Journal of Biomedical Engineering Research (대한의용생체공학회:의공학회지)

The Korean Society of Medical and Biological Engineering (대한의용생체공학회)
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Quantitative Analysis of Bayesian SPECT Reconstruction : Effects of Using Higher-Order Gibbs Priors

  • S. J. Lee (Department of Electronic Engineering, Cornma Paichai University)
  • Published : 1998.04.01
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Abstract

In Bayesian SPECT reconstruction, the incorporation of elaborate forms of priors can lead to improved quantitative performance in various statistical terms, such as bias and variance. In particular, the use of higher-order smoothing priors, such as the thin-plate prior, is known to exhibit improved bias behavior compared to the conventional smoothing priors such as the membrane prior. However, the bias advantage of the higher-order priors is effective only when the hyperparameters involved in the reconstruction algorithm are properly chosen. In this work, we further investigate the quantitative performance of the two representative smoothing priors-the thin plate and the membrane-by observing the behavior of the associated hyperparameters of the prior distributions. In our experiments we use Monte Carlo noise trials to calculate bias and variance of reconstruction estimates, and compare the performance of ML-EM estimates to that of regularized EM using both membrane and thin-plate priors, and also to that of filtered backprojection, where the membrane and thin plate models become simple apodizing filters of specified form. We finally show that the use of higher-order models yields excellent "robustness" in quantitative performance by demonstrating that the thin plate leads to very low bias error over a large range of hyperparameters, while keeping a reasonable variance. variance.

Bayesian SPECT 영상재구성에 있어서 정교한 형태의 사전정보를 사용할 경우 bias 및 variance와 같은 통계적 차원에서의 정량적 성능을 향상시킬 수 있다. 특히, "thin plate" 와 같은 고차의 smoothing 사전정보는 "membrane"과 같은 일반적인 다른 사전 정보에 비해 bias를 개선시키는 것으로 알려져 있다. 그러나, 이와 같은 장점은 영상재구성 알고리즘에 내재하는 hyperparameters의 값을 최적으로 선택하였을 경우에만 적용된다. 본 연구에서는 thin plate와 membrane의 두가지 대표적인 사전정보를 포함하는 영상재구성 알고리즘의 정량적 성능에 대해 집중 고찰한다. 즉, 알고리즘에 내재하는 hyperparameters 가 통계적 차원에서 bias와 variance에 어떠한 영향을 미치는지 관찰한다. 실험에서 Monte Carlo noise trials를 사용하여 bias와 variance를 계산하며, 각 결과를 ML-EM 및 filtered backprojection으로부터 얻어진 bias 및 variance와 비교한다. 결론적으로 thin plate와 같은 고차의 사전정보는 hyperparameters의 선택에 민감하지 않으며, hyperparameters 값의 전 범위에 걸쳐 bias를 개선시킴을 보인다. 걸쳐 bias를 개선시킴을 보인다.

Keywords

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