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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.


Reconstructed results in double source case under measurement noise level of 20% and system error level of 5%. (a), (b), and (c) separately show the x–y views at z = 15 mm plane of the results by Tikhonov + GCV, TTLS + MGCV, and TTLS + IGCV; (d), (e), and (f) are the corresponding y–z views at x = 9.5 mm plane of the reconstruction results, respectively; the white circle indicates the real source.
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fig4: Reconstructed results in double source case under measurement noise level of 20% and system error level of 5%. (a), (b), and (c) separately show the x–y views at z = 15 mm plane of the results by Tikhonov + GCV, TTLS + MGCV, and TTLS + IGCV; (d), (e), and (f) are the corresponding y–z views at x = 9.5 mm plane of the reconstruction results, respectively; the white circle indicates the real source.

Mentions: In the double sources case, both of the two sphere sources located in the left lung are tested. The final reconstruction results are listed in Table 3. Under all the noise conditions considered in this paper, the three methods can reconstruct the two sources at S1R = (−9.20 mm, −1.62 mm, 14.12 mm) and S2R = (−9.42 mm, 1.69 mm, 14.94 mm), which are 0.911 mm and 0.467 mm away from the actual ones, respectively. In fact, they are the nearest nodes to the original source locations under the FEM mesh used in our tests. However, with the increase of noise or error level, besides the optimal nodes S1R and S2R, some artifacts appear in the reconstruction results, which are illustrated in Figure 4. Simulation results in double sources case further show that although there are differences between the results of different noise pattern in matrix A, similar conclusions can be obtained. As shown in Table 3, the reconstruction results of TTLS combined with MGCV are comparable to that of TTLS combined with IGCV when noise level is low; whereas with the increase of noise or error, TTLS combined with IGCV outperforms the other methods in all quantitative indices.


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)

Reconstructed results in double source case under measurement noise level of 20% and system error level of 5%. (a), (b), and (c) separately show the x–y views at z = 15 mm plane of the results by Tikhonov + GCV, TTLS + MGCV, and TTLS + IGCV; (d), (e), and (f) are the corresponding y–z views at x = 9.5 mm plane of the reconstruction results, respectively; the white circle indicates the real source.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2874932&req=5

fig4: Reconstructed results in double source case under measurement noise level of 20% and system error level of 5%. (a), (b), and (c) separately show the x–y views at z = 15 mm plane of the results by Tikhonov + GCV, TTLS + MGCV, and TTLS + IGCV; (d), (e), and (f) are the corresponding y–z views at x = 9.5 mm plane of the reconstruction results, respectively; the white circle indicates the real source.
Mentions: In the double sources case, both of the two sphere sources located in the left lung are tested. The final reconstruction results are listed in Table 3. Under all the noise conditions considered in this paper, the three methods can reconstruct the two sources at S1R = (−9.20 mm, −1.62 mm, 14.12 mm) and S2R = (−9.42 mm, 1.69 mm, 14.94 mm), which are 0.911 mm and 0.467 mm away from the actual ones, respectively. In fact, they are the nearest nodes to the original source locations under the FEM mesh used in our tests. However, with the increase of noise or error level, besides the optimal nodes S1R and S2R, some artifacts appear in the reconstruction results, which are illustrated in Figure 4. Simulation results in double sources case further show that although there are differences between the results of different noise pattern in matrix A, similar conclusions can be obtained. As shown in Table 3, the reconstruction results of TTLS combined with MGCV are comparable to that of TTLS combined with IGCV when noise level is low; whereas with the increase of noise or error, TTLS combined with IGCV outperforms the other methods in all quantitative indices.

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.