• Title/Summary/Keyword: Expectation-Maximization algorithm

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A Neuro-Fuzzy System Modeling using Gaussian Mixture Model and Clustering Method (GMM과 클러스터링 기법에 의한 뉴로-퍼지 시스템 모델링)

  • Kim, Sung-Suk;Kwak, Keun-Chang;Ryu, Jeong-Woong;Chun, Myung-Geun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.12 no.6
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    • pp.571-576
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    • 2002
  • There have been a lot of considerations dealing with improving the performance of neuro-fuzzy system. The studies on the neuro-fuzzy modeling have largely been devoted to two approaches. First is to improve performance index of system. The other is to reduce the structure size. In spite of its satisfactory result, it should be noted that these are difficult to extend to high dimensional input or to increase the membership functions. We propose a novel neuro-fuzzy system based on the efficient clustering method for initializing the parameters of the premise part. It is a very useful method that maintains a few number of rules and improves the performance. It combine the various algorithms to improve the performance. The Expectation-Maximization algorithm of Gaussian mixture model is an efficient estimation method for unknown parameter estimation of mirture model. The obtained parameters are used for fuzzy clustering method. The proposed method satisfies these two requirements using the Gaussian mixture model and neuro-fuzzy modeling. Experimental results indicate that the proposed method is capable of giving reliable performance.

Preliminary Study on the Enhancement of Reconstruction Speed for Emission Computed Tomography Using Parallel Processing (병렬 연산을 이용한 방출 단층 영상의 재구성 속도향상 기초연구)

  • Park, Min-Jae;Lee, Jae-Sung;Kim, Soo-Mee;Kang, Ji-Yeon;Lee, Dong-Soo;Park, Kwang-Suk
    • Nuclear Medicine and Molecular Imaging
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    • v.43 no.5
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    • pp.443-450
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    • 2009
  • Purpose: Conventional image reconstruction uses simplified physical models of projection. However, real physics, for example 3D reconstruction, takes too long time to process all the data in clinic and is unable in a common reconstruction machine because of the large memory for complex physical models. We suggest the realistic distributed memory model of fast-reconstruction using parallel processing on personal computers to enable large-scale technologies. Materials and Methods: The preliminary tests for the possibility on virtual manchines and various performance test on commercial super computer, Tachyon were performed. Expectation maximization algorithm with common 2D projection and realistic 3D line of response were tested. Since the process time was getting slower (max 6 times) after a certain iteration, optimization for compiler was performed to maximize the efficiency of parallelization. Results: Parallel processing of a program on multiple computers was available on Linux with MPICH and NFS. We verified that differences between parallel processed image and single processed image at the same iterations were under the significant digits of floating point number, about 6 bit. Double processors showed good efficiency (1.96 times) of parallel computing. Delay phenomenon was solved by vectorization method using SSE. Conclusion: Through the study, realistic parallel computing system in clinic was established to be able to reconstruct by plenty of memory using the realistic physical models which was impossible to simplify.

Usability of Multiple Confocal SPECT SYSTEM in the Myocardial Perfusion SPECT Using $^{99m}Tc$ ($^{99m}Tc$을 이용한 심근 관류 SPECT에서 Multiple Confocal SPECT System의 유용성)

  • Shin, Chae-Ho;Pyo, Sung-Jai;Kim, Bong-Su;Cho, Yong-Gyi;Jo, Jin-Woo;Kim, Chang-Ho
    • The Korean Journal of Nuclear Medicine Technology
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    • v.15 no.2
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    • pp.65-71
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    • 2011
  • Purpose: The recently adopted multiple confocal SPECT SYSTEM (hereinafter called IQ SPECT$^{TM}$) has a high difference from the conventional myocardial perfusion SPECT in the collimator form, image capture method, and image reconstruction method. This study was conducted to compare this novice equipment with the conventional one to design a protocol meeting the IQ SPECT, and also determine the characteristics and usefulness of IQ SPECT. Materials and Methods: 1. For the objects of LEHR (Low energy high resolution) collimator and Multiple confocal collimator, $^{99m}Tc$ 37MBq was put in the acrylic dish then each sensitivity ($cpm/{\mu}Ci$) was measured at the distance of 5 cm, 10 cm, 20 cm, 30 cm, and 40 cm respectively. 2. Based on the sensitivity measure results, IQ SPECT Protocol was designed according to the conventional general myocardial SPECT, then respectively 278 kBq/mL, 7.4 kBq/mL, and 48 kBq/mL of $^{99m}Tc$ were injected into the myocardial and soft tissues and liver site by using the anthropomorphic torso phantom then the myocardial perfusion SPECT was run. 3. For the comparison of FWHMs (Full Width at Half Maximum) resulted from the image reconstruction of LEHR collimator, the FWHMs (mm) were measured with only algorithms changed, in the case of the FBP (Filtered Back projection) method- a reconstruction method of conventional myocardial perfusion SPECT, and the 3D OSEM (Ordered subsets expectation maximization) method of IQ SPECT, by using $^{99m}Tc$ Line source. Results: 1. The values of IQ SPECT collimator sensitivity ($cpm/{\mu}Ci$) were 302, 382, 655, 816, 1178, and those of LEHR collimator were measured as 204, 204, 202, 201, 198, both at the distance of 5 cm, 10 cm, 20 cm, 30 cm, and 40 cm respectively. It was found the difference of sensitivity increases up to 4 times at the distance of 30 cm in the cases of IQ SPECT and LEHR. 2. The myocardial perfusion SPECT Protocol was designed according to the geometric characteristics of IQ SPECT based on the sensitivity results, then the phantom test for the aforesaid protocol was conducted. As a result, it was found the examination time can be reduced 1/4 compared to the past. 3. In the comparison of FWHMs according to the reconstructed algorithm in the FBP method and 3D OSEM method followed after the SEPCT test using a LEHR collimator, the result was obtained that FWHM rose around twice in the 3D OSEM method. Conclusion : The IQ SPECT uses the Multiple confocal collimator for the myocardial perfusion SPECT to enhance the sensitivity and also reduces examination time and contributes to improvement of visual screen quality through the myocardial-specific geometric image capture method and image reconstruction method. Due to such benefits, it is expected patients will receive more comfortable and more accurate examinations and it is considered a further study is required using additional clinical materials.

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Quantitative Comparisons between CT and $^{68}Ge$ Transmission Attenuation Corrected $^{18}F-FDG$ PET Images: Measured Attenuation Correction vs. Segmented Attenuation Correction (CT와 $^{68}Ge$ 감쇠보정 $^{18}F-FDG$ PET 영상의 정량적 비교: 측정감쇠보정대 분할감쇠보정)

  • Choi, Joon-Young;Woo, Sang-Keun;Choi, Yong;Choe, Yearn-Seong;Lee, Kyung-Han;Kim, Byung-Tae
    • Nuclear Medicine and Molecular Imaging
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    • v.41 no.1
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    • pp.49-53
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    • 2007
  • Purpose: It was reported that CT-based measured attenuation correction (CT-MAC) produced radioactivity concentration values significantly higher than $^{68}Ge$-based segmented attenuation correction (Ge-SAC) in PET images. However, it was unknown whether the radioactivity concentration difference resulted from different sources (CT vs. Ge) or types (MAC vs. SAC) of attenuation correction (AC). We evaluated the influences of the source and type of AC on the radioactivity concentration differences between reconstructed PET images in normal subjects and patients. Material and Methods: Five normal subjects and 35 patients with a known or suspected cancer underwent $^{18}F-FDG$ PET/CT. In each subject, attenuation corrected PET images using OSEM algorithm (28 subsets, 2 iterations) were reconstructed by 4 methods: CT-MAC, CT-SAC, Ge-MAC, and Ge-SAC. The physiological uptake in normal subjects and pathological uptake in patients were quantitatively compared between the PET images according to the source and type of AC. Results: The SUVs of physiological uptake measured in CT-MAC PET images were significantly higher than other 3 differently corrected PET images. Maximum SUVs of the 145 foci with abnormal FDG uptake in CT-MAC images were significantly highest among 4 differently corrected PET images with a difference of 2.4% to 5.1% (p<0.001). The SUVs of pathological uptake in Ge-MAC images were significantly higher than those in CT-SAC and Ge-MAC PET images (p<0.001). Conclusion: Quantitative radioactivity values were highest in CT-MAC PET images. The adoption of MAC may make a more contribution than the adoption of CT attenuation map to such differences.

Quantitative Assessment Technology of Small Animal Myocardial Infarction PET Image Using Gaussian Mixture Model (다중가우시안혼합모델을 이용한 소동물 심근경색 PET 영상의 정량적 평가 기술)

  • Woo, Sang-Keun;Lee, Yong-Jin;Lee, Won-Ho;Kim, Min-Hwan;Park, Ji-Ae;Kim, Jin-Su;Kim, Jong-Guk;Kang, Joo-Hyun;Ji, Young-Hoon;Choi, Chang-Woon;Lim, Sang-Moo;Kim, Kyeong-Min
    • Progress in Medical Physics
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    • v.22 no.1
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    • pp.42-51
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    • 2011
  • Nuclear medicine images (SPECT, PET) were widely used tool for assessment of myocardial viability and perfusion. However it had difficult to define accurate myocardial infarct region. The purpose of this study was to investigate methodological approach for automatic measurement of rat myocardial infarct size using polar map with adaptive threshold. Rat myocardial infarction model was induced by ligation of the left circumflex artery. PET images were obtained after intravenous injection of 37 MBq $^{18}F$-FDG. After 60 min uptake, each animal was scanned for 20 min with ECG gating. PET data were reconstructed using ordered subset expectation maximization (OSEM) 2D. To automatically make the myocardial contour and generate polar map, we used QGS software (Cedars-Sinai Medical Center). The reference infarct size was defined by infarction area percentage of the total left myocardium using TTC staining. We used three threshold methods (predefined threshold, Otsu and Multi Gaussian mixture model; MGMM). Predefined threshold method was commonly used in other studies. We applied threshold value form 10% to 90% in step of 10%. Otsu algorithm calculated threshold with the maximum between class variance. MGMM method estimated the distribution of image intensity using multiple Gaussian mixture models (MGMM2, ${\cdots}$ MGMM5) and calculated adaptive threshold. The infarct size in polar map was calculated as the percentage of lower threshold area in polar map from the total polar map area. The measured infarct size using different threshold methods was evaluated by comparison with reference infarct size. The mean difference between with polar map defect size by predefined thresholds (20%, 30%, and 40%) and reference infarct size were $7.04{\pm}3.44%$, $3.87{\pm}2.09%$ and $2.15{\pm}2.07%$, respectively. Otsu verse reference infarct size was $3.56{\pm}4.16%$. MGMM methods verse reference infarct size was $2.29{\pm}1.94%$. The predefined threshold (30%) showed the smallest mean difference with reference infarct size. However, MGMM was more accurate than predefined threshold in under 10% reference infarct size case (MGMM: 0.006%, predefined threshold: 0.59%). In this study, we was to evaluate myocardial infarct size in polar map using multiple Gaussian mixture model. MGMM method was provide adaptive threshold in each subject and will be a useful for automatic measurement of infarct size.