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Level set method for positron emission tomography.

Chan TF, Li H, Lysaker M, Tai XC - Int J Biomed Imaging (2007)

Bottom Line: Expectation maximization (EM) reconstruction algorithms are iterative techniques which estimate the concentration coefficients that provide the best fitted solution, for example, a maximum likelihood estimate.An intrinsic advantage of the level set formulation is that anatomical information can be efficiently incorporated and used in an easy and natural way.We utilize a multiple level set formulation to represent the geometry of the objects in the scene.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of California, Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90095-1555, USA.

ABSTRACT
In positron emission tomography (PET), a radioactive compound is injected into the body to promote a tissue-dependent emission rate. Expectation maximization (EM) reconstruction algorithms are iterative techniques which estimate the concentration coefficients that provide the best fitted solution, for example, a maximum likelihood estimate. In this paper, we combine the EM algorithm with a level set approach. The level set method is used to capture the coarse scale information and the discontinuities of the concentration coefficients. An intrinsic advantage of the level set formulation is that anatomical information can be efficiently incorporated and used in an easy and natural way. We utilize a multiple level set formulation to represent the geometry of the objects in the scene. The proposed algorithm can be applied to any PET configuration, without major modifications.

No MeSH data available.


Interfaces given by the zero level set of the function ϕ1 and ϕ2.
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Related In: Results  -  Collection


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fig4: Interfaces given by the zero level set of the function ϕ1 and ϕ2.

Mentions: The major drawback with the EM algorithm is its lackof termination criterion and the introduction of noise as the number ofiterations increases. In Figure 3(b), the intensity values in the outer circleare almost constant (as it should be in this test), but it is difficult todecide the exact boundary for the inner circle. After 30 iterations, the edgesare emphasized but so is the noise, as seen in Figure 3(c). After 100iterations, the noise becomes dominant and degrades the quality of therecovered intensity function. The same sinogram data were thereafter used forthe TV-EM and the LSEM algorithms. The results are shown in Figure 4. For thetwo level set functions of the LSEM algorithm, we started with random initialguesses (cf. Figures 4(a) and 4(e)).


Level set method for positron emission tomography.

Chan TF, Li H, Lysaker M, Tai XC - Int J Biomed Imaging (2007)

Interfaces given by the zero level set of the function ϕ1 and ϕ2.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2266822&req=5

fig4: Interfaces given by the zero level set of the function ϕ1 and ϕ2.
Mentions: The major drawback with the EM algorithm is its lackof termination criterion and the introduction of noise as the number ofiterations increases. In Figure 3(b), the intensity values in the outer circleare almost constant (as it should be in this test), but it is difficult todecide the exact boundary for the inner circle. After 30 iterations, the edgesare emphasized but so is the noise, as seen in Figure 3(c). After 100iterations, the noise becomes dominant and degrades the quality of therecovered intensity function. The same sinogram data were thereafter used forthe TV-EM and the LSEM algorithms. The results are shown in Figure 4. For thetwo level set functions of the LSEM algorithm, we started with random initialguesses (cf. Figures 4(a) and 4(e)).

Bottom Line: Expectation maximization (EM) reconstruction algorithms are iterative techniques which estimate the concentration coefficients that provide the best fitted solution, for example, a maximum likelihood estimate.An intrinsic advantage of the level set formulation is that anatomical information can be efficiently incorporated and used in an easy and natural way.We utilize a multiple level set formulation to represent the geometry of the objects in the scene.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of California, Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90095-1555, USA.

ABSTRACT
In positron emission tomography (PET), a radioactive compound is injected into the body to promote a tissue-dependent emission rate. Expectation maximization (EM) reconstruction algorithms are iterative techniques which estimate the concentration coefficients that provide the best fitted solution, for example, a maximum likelihood estimate. In this paper, we combine the EM algorithm with a level set approach. The level set method is used to capture the coarse scale information and the discontinuities of the concentration coefficients. An intrinsic advantage of the level set formulation is that anatomical information can be efficiently incorporated and used in an easy and natural way. We utilize a multiple level set formulation to represent the geometry of the objects in the scene. The proposed algorithm can be applied to any PET configuration, without major modifications.

No MeSH data available.