.

28. A method for obtaining a time series of images of a target medium, comprising:

positioning detectors about a boundary of the target medium for measuring energy that emerges from the target medium at different points in the time series, wherein the energy originates within the target medium;

selecting a reference medium;

providing a weight matrix describing an influence that volume elements of the reference medium have on energy originating within the reference medium and emerging from the reference medium at detectors positioned about a boundary of the reference medium; and

for the different points in the time series, solving a system equation for the target medium to determine properties of volume elements of the target medium corresponding to the volume elements of the reference medium by;

decomposing the weight matrix using at least one of singular value decomposition and direct matrix decomposition;

transforming the weight matrix to reduce its dimensions; and

back-substituting values of the measured energy emerging from the target medium into the system equation for the different points in the time series;

wherein the system equation is solved for at least some of the different points in the time series without repeatedly calculating the weight matrix.