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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.


Gamma rays escape the body and are observed by the detectors.
© Copyright Policy - open-access
Related In: Results  -  Collection


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fig1: Gamma rays escape the body and are observed by the detectors.

Mentions: One of the most important quality of PET is itsabilities to model biological and physiological functions in vivo to enhanceour understanding of the biochemical basis of normal and abnormal functionswithin the body. PET is also useful for the detection of cancer, coronaryartery disease, and brain disease. During a PET acquisition, a compoundcontaining a radiative isotope is injected into the body to form an (unknown)emission density λ(x, y) ≥ 0. The positron emitted finds a nearby electron andthey annihilate into two photons of 511 keV according to the equation E = mc2. This energy is strong enough to escape the body.Since the two photons travel at almost opposite directions, a detector ringsurrounds the patient and tries to collect the emissions. For an emission eventto be counted, both photons must be registered nearly simultaneously at twoopposite detectors. In Figure 1, emission paths from two different regions areshown, that is, along the tube covered by detector pair AD, and along the tubecovered by detector pair BC. Regions with higher concentration of radioactivitycause a higher emission rate. Given the total number of measured counts foreach detector pair, the challenge is to locate all the emission sources insidethe detector ring. Emissions measured between two detectors could have takenplace anywhere along the tube between these two detectors, but with asystematic inspection of all detector pairs, it is possible to reveal variancein the emission rate along the same tube.


Level set method for positron emission tomography.

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

Gamma rays escape the body and are observed by the detectors.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig1: Gamma rays escape the body and are observed by the detectors.
Mentions: One of the most important quality of PET is itsabilities to model biological and physiological functions in vivo to enhanceour understanding of the biochemical basis of normal and abnormal functionswithin the body. PET is also useful for the detection of cancer, coronaryartery disease, and brain disease. During a PET acquisition, a compoundcontaining a radiative isotope is injected into the body to form an (unknown)emission density λ(x, y) ≥ 0. The positron emitted finds a nearby electron andthey annihilate into two photons of 511 keV according to the equation E = mc2. This energy is strong enough to escape the body.Since the two photons travel at almost opposite directions, a detector ringsurrounds the patient and tries to collect the emissions. For an emission eventto be counted, both photons must be registered nearly simultaneously at twoopposite detectors. In Figure 1, emission paths from two different regions areshown, that is, along the tube covered by detector pair AD, and along the tubecovered by detector pair BC. Regions with higher concentration of radioactivitycause a higher emission rate. Given the total number of measured counts foreach detector pair, the challenge is to locate all the emission sources insidethe detector ring. Emissions measured between two detectors could have takenplace anywhere along the tube between these two detectors, but with asystematic inspection of all detector pairs, it is possible to reveal variancein the emission rate along the same tube.

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.