Yong Xu, Harry L. Graber, Yaling Pei, and Randall L. Barbour, "Improved accuracy of reconstructed diffuse optical tomographic images by means of spatial deconvolution: two-dimensional quantitative characterization," Appl. Opt. 44, 2115-2139 (2005)
Systematic characterization studies are presented, relating to a previously reported spatial deconvolution operation that seeks to compensate for the information-blurring property of first-order perturbation algorithms for diffuse optical tomography (DOT) image reconstruction. In simulation results that are presented, this deconvolution operation has been applied to two-dimensional DOT images reconstructed by solving a first-order perturbation equation. Under study was the effect on algorithm performance of control parameters in the measurement (number and spatial distribution of sources and detectors, presence of noise, and presence of systematic error), target (medium shape; and number, location, size, and contrast of inclusions), and computational (number of finite-element-method mesh nodes, length of filter-generating linear system, among others) parameter spaces associated with computation and the use of the deconvolution operators. Substantial improvements in reconstructed image quality, in terms of recovered inclusion location, size, and contrast, are found in all cases. A finding of practical importance is that the method is robust to appreciable differences between the optical coefficients of the media used for filter generation and those of the target media to which the filters are subsequently applied.
S. B. Colak, D. G. Papaioannou, G. W. ’t Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, and N. A. A. J. van Asten Appl. Opt. 36(1) 180-213 (1997)
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s = single inclusion, m = multiple inclusions; P = point inclusion (i.e., exactly one FEM mesh node).
The distinction between these two cases lies in the S–D configuration: full tomographic in study 6; limited view in study 9.
Table 2
Properties of Media and S–D Configurations for Which Deconvolution Operators Were Computeda
Shape
Dimensions
Measurement Type
Mean μa (mm−1)
Numbers of Sources (S) and Detectors (D)
Geometric Distribution of S and D Locations
Does S Have a Colocated D?
Numbers of FEM Mesh Nodes and Elements
Study Number
Circle
80-mm diameter
Full tomographic
0.005
16S, 16D (256 channels total)
Uniform, Δθc = 22.5°
Yes
717/1368
4
16S, 48D (768)
S: uniform, Δθc = 22.5°
D: uniform, Δθc = 7.5°
717/1368
1, 3, 4, 5, 6
32S, 32D (1024)
Uniform, Δθc = 11.25°
1019/1940
1, 2, 3
1610/3090
1
0.002
16S, 16D, (256)
Uniform, Δθc = 22.5°
717/1368
7
Limited view: backreflection
0.005
9S, 24D (216)
S: uniform from θc = 0° to θc = 180°, Δθc = 22.5°
No
717/1368
9, 10
D: three uniformly spaced between pairs of S, Δθc = 5.625°
86-mm diameter
Full tomographic
0.01
16S, 16D (256)
Uniform, Δθc = 22.5°
Yes
1019/1940
8
Rectangle
100-mm wide (X dimension),
Backreflection
0.01
33S, 33D (1089)
Uniformly spaced along 100-mm edge,
Yes
11
60-mm thick (Y dimension)
ΔX = 2.5 mm
Transmission
0.005
9S, 9D (81)
Uniformly spaced along 100-mm edges,
N/A
1025/1920
12
ΔX = 10 mm
17S, 17D (289)
ΔX= 5 mm
33S, 33D (1089)
ΔX = 2.5 mm
θc, central angle; Δθc, central angle interval between adjacent sources or detectors; ΔX, distance between adjacent sources or detectors along the medium surface.
Table 3
Properties of Inclusions Used in Deconvolution Procedure Characterization Simulations
Tabulated dimension is the diameter for circular inclusions, length × width for rectangular and square inclusions.
This approximate linear dimension is the square root of the mean area of the forward-problem finite elements.
Table 4
Quantitative Accuracy Indices for Study 7 (Systematic Error Study)
The case for which the filter-generating and target media have identical background properties.
This target medium, out of all considered, yields the greatest percentage increase of rs.
This target medium, out of all considered, yields the greatest percentage decrease of ε.
Table 5
Accuracy of Recovered Inclusion Properties for Study 8 and Ref. 12
s = single inclusion, m = multiple inclusions; P = point inclusion (i.e., exactly one FEM mesh node).
The distinction between these two cases lies in the S–D configuration: full tomographic in study 6; limited view in study 9.
Table 2
Properties of Media and S–D Configurations for Which Deconvolution Operators Were Computeda
Shape
Dimensions
Measurement Type
Mean μa (mm−1)
Numbers of Sources (S) and Detectors (D)
Geometric Distribution of S and D Locations
Does S Have a Colocated D?
Numbers of FEM Mesh Nodes and Elements
Study Number
Circle
80-mm diameter
Full tomographic
0.005
16S, 16D (256 channels total)
Uniform, Δθc = 22.5°
Yes
717/1368
4
16S, 48D (768)
S: uniform, Δθc = 22.5°
D: uniform, Δθc = 7.5°
717/1368
1, 3, 4, 5, 6
32S, 32D (1024)
Uniform, Δθc = 11.25°
1019/1940
1, 2, 3
1610/3090
1
0.002
16S, 16D, (256)
Uniform, Δθc = 22.5°
717/1368
7
Limited view: backreflection
0.005
9S, 24D (216)
S: uniform from θc = 0° to θc = 180°, Δθc = 22.5°
No
717/1368
9, 10
D: three uniformly spaced between pairs of S, Δθc = 5.625°
86-mm diameter
Full tomographic
0.01
16S, 16D (256)
Uniform, Δθc = 22.5°
Yes
1019/1940
8
Rectangle
100-mm wide (X dimension),
Backreflection
0.01
33S, 33D (1089)
Uniformly spaced along 100-mm edge,
Yes
11
60-mm thick (Y dimension)
ΔX = 2.5 mm
Transmission
0.005
9S, 9D (81)
Uniformly spaced along 100-mm edges,
N/A
1025/1920
12
ΔX = 10 mm
17S, 17D (289)
ΔX= 5 mm
33S, 33D (1089)
ΔX = 2.5 mm
θc, central angle; Δθc, central angle interval between adjacent sources or detectors; ΔX, distance between adjacent sources or detectors along the medium surface.
Table 3
Properties of Inclusions Used in Deconvolution Procedure Characterization Simulations
Tabulated dimension is the diameter for circular inclusions, length × width for rectangular and square inclusions.
This approximate linear dimension is the square root of the mean area of the forward-problem finite elements.
Table 4
Quantitative Accuracy Indices for Study 7 (Systematic Error Study)
The case for which the filter-generating and target media have identical background properties.
This target medium, out of all considered, yields the greatest percentage increase of rs.
This target medium, out of all considered, yields the greatest percentage decrease of ε.
Table 5
Accuracy of Recovered Inclusion Properties for Study 8 and Ref. 12
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