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Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography
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10.1118/1.2733803
/content/aapm/journal/medphys/34/6/10.1118/1.2733803
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/34/6/10.1118/1.2733803

Figures

Image of FIG. 1.
FIG. 1.

An illustration of the forward and inverse problem in diffuse optical tomography is shown (see Ref. 64), where (a) the data is estimated given values of and and source/detector positions. In the inverse problem (b), the values of and must be obtained given a set of measurements .

Image of FIG. 2.
FIG. 2.

The chosen optical property distribution/domain for the generation of synthetic data is shown. The diameter of the domain was .

Image of FIG. 3.
FIG. 3.

Reconstruction results (top of the first row, abbreviations are given in Appendix A) are shown using noiseless data (bias calculations) (a) without spatial priors and (b) with spatial priors. The top row contains images of and bottom row shows images.

Image of FIG. 4.
FIG. 4.

Reconstruction results (top of the first row, abbreviations are given in Appendix A) are shown using 5% noisy data (a) without spatial priors and (b) with spatial priors. The top row gives images of and bottom row shows images.

Image of FIG. 5.
FIG. 5.

Reconstruction results (top of the first row, abbreviations are given in Appendix A) are shown using 10% noisy data (a) without spatial priors and (b) with spatial priors. The top row gives images of and bottom row shows images.

Image of FIG. 6.
FIG. 6.

A plot of the rms error in the estimated optical properties is shown as a function of increasing noise level for all reconstruction techniques.

Image of FIG. 7.
FIG. 7.

Reconstruction results (top of the first row, abbreviations are given in Appendix A) are shown using 3% noisy data (a) without spatial priors and (b) with spatial priors for four targets in the tissue as shown. The top row gives images of and bottom row shows images. The actual and with target numbers are given in the first column of (a).

Image of FIG. 8.
FIG. 8.

Plot of the rms error in the estimated optical properties is shown for increasing number of targets with 3% noise in the data for all reconstruction techniques (legend of the figure). Abbreviations used for the techniques are given in Appendix A. The targets used are numbered in the images presented in Fig. 7(a).

Tables

Generic image for table
TABLE I.

Mean and standard deviation of the reconstructed: (a) and (b) values (in ) for different regions [labeled in first column of Fig. 3(a)] recovered with data having 0%, 5%, 10% noise for images shown in Figs. 3–5.

Generic image for table
TABLE II.

Mean and standard deviation of the reconstructed: (a) and (b) values (in ) for different regions [labeled in first column of Fig. 7(a)] recovered with data having 3% noise for images shown in Fig. 7.

Generic image for table
TABLE III.

Comparison of computation time per iteration for different reconstruction techniques on Pentium IV (dual core) , RAM Linux work station. the abbreviations used for the reconstruction techniques are given in Appendix A.

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/content/aapm/journal/medphys/34/6/10.1118/1.2733803
2007-05-17
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/34/6/10.1118/1.2733803
10.1118/1.2733803
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