Journal of the Institute of Electronics Engineers of Korea SC (전자공학회논문지SC)

The Institute of Electronics and Information Engineers (대한전자공학회)
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A Study on the Dyadic Sorting method for the Regularization in DT-MRI

Dyadic Sorting 방법을 이용한 DT-MRI Regularization에 관한 연구

  • Kim, Tae-Hwan (Department of Biomedica1 Engineering, Yonsei Univ.) ;
  • Woo, Jong-Hyung (Department of Biomedica1 Engineering, Yonsei Univ.) ;
  • Lee, Hoon (Department of Biomedica1 Engineering, Yonsei Univ.) ;
  • Kim, Dong-Youn (Department of Biomedica1 Engineering, Yonsei Univ.)
  • 김태환 (연세대학교 의공학과) ;
  • 우종형 (연세대학교 의공학과) ;
  • 이훈 (연세대학교 의공학과) ;
  • 김동윤 (연세대학교 의공학과)
  • Received : 2010.06.21
  • Accepted : 2010.06.28
  • Published : 2010.07.25
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Abstract

Since Diffusion tensor from Diffusion Tensor Magnetic Resonance Imaging(DT-MRI) is so sensitive to noise, the principle eigenvector(PEV) calculated from Diffusion tensor could be erroneous. Tractography obtained from PEV could be deviated from the real fiber tract. Therefore regularization process is needed to eliminate noise. In this paper, to reduce noise in DT-MRI measurements, the Dyadic Sorting(DS) method as regularization of the eigenvalue and the eigenvector is applied in the tractography. To resort the eigenvalues and the eignevectors, the DS method uses the intervoxel overlap function which can measure the overlap between eigenvalue-eigenvector pairs in the $3\times3$ pixel. In this paper, we applied the DS method to the three-dimensional volume. We discuss the error analysis and numerical study to the synthetic and the experimental data. As a result, we have shown that the DS method is more efficient than the median filtering methods as much as 79.97%~83.64%, 85.62%~87.76% in AAE, AFA respectively for the corticospinal tract of the experimental data.

자기공명확산텐서영상(diffusion tensor magnetic resonance image, DT-MRI)으로부터 얻어진 확산텐서는 잡음에 민감하므로 주 고유벡터(principle eigenvector, PEV)의 필드에도 잡음이 포함되기 쉽다. 신경다발영상은 잡음에 매우 민감한 PEV로부터 얻어지기 때문에 실제 신경다발의 방향과 다를 수 있다. 따라서 잡음을 제거하기 위한 정규화(regularization) 과정이 필요하다. 본 연구에서는 고유값과 고유벡터를 정규화 하기 위한 방법으로 Dyadic Sorting(DS) 방법을 사용하였고 이를 구현하기 위한 알고리듬을 제시하였다. DS 방법은 $3\times3$ 화소에서의 고유값-고유벡터 쌍의 오버랩 정도를 측정할 수 있는 Intervoxel overlap function을 이용하여 고유값, 고유벡터를 재배열하는 방법이다. 본 연구에서는 이 방법을 3차원으로 적용하여 주 고유 벡터가 $45^{\circ}$인 합성영상과 임상데이터에 적용하였고, 그 결과 임상데이터의 피질척수로에 적용한 경우 제안한 DS 방법이 중간값 필터 방법에 비하여 AAE, AFA가 각각 79.97%~83.64%, 85.62%~87.76% 우수함을 보였다.

Keywords

References

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