Tensor interpolation is a key step in the processing algorithms of diffusion tensor imaging (DTI), such as registration and tractography. The diffusion tensor (DT) in biological tissues is assumed to be positive defin...Tensor interpolation is a key step in the processing algorithms of diffusion tensor imaging (DTI), such as registration and tractography. The diffusion tensor (DT) in biological tissues is assumed to be positive definite. However, the tensor interpolations in most clinical applications have used a Euclidian scheme that does not take this assumption into account. Several Rie-mannian schemes were developed to overcome this limitation. Although each of the Riemannian schemes uses different metrics, they all result in a ‘fixed’ interpolation profile that cannot adapt to a variety of diffusion patterns in biological tissues. In this paper, we propose a DT interpolation scheme to control the interpolation profile, and explore its feasibility in clinical applications. The profile controllability comes from the non-uniform motion of interpolation on the Riemannian geodesic. The interpolation experiment with medical DTI data shows that the profile control improves the interpolation quality by assessing the reconstruction errors with the determinant error, Euclidean norm, and Riemannian norm.展开更多
An advanced Gauss pseudospectral method(AGPM) was proposed to estimate the parameters of the continuous-time(CT)Hammerstein model.The nonlinear part of the Hammerstein system is approximated with pseudospectral approx...An advanced Gauss pseudospectral method(AGPM) was proposed to estimate the parameters of the continuous-time(CT)Hammerstein model.The nonlinear part of the Hammerstein system is approximated with pseudospectral approximation method.The linear part was written as a controllable canonical form to circumvent the high order time-derivative of the input and output(I/O) signals,which could multiply the measurement noise in the identification procession.Furthermore,an output error minimization was constructed for the CT Hammerstein model identification,which was then transcribed into a nonlinear programming(NLP) problem by AGPM.AGPM could converge to the true values of the CT Hammerstein model with few interpolated Legendre-Gauss(LG) nodes.Lastly,two illustrative examples were proposed to verify the accuracy and efficiency of the method.展开更多
基金Project (No. 60772092) supported by the National Natural Science Foundation of China
文摘Tensor interpolation is a key step in the processing algorithms of diffusion tensor imaging (DTI), such as registration and tractography. The diffusion tensor (DT) in biological tissues is assumed to be positive definite. However, the tensor interpolations in most clinical applications have used a Euclidian scheme that does not take this assumption into account. Several Rie-mannian schemes were developed to overcome this limitation. Although each of the Riemannian schemes uses different metrics, they all result in a ‘fixed’ interpolation profile that cannot adapt to a variety of diffusion patterns in biological tissues. In this paper, we propose a DT interpolation scheme to control the interpolation profile, and explore its feasibility in clinical applications. The profile controllability comes from the non-uniform motion of interpolation on the Riemannian geodesic. The interpolation experiment with medical DTI data shows that the profile control improves the interpolation quality by assessing the reconstruction errors with the determinant error, Euclidean norm, and Riemannian norm.
文摘An advanced Gauss pseudospectral method(AGPM) was proposed to estimate the parameters of the continuous-time(CT)Hammerstein model.The nonlinear part of the Hammerstein system is approximated with pseudospectral approximation method.The linear part was written as a controllable canonical form to circumvent the high order time-derivative of the input and output(I/O) signals,which could multiply the measurement noise in the identification procession.Furthermore,an output error minimization was constructed for the CT Hammerstein model identification,which was then transcribed into a nonlinear programming(NLP) problem by AGPM.AGPM could converge to the true values of the CT Hammerstein model with few interpolated Legendre-Gauss(LG) nodes.Lastly,two illustrative examples were proposed to verify the accuracy and efficiency of the method.
