Time-resolved diffusion tomographic imaging in highly scattering turbid media
First Claim
1. A method of imaging an object located in a highly scattering turbid medium, said method comprising the steps of:
- (a) illuminating the object through the highly scattering turbid medium with a pulse of light, whereby the light emergent from the highly scattering turbid medium consists of a ballistic component, a snake-like component and a diffusive component;
(b) determining the intensity of said diffusive component at a plurality of points in time; and
(c) using said intensity determinations to form an image of the object in the highly scattering turbid medium, said using step comprising using a mathematical inversion algorithm to generate an image of the highly scattering turbid medium, said mathematical inversion algorithm being
space="preserve" listing-type="equation">X.sup.(K+1).spsp.T = Y.sup.T W+X.sup.(K).spsp.T Λ
! W.sup.T W+Λ
!.sup.-1wherein W is a matrix relating output at detector position rd, at time t, to source at position rs, Λ
is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, <
nn>
to fluctuations in the absorption (or diffusion) Xj that we are trying to determine;
space="preserve" listing-type="equation">Λ
.sub.ij =λ
.sub.j δ
.sub.ij with λ
.sub.j =<
nn>
/<
Δ
X.sub.j Δ
X.sub.j >
Here Y is the data collected at the detector, and Xk is the kth iterate toward the desired absorption information.
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Abstract
A method for imaging objects in highly scattering turbid media. According to one embodiment of the invention, the method involves using a plurality of intersecting source/detectors sets and time-resolving equipment to generate a plurality of time-resolved intensity curves for the diffusive component of light emergent from the medium. For each of the curves, the intensities at a plurality of times are then inputted into the following inverse reconstruction algorithm to form an image of the medium:
X.sup.(k+1).spsp.T = Y.sup.T W+X.sup.(k).spsp.T Λ! W.sup.T
W+Λ!-1
wherein W is a matrix relating output at detector position rd, at time t, to source at position rs, Λ is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, <nn> to fluctuations in the absorption (or diffusion) Xj that we are trying to determine:
Λ.sub.ij =λ.sub.j δ.sub.ij with λ.sub.j
=<nn>/<ΔXjΔXj>
Here Y is the data collected at the detectors, and Xk is the kth iterate toward the desired absoption information.
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Citations
26 Claims
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1. A method of imaging an object located in a highly scattering turbid medium, said method comprising the steps of:
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(a) illuminating the object through the highly scattering turbid medium with a pulse of light, whereby the light emergent from the highly scattering turbid medium consists of a ballistic component, a snake-like component and a diffusive component; (b) determining the intensity of said diffusive component at a plurality of points in time; and (c) using said intensity determinations to form an image of the object in the highly scattering turbid medium, said using step comprising using a mathematical inversion algorithm to generate an image of the highly scattering turbid medium, said mathematical inversion algorithm being
space="preserve" listing-type="equation">X.sup.(K+1).spsp.T = Y.sup.T W+X.sup.(K).spsp.T Λ
! W.sup.T W+Λ
!.sup.-1wherein W is a matrix relating output at detector position rd, at time t, to source at position rs, Λ
is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, <
nn>
to fluctuations in the absorption (or diffusion) Xj that we are trying to determine;
space="preserve" listing-type="equation">Λ
.sub.ij =λ
.sub.j δ
.sub.ij with λ
.sub.j =<
nn>
/<
Δ
X.sub.j Δ
X.sub.j >Here Y is the data collected at the detector, and Xk is the kth iterate toward the desired absorption information. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
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12. A method of forming a map of a highly scattering turbid medium, said method comprising the steps of:
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(a) illuminating the highly scattering turbid medium with a first pulse of light along a first axis of incidence, whereby the light emergent from the highly scattering turbid medium due to said first pulse of light consists of a ballistic component, a snake component and a diffusive component; (b) determining, at a plurality of times, the intensity of said diffusive component of the first pulse of light emergent from the highly scattering turbid medium at a plurality of locations; (c) illuminating the highly scattering turbid medium with a second pulse of light along a second axis of incidence, said second axis of incidence intersecting with said first axis of incidence, whereby the light emergent from the highly scattering turbid medium due to said second pulse of light consists of a ballistic component, a snake component and a diffusive component; (d) determining, at a plurality of times, the intensity of said diffusive component of the second pulse of light emergent from the highly scattering turbid medium at a plurality of locations; and (e) using the intensity determinations from steps (b) and (d) to generate a map of the highly scattering turbid medium, said using step comprising using a mathematical inversion algorithm to generate a map of the highly scattering turbid medium, said mathematical inversion algorithm being
space="preserve" listing-type="equation">X.sup.(K+1).spsp.T = Y.sup.T W+X.sup.(K).spsp.T Λ
! W.sup.T W+Λ
!.sup.-1wherein W is a matrix relating output at detector position rd, at time t, to source at position rs, Λ
is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, <
nn>
to fluctuations in the absorption (or diffusion) Xj that we are trying to determine;
space="preserve" listing-type="equation">Λ
.sub.ij =λ
.sub.j δ
.sub.ij with λ
.sub.j =<
nn>
/<
Δ
X.sub.j Δ
X.sub.j >Here Y is the data collected at the detectors, and Xk is the kth iterate toward the desired absorption information. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26)
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Specification