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Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem.

He X, Liang J, Qu X, Huang H, Hou Y, Tian J - Int J Biomed Imaging (2010)

Bottom Line: Most regularization techniques such as Tikhonov method only consider measurement noise, whereas the influences of system errors have not been investigated.Based on the modified generalized cross validation (MGCV) criterion and residual error minimization, a practical parameter-choice scheme referred to as improved GCV (IGCV) is proposed for TTLS.Numerical simulations with different noise levels and physical experiments demonstrate the effectiveness and potential of TTLS combined with IGCV for solving the BLT inverse problem.

View Article: PubMed Central - PubMed

Affiliation: Life Sciences Research Center, School of Life Sciences and Technology, Xidian University, Xi'an 710071, China.

ABSTRACT
In bioluminescence tomography (BLT), reconstruction of internal bioluminescent source distribution from the surface optical signals is an ill-posed inverse problem. In real BLT experiment, apart from the measurement noise, the system errors caused by geometry mismatch, numerical discretization, and optical modeling approximations are also inevitable, which may lead to large errors in the reconstruction results. Most regularization techniques such as Tikhonov method only consider measurement noise, whereas the influences of system errors have not been investigated. In this paper, the truncated total least squares method (TTLS) is introduced into BLT reconstruction, in which both system errors and measurement noise are taken into account. Based on the modified generalized cross validation (MGCV) criterion and residual error minimization, a practical parameter-choice scheme referred to as improved GCV (IGCV) is proposed for TTLS. Numerical simulations with different noise levels and physical experiments demonstrate the effectiveness and potential of TTLS combined with IGCV for solving the BLT inverse problem.

No MeSH data available.


Regularization parameter determination in single-source case under measurement noise level of 10% and Gaussian system error level of 1%: (a) GCV function curve for Tikhonov, (b) MGCV function curve for TTLS, (c) illustration of the truncation parameter selection for TTLS with IGCV.
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fig2: Regularization parameter determination in single-source case under measurement noise level of 10% and Gaussian system error level of 1%: (a) GCV function curve for Tikhonov, (b) MGCV function curve for TTLS, (c) illustration of the truncation parameter selection for TTLS with IGCV.

Mentions: As discussed in Section 2, regularization parameter is the crucial factor that affects the quality of regularization solution to inverse problem. Figure 2 illustrates the determination of regularization parameters in single source case with measurement noise level of 10% and Gaussian system error level of 1%. Among them, Figure 2(c) shows the residual error values of all the local minimum points described in our improved scheme IGCV, which are used for the selection of an optimal truncation parameter k for TTLS. It should be noticed that the parameter k identified by MGCV is 64, whereas the optimal parameter k obtained by IGCV is 78. It is because //ASTTLS,78′ − Φm// is 0.0038 and //ASTTLS,64′ − Φm// is 0.0046, which indicate that 64 is not the optimal parameter value according to IGCV criterion. The determination of regularization parameter in double sources case is similar to that of single source case. For space limitation, we just provide the final regularization parameter obtained in various noise settings in Tables 2 and 3.


Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem.

He X, Liang J, Qu X, Huang H, Hou Y, Tian J - Int J Biomed Imaging (2010)

Regularization parameter determination in single-source case under measurement noise level of 10% and Gaussian system error level of 1%: (a) GCV function curve for Tikhonov, (b) MGCV function curve for TTLS, (c) illustration of the truncation parameter selection for TTLS with IGCV.
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2874932&req=5

fig2: Regularization parameter determination in single-source case under measurement noise level of 10% and Gaussian system error level of 1%: (a) GCV function curve for Tikhonov, (b) MGCV function curve for TTLS, (c) illustration of the truncation parameter selection for TTLS with IGCV.
Mentions: As discussed in Section 2, regularization parameter is the crucial factor that affects the quality of regularization solution to inverse problem. Figure 2 illustrates the determination of regularization parameters in single source case with measurement noise level of 10% and Gaussian system error level of 1%. Among them, Figure 2(c) shows the residual error values of all the local minimum points described in our improved scheme IGCV, which are used for the selection of an optimal truncation parameter k for TTLS. It should be noticed that the parameter k identified by MGCV is 64, whereas the optimal parameter k obtained by IGCV is 78. It is because //ASTTLS,78′ − Φm// is 0.0038 and //ASTTLS,64′ − Φm// is 0.0046, which indicate that 64 is not the optimal parameter value according to IGCV criterion. The determination of regularization parameter in double sources case is similar to that of single source case. For space limitation, we just provide the final regularization parameter obtained in various noise settings in Tables 2 and 3.

Bottom Line: Most regularization techniques such as Tikhonov method only consider measurement noise, whereas the influences of system errors have not been investigated.Based on the modified generalized cross validation (MGCV) criterion and residual error minimization, a practical parameter-choice scheme referred to as improved GCV (IGCV) is proposed for TTLS.Numerical simulations with different noise levels and physical experiments demonstrate the effectiveness and potential of TTLS combined with IGCV for solving the BLT inverse problem.

View Article: PubMed Central - PubMed

Affiliation: Life Sciences Research Center, School of Life Sciences and Technology, Xidian University, Xi'an 710071, China.

ABSTRACT
In bioluminescence tomography (BLT), reconstruction of internal bioluminescent source distribution from the surface optical signals is an ill-posed inverse problem. In real BLT experiment, apart from the measurement noise, the system errors caused by geometry mismatch, numerical discretization, and optical modeling approximations are also inevitable, which may lead to large errors in the reconstruction results. Most regularization techniques such as Tikhonov method only consider measurement noise, whereas the influences of system errors have not been investigated. In this paper, the truncated total least squares method (TTLS) is introduced into BLT reconstruction, in which both system errors and measurement noise are taken into account. Based on the modified generalized cross validation (MGCV) criterion and residual error minimization, a practical parameter-choice scheme referred to as improved GCV (IGCV) is proposed for TTLS. Numerical simulations with different noise levels and physical experiments demonstrate the effectiveness and potential of TTLS combined with IGCV for solving the BLT inverse problem.

No MeSH data available.