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A penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography.

Shang S, Bai J, Song X, Wang H, Lau J - Int J Biomed Imaging (2007)

Bottom Line: A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem.It has a better performance than the conventional conjugate gradient-based reconstruction algorithms.It offers an effective approach to reconstruct fluorochrome information for FMT.

View Article: PubMed Central - PubMed

Affiliation: Medical Engineering and Health Technology Research Group, Department of Biomedical Engineering, Tsinghua University, Beijing 100084, China.

ABSTRACT
Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

No MeSH data available.


Images reconstructed with different initial guesses,using N-CG (Column 1), L-CG (Column 2), and PLN-CG (Column 3). Initial guessfor (a)–(c) was an all-0.005 vector, and for (d)–(f) was an all-0.01 vector.Results were all obtained with one hundred iterations. γ was 50 for thePLN-CG approach. The small circle in each figure shows the real distribution ofthe fluorophore.
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fig4: Images reconstructed with different initial guesses,using N-CG (Column 1), L-CG (Column 2), and PLN-CG (Column 3). Initial guessfor (a)–(c) was an all-0.005 vector, and for (d)–(f) was an all-0.01 vector.Results were all obtained with one hundred iterations. γ was 50 for thePLN-CG approach. The small circle in each figure shows the real distribution ofthe fluorophore.

Mentions: Figure 4 shows the results reconstructed withdifferent initial values, using N-CG (Column 1), L-CG (Column 2), and PLN-CG(Column 3), respectively. Since most elements of the original solution are zeroand the quantity of the fluorochrome intensity in FMT is relatively small, azero vector is closer to the solution of the problem and is a better choice tobe the initial value (Figure 3). When the initial value is increased to 0.005and 0.01, the reconstructed images of N-CG (Figures 4(a) and 4(d)) and L-CG(Figures 4(b) and 4(e)) become perturbed, with artifacts distributed in thebackground. Whereas the PLN-CG (Figures 4(c) and 4(f)) is still giving a clearresult, with only a slight blur on the edge.


A penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography.

Shang S, Bai J, Song X, Wang H, Lau J - Int J Biomed Imaging (2007)

Images reconstructed with different initial guesses,using N-CG (Column 1), L-CG (Column 2), and PLN-CG (Column 3). Initial guessfor (a)–(c) was an all-0.005 vector, and for (d)–(f) was an all-0.01 vector.Results were all obtained with one hundred iterations. γ was 50 for thePLN-CG approach. The small circle in each figure shows the real distribution ofthe fluorophore.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2267888&req=5

fig4: Images reconstructed with different initial guesses,using N-CG (Column 1), L-CG (Column 2), and PLN-CG (Column 3). Initial guessfor (a)–(c) was an all-0.005 vector, and for (d)–(f) was an all-0.01 vector.Results were all obtained with one hundred iterations. γ was 50 for thePLN-CG approach. The small circle in each figure shows the real distribution ofthe fluorophore.
Mentions: Figure 4 shows the results reconstructed withdifferent initial values, using N-CG (Column 1), L-CG (Column 2), and PLN-CG(Column 3), respectively. Since most elements of the original solution are zeroand the quantity of the fluorochrome intensity in FMT is relatively small, azero vector is closer to the solution of the problem and is a better choice tobe the initial value (Figure 3). When the initial value is increased to 0.005and 0.01, the reconstructed images of N-CG (Figures 4(a) and 4(d)) and L-CG(Figures 4(b) and 4(e)) become perturbed, with artifacts distributed in thebackground. Whereas the PLN-CG (Figures 4(c) and 4(f)) is still giving a clearresult, with only a slight blur on the edge.

Bottom Line: A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem.It has a better performance than the conventional conjugate gradient-based reconstruction algorithms.It offers an effective approach to reconstruct fluorochrome information for FMT.

View Article: PubMed Central - PubMed

Affiliation: Medical Engineering and Health Technology Research Group, Department of Biomedical Engineering, Tsinghua University, Beijing 100084, China.

ABSTRACT
Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

No MeSH data available.