The Korean Journal of Nuclear Medicine (대한핵의학회지)

The Korean Society of Nuclear Medicine (대한핵의학회)
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Development of Regularized Expectation Maximization Algorithms for Fan-Beam SPECT Data

부채살 SPECT 데이터를 위한 정칙화된 기댓값 최대화 재구성기법 개발

  • Kim, Soo-Mee (Department of Nuclear Medicine and Interdisciplinary Program in Radiation Applied Life Science Major, Seoul National University College of Medicine) ;
  • Lee, Jae-Sung (Department of Nuclear Medicine and Interdisciplinary Program in Radiation Applied Life Science Major, Seoul National University College of Medicine) ;
  • Lee, Soo-Jin (Department of Electronic Engineering, Paichai University) ;
  • Kim, Kyeong-Min (Department of Nuclear Medicine, Korea Institute of Radiology & Medical Sciences) ;
  • Lee, Dong-Soo (Department of Nuclear Medicine and Interdisciplinary Program in Radiation Applied Life Science Major, Seoul National University College of Medicine)
  • 김수미 (서울대학교 의과대학 핵의학교실 및 방사선응용생명과학 협동과정) ;
  • 이재성 (서울대학교 의과대학 핵의학교실 및 방사선응용생명과학 협동과정) ;
  • 이수진 (배재대학교 전자공학과) ;
  • 김경민 (원자력의학원 핵의학과) ;
  • 이동수 (서울대학교 의과대학 핵의학교실 및 방사선응용생명과학 협동과정)
  • Published : 2005.12.31
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Abstract

Purpose: SPECT using a fan-beam collimator improves spatial resolution and sensitivity. For the reconstruction from fan-beam projections, it is necessary to implement direct fan-beam reconstruction methods without transforming the data into the parallel geometry. In this study, various fan-beam reconstruction algorithms were implemented and their performances were compared. Materials and Methods: The projector for fan-beam SPECT was implemented using a ray-tracing method. The direct reconstruction algorithms implemented for fan-beam projection data were FBP (filtered backprojection), EM (expectation maximization), OS-EM (ordered subsets EM) and MAP-EM OSL (maximum a posteriori EM using the one-step late method) with membrane and thin-plate models as priors. For comparison, the fan-beam protection data were also rebinned into the parallel data using various interpolation methods, such as the nearest neighbor, bilinear and bicubic interpolations, and reconstructed using the conventional EM algorithm for parallel data. Noiseless and noisy projection data from the digital Hoffman brain and Shepp/Logan phantoms were reconstructed using the above algorithms. The reconstructed images were compared in terms of a percent error metric. Results: for the fan-beam data with Poisson noise, the MAP-EM OSL algorithm with the thin-plate prior showed the best result in both percent error and stability. Bilinear interpolation was the most effective method for rebinning from the fan-beam to parallel geometry when the accuracy and computation load were considered. Direct fan-beam EM reconstructions were more accurate than the standard EM reconstructions obtained from rebinned parallel data. Conclusion: Direct fan-beam reconstruction algorithms were implemented, which provided significantly improved reconstructions.

목적: 부채살 단일광자단층촬영(SPECT)은 공간분해능과 민감도를 개선하는 것으로 알려져 있다. 보다 정확한 영상을 얻고 인체에 대한 SPECT의 영상화 과정을 정확하게 묘사하기 위하여 평행 데이터로 재배열하는 과정 없이 직접 부채살 데이터를 이용하여 재구성하는 알고리즘이 필요하다. 본 연구는 다양한 부채살 재구성 알고리즘을 구현하였고 각 방법의 성능을 비교하였다. 대상 및 방법: 선추적법을 적용하여 부채살 투사기와 이로부터 얻은 데이터를 직접 재구성할 수 있는 FBP, EM, OS-EM과 MAP-EM OSL 알고리즘을 구현하였다. OSL 알고리즘의 경우에는 membrane과 thin plate prior를 사용하였다. 직접 부채살 데이터를 재구성하는 방법의 성능을 평가하기 위해 양방향 최근접 이웃, 양방향 1차와 양방향 3차 보간법을 사용하여 재배열된 평행 데이터를 얻었고 이 데이터를 기존의 평행 데이터에 대한 EM 알고리즘을 사용하여 재구성하였다. Hoffman 두뇌와 Shepp/Logan 팬텀으로부터 얻은 잡음 없는 데이터와 잡음 있는 데이터는 각 방법으로 재구성하였으며 퍼센트 오차를 계산하여 각 재구성된 영상을 비교하였다. 결과: Thin-plate 사전 분포함수를 사용한 OSL 방법이 가장 낮은 오차를 가지며 잡음으로 인한 결과 영상의 불안정성을 효과적으로 제어함을 확인할 수 있었다. 부채살 데이터를 평행 데이터로 재배열시 양방향 1차 보간법이 정확성과 계산 시간 측면에서 가장 효율적인 방법임을 확인하였다. 재배열된 평행 데이터의 EM결과에 비해 직접 부채살 데이터를 재구성하여 얻은 결과영상이 더 정확하게 재구성되었다. 결론: 본 연구에서는 평행 데이터로 재배열한 경우에 비하여 보다 정확한 영상을 재구성하는 직접 부채살 재구성 알고리즘을 구현하였으며 이는 정량적으로 월등히 개선된 결과를 제공함을 확인하였다.

Keywords

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