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Normalized–constraint algorithm for minimizing inter–parameter crosstalk in DC optical tomography

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Abstract

In this report, we present a method for reducing the inter–coefficient crosstalk problem in optical tomography. The method described is an extension of a previously reported normalized difference method that evaluates relative detector values, and employs a weight matrix scaling technique together with a constrained CGD method for image reconstruction. Results from numerical and experimental studies using DC measurement data demonstrate that the approach can effectively isolate absorption and scattering heterogeneities, even for complex combinations of perturbations in optical properties. The significance of these results in light of recent theoretical findings is discussed.

©2001 Optical Society of America

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Supplementary Material (18)

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Figures (6)

Figure 1.
Figure 1. Target geometry and source–detector configuration for simulation cases.
Figure 2.
Figure 2. Original and reconstructed profiles for the target medium considered (7 types). Rows one and two are the original and reconstructed profiles for δµa , respectively; rows three and four are the corresponding original and reconstructed D profiles, respectively. Color scale indicates amplitude of perturbation.
Figure 3.
Figure 3. Experimental phantom cases 1, 2, 3, and 4.
Figure 4.
Figure 4. The reconstructed diffusion (top row) and absorption (bottom row) profiles for (left to right) cases one through four. Click on figure with mouse to see movie (<1.2 Mb for each). [Media 1] [Media 2] [Media 3] [Media 4] [Media 5] [Media 6] [Media 7] [Media 8]
Figure 5.
Figure 5. Reconstructed diffusion (top row) and absorption (bottom row) profiles for experimental case one using standard CGD method only (column one), CGD method with range constraints (column two), CGD method with weight matrix scaling (column three) and CGD method with range constraints and matrix scaling (column four). Click on figure with mouse to see movie (<1.2 Mb for each). [Media 9] [Media 10] [Media 11] [Media 12] [Media 13] [Media 14] [Media 15] [Media 16]
Figure 6.
Figure 6. Weight functions corresponding to source–detector pairs with source 1 and detectors 1 to 16 for absorption (A and B) and diffusion (C and D) coefficients, before (A and C) and after (B and D) applying matrix scaling. Click on figure with mouse to see movie (<0.5 Mb for each). [Media 17] [Media 18]

Equations (10)

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· [ D ( r ) u ( r ) ] μ a ( r ) u ( r ) = δ ( r r s ) , r Λ
W r ( μ a ) · δ μ a + W r ( D ) · δ D = δ u r ,
( δ u r ) i = ( ( u 1 ) i ( u 2 ) i ( u 2 ) i ) ( u r ) i , i = 1 , 2 , , M .
W ˜ r ( k ) = W r ( k ) · R ( k ) ,
( R ( k ) ) i j = { 1 1 M Σ m = 1 M ( W r ( k ) ) m j j = i , 0 j i , i , j = 1 , 2 , , N ,
W ˜ r ( μ a ) · δ μ ˜ a + W ˜ r ( D ) · δ D ˜ = δ u r ,
E = 1 2 ( W ˜ r · δ x ˜ δ u r ) T ( W ˜ r · δ x ˜ δ u r ) = 1 2 δ x ˜ T · A · δ x ˜ b T · δ x ˜ + 1 2 δ u r T · δ u r ,
g ( δ x ˜ ) = E ( δ x ˜ ) = A · δ x ˜ b = 0
δ x ˜ ( n ) = δ x ˜ ( n 1 ) α ( n ) d ( n ) .
δ μ a = R ( μ a ) · δ μ ˜ a , δ D = R ( D ) · δ D ˜ .
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