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

A method for obtaining a time series of tomographic images of a target medium from an imaging apparatus, 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, wherein said detectors measure an intensity of scattered energy;
• 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 employing a weight transformation technique, wherein an M×N matrix is transformed to an M×M matrix by said transforming, wherein N is a number of nodes comprising a finite element mesh and wherein M is the number of said source-detector pairs;
• 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 one or more of the properties of volume elements is employed at least for providing a time series of tomographic images of a target medium.

A method for obtaining a time series of images of a target medium from an imaging apparatus, 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, wherein said detectors measure an intensity of scattered energy;
• decomposing the weight matrix using at least one of singular value decomposition and direct matrix decomposition employing a weight transformation technique, wherein an M×N matrix is transformed to an M×M matrix by said transforming, wherein N is a number of nodes comprising a finite element mesh and wherein M is the number of said source-detector pairs, wherein a dimension of the weight matrix is reduced by said decomposition of said weight matrix;
• 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, wherein one or more of the properties of volume elements is employed at least for providing a time series of tomographic images of a target medium.

A method for obtaining a time series of images of a target medium from an imaging apparatus, 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, wherein said detectors measure an intensity of scattered energy;
• 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 employing a weight transformation technique, wherein an M×N matrix is transformed to an M×M matrix by said transforming, wherein N is a number of nodes comprising a finite element mesh and wherein M is the number of said source-detector pairs;
• 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 one or more of the properties of volume elements is employed at least for providing a time series of tomographic images of a target medium.