Journal of Biomedical Engineering Research (대한의용생체공학회:의공학회지)

The Korean Society of Medical and Biological Engineering (대한의용생체공학회)
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A Study on the Tensor-Valued Median Filter Using the Modified Gradient Descent Method in DT-MRI

확산텐서자기공명영상에서 수정된 기울기강하법을 이용한 텐서 중간값 필터에 관한 연구

  • Kim, Sung-Hee (Department of Biomedical Engineering, Yonsei University) ;
  • Kwon, Ki-Woon (Department of Biomedical Engineering, Yonsei University) ;
  • Park, In-Sung (Department of Biomedical Engineering, Yonsei University) ;
  • Han, Bong-Soo (Department of Radiological Science, Yonsei University) ;
  • Kim, Dong-Youn (Department of Biomedical Engineering, Yonsei University)
  • 김성희 (연세대학교 보건과학대학) ;
  • 권기운 (연세대학교 보건과학대학) ;
  • 박인성 (연세대학교 보건과학대학) ;
  • 한봉수 (연세대학교 방사선학과) ;
  • 김동윤 (연세대학교 보건과학대학)
  • Published : 2007.12.31
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Abstract

Tractography using Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of the principal eigenvector in the white matter of the brain. However, the fiber tracking methods suffer from the noise included in the diffusion tensor images that affects the determination of the principal eigenvector. As the fiber tracking progresses, the accumulated error creates a large deviation between the calculated fiber and the real fiber. This problem of the DT-MRI tractography is known mathematically as the ill-posed problem which means that tractography is very sensitive to perturbations by noise. To reduce the noise in DT-MRI measurements, a tensor-valued median filter which is reported to be denoising and structure-preserving in fiber tracking, is applied in the tractography. In this paper, we proposed the modified gradient descent method which converges fast and accurately to the optimal tensor-valued median filter by changing the step size. In addition, the performance of the modified gradient descent method is compared with others. We used the synthetic image which consists of 45 degree principal eigenvectors and the corticospinal tract. For the synthetic image, the proposed method achieved 4.66%, 16.66% and 15.08% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively. For the corticospinal tract, at iteration number ten the proposed method achieved 3.78%, 25.71 % and 11.54% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively.

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References

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