Maximum likelihood positioning algorithm for high-resolution PET scanners
Purpose: In high-resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator arrays in which one scintillator element (crystal) is smaller than the size of the readout channel. In order to identify the hit crystal by mea...
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| Published in | Medical physics (Lancaster) Vol. 43; no. 6; pp. 3049 - 3061 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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United States
American Association of Physicists in Medicine
01.06.2016
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| Abstract | Purpose:
In high-resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator arrays in which one scintillator element (crystal) is smaller than the size of the readout channel. In order to identify the hit crystal by means of the measured light distribution, a positioning algorithm is required. One commonly applied positioning algorithm uses the center of gravity (COG) of the measured light distribution. The COG algorithm is limited in spatial resolution by noise and intercrystal Compton scatter. The purpose of this work is to develop a positioning algorithm which overcomes this limitation.
Methods:
The authors present a maximum likelihood (ML) algorithm which compares a set of expected light distributions given by probability density functions (PDFs) with the measured light distribution. Instead of modeling the PDFs by using an analytical model, the PDFs of the proposed ML algorithm are generated assuming a single-gamma-interaction model from measured data. The algorithm was evaluated with a hot-rod phantom measurement acquired with the preclinical hyperion II
D PET scanner. In order to assess the performance with respect to sensitivity, energy resolution, and image quality, the ML algorithm was compared to a COG algorithm which calculates the COG from a restricted set of channels. The authors studied the energy resolution of the ML and the COG algorithm regarding incomplete light distributions (missing channel information caused by detector dead time). Furthermore, the authors investigated the effects of using a filter based on the likelihood values on sensitivity, energy resolution, and image quality.
Results:
A sensitivity gain of up to 19% was demonstrated in comparison to the COG algorithm for the selected operation parameters. Energy resolution and image quality were on a similar level for both algorithms. Additionally, the authors demonstrated that the performance of the ML algorithm is less prone to missing channel information. A likelihood filter visually improved the image quality, i.e., the peak-to-valley increased up to a factor of 3 for 2-mm-diameter phantom rods by rejecting 87% of the coincidences. A relative improvement of the energy resolution of up to 12.8% was also measured rejecting 91% of the coincidences.
Conclusions:
The developed ML algorithm increases the sensitivity by correctly handling missing channel information without influencing energy resolution or image quality. Furthermore, the authors showed that energy resolution and image quality can be improved substantially by rejecting events that do not comply well with the single-gamma-interaction model, such as Compton-scattered events. |
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| AbstractList | Purpose: In high-resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator arrays in which one scintillator element (crystal) is smaller than the size of the readout channel. In order to identify the hit crystal by means of the measured light distribution, a positioning algorithm is required. One commonly applied positioning algorithm uses the center of gravity (COG) of the measured light distribution. The COG algorithm is limited in spatial resolution by noise and intercrystal Compton scatter. The purpose of this work is to develop a positioning algorithm which overcomes this limitation. Methods: The authors present a maximum likelihood (ML) algorithm which compares a set of expected light distributions given by probability density functions (PDFs) with the measured light distribution. Instead of modeling the PDFs by using an analytical model, the PDFs of the proposed ML algorithm are generated assuming a single-gamma-interaction model from measured data. The algorithm was evaluated with a hot-rod phantom measurement acquired with the preclinical HYPERION II {sup D} PET scanner. In order to assess the performance with respect to sensitivity, energy resolution, and image quality, the ML algorithm was compared to a COG algorithm which calculates the COG from a restricted set of channels. The authors studied the energy resolution of the ML and the COG algorithm regarding incomplete light distributions (missing channel information caused by detector dead time). Furthermore, the authors investigated the effects of using a filter based on the likelihood values on sensitivity, energy resolution, and image quality. Results: A sensitivity gain of up to 19% was demonstrated in comparison to the COG algorithm for the selected operation parameters. Energy resolution and image quality were on a similar level for both algorithms. Additionally, the authors demonstrated that the performance of the ML algorithm is less prone to missing channel information. A likelihood filter visually improved the image quality, i.e., the peak-to-valley increased up to a factor of 3 for 2-mm-diameter phantom rods by rejecting 87% of the coincidences. A relative improvement of the energy resolution of up to 12.8% was also measured rejecting 91% of the coincidences. Conclusions: The developed ML algorithm increases the sensitivity by correctly handling missing channel information without influencing energy resolution or image quality. Furthermore, the authors showed that energy resolution and image quality can be improved substantially by rejecting events that do not comply well with the single-gamma-interaction model, such as Compton-scattered events. PURPOSEIn high-resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator arrays in which one scintillator element (crystal) is smaller than the size of the readout channel. In order to identify the hit crystal by means of the measured light distribution, a positioning algorithm is required. One commonly applied positioning algorithm uses the center of gravity (COG) of the measured light distribution. The COG algorithm is limited in spatial resolution by noise and intercrystal Compton scatter. The purpose of this work is to develop a positioning algorithm which overcomes this limitation.METHODSThe authors present a maximum likelihood (ML) algorithm which compares a set of expected light distributions given by probability density functions (PDFs) with the measured light distribution. Instead of modeling the PDFs by using an analytical model, the PDFs of the proposed ML algorithm are generated assuming a single-gamma-interaction model from measured data. The algorithm was evaluated with a hot-rod phantom measurement acquired with the preclinical hyperion II (D) PET scanner. In order to assess the performance with respect to sensitivity, energy resolution, and image quality, the ML algorithm was compared to a COG algorithm which calculates the COG from a restricted set of channels. The authors studied the energy resolution of the ML and the COG algorithm regarding incomplete light distributions (missing channel information caused by detector dead time). Furthermore, the authors investigated the effects of using a filter based on the likelihood values on sensitivity, energy resolution, and image quality.RESULTSA sensitivity gain of up to 19% was demonstrated in comparison to the COG algorithm for the selected operation parameters. Energy resolution and image quality were on a similar level for both algorithms. Additionally, the authors demonstrated that the performance of the ML algorithm is less prone to missing channel information. A likelihood filter visually improved the image quality, i.e., the peak-to-valley increased up to a factor of 3 for 2-mm-diameter phantom rods by rejecting 87% of the coincidences. A relative improvement of the energy resolution of up to 12.8% was also measured rejecting 91% of the coincidences.CONCLUSIONSThe developed ML algorithm increases the sensitivity by correctly handling missing channel information without influencing energy resolution or image quality. Furthermore, the authors showed that energy resolution and image quality can be improved substantially by rejecting events that do not comply well with the single-gamma-interaction model, such as Compton-scattered events. Purpose: In high-resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator arrays in which one scintillator element (crystal) is smaller than the size of the readout channel. In order to identify the hit crystal by means of the measured light distribution, a positioning algorithm is required. One commonly applied positioning algorithm uses the center of gravity (COG) of the measured light distribution. The COG algorithm is limited in spatial resolution by noise and intercrystal Compton scatter. The purpose of this work is to develop a positioning algorithm which overcomes this limitation. Methods: The authors present a maximum likelihood (ML) algorithm which compares a set of expected light distributions given by probability density functions (PDFs) with the measured light distribution. Instead of modeling the PDFs by using an analytical model, the PDFs of the proposed ML algorithm are generated assuming a single-gamma-interaction model from measured data. The algorithm was evaluated with a hot-rod phantom measurement acquired with the preclinical hyperion II D PET scanner. In order to assess the performance with respect to sensitivity, energy resolution, and image quality, the ML algorithm was compared to a COG algorithm which calculates the COG from a restricted set of channels. The authors studied the energy resolution of the ML and the COG algorithm regarding incomplete light distributions (missing channel information caused by detector dead time). Furthermore, the authors investigated the effects of using a filter based on the likelihood values on sensitivity, energy resolution, and image quality. Results: A sensitivity gain of up to 19% was demonstrated in comparison to the COG algorithm for the selected operation parameters. Energy resolution and image quality were on a similar level for both algorithms. Additionally, the authors demonstrated that the performance of the ML algorithm is less prone to missing channel information. A likelihood filter visually improved the image quality, i.e., the peak-to-valley increased up to a factor of 3 for 2-mm-diameter phantom rods by rejecting 87% of the coincidences. A relative improvement of the energy resolution of up to 12.8% was also measured rejecting 91% of the coincidences. Conclusions: The developed ML algorithm increases the sensitivity by correctly handling missing channel information without influencing energy resolution or image quality. Furthermore, the authors showed that energy resolution and image quality can be improved substantially by rejecting events that do not comply well with the single-gamma-interaction model, such as Compton-scattered events. In high-resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator arrays in which one scintillator element (crystal) is smaller than the size of the readout channel. In order to identify the hit crystal by means of the measured light distribution, a positioning algorithm is required. One commonly applied positioning algorithm uses the center of gravity (COG) of the measured light distribution. The COG algorithm is limited in spatial resolution by noise and intercrystal Compton scatter. The purpose of this work is to develop a positioning algorithm which overcomes this limitation. The authors present a maximum likelihood (ML) algorithm which compares a set of expected light distributions given by probability density functions (PDFs) with the measured light distribution. Instead of modeling the PDFs by using an analytical model, the PDFs of the proposed ML algorithm are generated assuming a single-gamma-interaction model from measured data. The algorithm was evaluated with a hot-rod phantom measurement acquired with the preclinical hyperion II (D) PET scanner. In order to assess the performance with respect to sensitivity, energy resolution, and image quality, the ML algorithm was compared to a COG algorithm which calculates the COG from a restricted set of channels. The authors studied the energy resolution of the ML and the COG algorithm regarding incomplete light distributions (missing channel information caused by detector dead time). Furthermore, the authors investigated the effects of using a filter based on the likelihood values on sensitivity, energy resolution, and image quality. A sensitivity gain of up to 19% was demonstrated in comparison to the COG algorithm for the selected operation parameters. Energy resolution and image quality were on a similar level for both algorithms. Additionally, the authors demonstrated that the performance of the ML algorithm is less prone to missing channel information. A likelihood filter visually improved the image quality, i.e., the peak-to-valley increased up to a factor of 3 for 2-mm-diameter phantom rods by rejecting 87% of the coincidences. A relative improvement of the energy resolution of up to 12.8% was also measured rejecting 91% of the coincidences. The developed ML algorithm increases the sensitivity by correctly handling missing channel information without influencing energy resolution or image quality. Furthermore, the authors showed that energy resolution and image quality can be improved substantially by rejecting events that do not comply well with the single-gamma-interaction model, such as Compton-scattered events. Purpose: In high‐resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator arrays in which one scintillator element (crystal) is smaller than the size of the readout channel. In order to identify the hit crystal by means of the measured light distribution, a positioning algorithm is required. One commonly applied positioning algorithm uses the center of gravity (COG) of the measured light distribution. The COG algorithm is limited in spatial resolution by noise and intercrystal Compton scatter. The purpose of this work is to develop a positioning algorithm which overcomes this limitation. Methods: The authors present a maximum likelihood (ML) algorithm which compares a set of expected light distributions given by probability density functions (PDFs) with the measured light distribution. Instead of modeling the PDFs by using an analytical model, the PDFs of the proposed ML algorithm are generated assuming a single‐gamma‐interaction model from measured data. The algorithm was evaluated with a hot‐rod phantom measurement acquired with the preclinical hyperion II D PET scanner. In order to assess the performance with respect to sensitivity, energy resolution, and image quality, the ML algorithm was compared to a COG algorithm which calculates the COG from a restricted set of channels. The authors studied the energy resolution of the ML and the COG algorithm regarding incomplete light distributions (missing channel information caused by detector dead time). Furthermore, the authors investigated the effects of using a filter based on the likelihood values on sensitivity, energy resolution, and image quality. Results: A sensitivity gain of up to 19% was demonstrated in comparison to the COG algorithm for the selected operation parameters. Energy resolution and image quality were on a similar level for both algorithms. Additionally, the authors demonstrated that the performance of the ML algorithm is less prone to missing channel information. A likelihood filter visually improved the image quality, i.e., the peak‐to‐valley increased up to a factor of 3 for 2‐mm‐diameter phantom rods by rejecting 87% of the coincidences. A relative improvement of the energy resolution of up to 12.8% was also measured rejecting 91% of the coincidences. Conclusions: The developed ML algorithm increases the sensitivity by correctly handling missing channel information without influencing energy resolution or image quality. Furthermore, the authors showed that energy resolution and image quality can be improved substantially by rejecting events that do not comply well with the single‐gamma‐interaction model, such as Compton‐scattered events. |
| Author | Schulz, Volkmar Gross-Weege, Nicolas Hallen, Patrick Schug, David |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/27277052$$D View this record in MEDLINE/PubMed https://www.osti.gov/biblio/22685109$$D View this record in Osti.gov |
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| Keywords | scintillation cameras maximum likelihood estimation PET data processing |
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| Notes | nicolas.gross‐weege@pmi.rwth‐aachen.de Authors to whom correspondence should be addressed. Electronic mail schulz@pmi.rwth‐aachen.de and ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
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In high-resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator... Purpose: In high‐resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator... In high-resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator arrays in... PURPOSEIn high-resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator... Purpose: In high-resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator... |
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| SubjectTerms | 60 APPLIED LIFE SCIENCES ALGORITHMS Biological material, e.g. blood, urine; Haemocytometers Compton effect data processing Digital computing or data processing equipment or methods, specially adapted for specific applications DISTRIBUTION ENERGY RESOLUTION General statistical methods Image data processing or generation, in general Image reconstruction image resolution maximum likelihood estimation Measuring half‐life of a radioactive substance medical image processing Medical image quality PET phantoms Photodiodes Photons Position sensitive detectors POSITIONING POSITRON COMPUTED TOMOGRAPHY positron emission tomography Positron emission tomography (PET) PROBABILITY DENSITY FUNCTIONS Probability theory RADIATION PROTECTION AND DOSIMETRY READOUT SYSTEMS Scintigraphy scintillation scintillation cameras Scintillation detectors SENSITIVITY SIMULATION SPATIAL RESOLUTION VISIBLE RADIATION |
| Title | Maximum likelihood positioning algorithm for high-resolution PET scanners |
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