Modification of the normalized difference method for real-time optical tomography
First Claim
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.
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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.
156 Citations
28 Claims
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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:
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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. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19)
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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:
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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.
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21. A method for obtaining a time series of images of a target medium, comprising:
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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. - View Dependent Claims (22, 23, 24, 25, 26, 27)
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28. A method for obtaining a time series of images of a target medium, comprising:
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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.
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Specification