The Experts below are selected from a list of 222 Experts worldwide ranked by ideXlab platform
Craighead W Tennant - One of the best experts on this subject based on the ideXlab platform.
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higher order zeeman and spin terms in the electron paramagnetic resonance spin hamiltonian their description in irreducible form using Cartesian tesseral spherical Tensor and stevens operator expressions
Journal of Physics: Condensed Matter, 2009Co-Authors: Dennis G Mcgavin, Craighead W TennantAbstract:In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical Tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian Tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS3 and BS5. Starting from the well-known decomposition of the general Cartesian Tensor of second rank to three irreducible Tensors of ranks 0, 1 and 2, the decomposition of Cartesian Tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical Tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.
Yonas T Weldeselassie - One of the best experts on this subject based on the ideXlab platform.
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symmetric positive semi definite Cartesian Tensor fiber orientation distributions ct fod
Medical Image Analysis, 2012Co-Authors: Yonas T Weldeselassie, Angelos Barmpoutis, Stella M AtkinsAbstract:A novel method for estimating a field of fiber orientation distribution (FOD) based on signal de-convolution from a given set of diffusion weighted magnetic resonance (DW-MR) images is presented. We model the FOD by higher order Cartesian Tensor basis using a parametrization that explicitly enforces the positive semi-definite property to the computed FOD. The computed Cartesian Tensors, dubbed Cartesian TensorFOD (CT-FOD), are symmetric positive semi-definite Tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Next, we show how to use our method for converting higher-order diffusion Tensors to CT-FODs, which is an essential task since the maxima of higher-order Tensors do not correspond to the underlying fiber orientations. Finally, we propose a diffusion anisotropy index computed directly from CT-FODs using higher order Tensor distance measures thus consolidating the whole analysis pipeline of diffusion imaging solely using CT-FODs. We evaluate our method qualitatively and quantitatively using simulated DW-MR images, phantom images, and human brain real dataset. The results conclusively demonstrate the superiority of the proposed technique over several existing multi-fiber reconstruction methods.
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symmetric positive definite Cartesian Tensor orientation distribution functions ct odf
Medical Image Computing and Computer-Assisted Intervention, 2010Co-Authors: Yonas T Weldeselassie, Angelos Barmpoutis, Stella M AtkinsAbstract:A novel method for estimating a field of orientation distribution functions (ODF) from a given set of DW-MR images is presented. We model the ODF by Cartesian Tensor basis using a parametrization that explicitly enforces the positive definite property to the computed ODF. The computed Cartesian Tensors, dubbed Cartesian Tensor-ODF (CT-ODF), are symmetric positive definite Tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Furthermore, we show how to use our method for converting higher-order diffusion Tensors to CT-ODFs, which is an essential task since the maxima of higher-order Tensors do not correspond to the underlying fiber orientations. We quantitatively evaluate our method using simulated DW-MR images as well as a real brain dataset from a post-mortem porcine brain. The results conclusively demonstrate the superiority of the proposed technique over several existing multifiber reconstruction methods.
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MICCAI (1) - Symmetric positive-definite Cartesian Tensor orientation distribution functions (CT-ODF)
Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Inte, 2010Co-Authors: Yonas T Weldeselassie, Angelos Barmpoutis, M. Stella AtkinsAbstract:A novel method for estimating a field of orientation distribution functions (ODF) from a given set of DW-MR images is presented. We model the ODF by Cartesian Tensor basis using a parametrization that explicitly enforces the positive definite property to the computed ODF. The computed Cartesian Tensors, dubbed Cartesian Tensor-ODF (CT-ODF), are symmetric positive definite Tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Furthermore, we show how to use our method for converting higher-order diffusion Tensors to CT-ODFs, which is an essential task since the maxima of higher-order Tensors do not correspond to the underlying fiber orientations. We quantitatively evaluate our method using simulated DW-MR images as well as a real brain dataset from a post-mortem porcine brain. The results conclusively demonstrate the superiority of the proposed technique over several existing multifiber reconstruction methods.
Stella M Atkins - One of the best experts on this subject based on the ideXlab platform.
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symmetric positive semi definite Cartesian Tensor fiber orientation distributions ct fod
Medical Image Analysis, 2012Co-Authors: Yonas T Weldeselassie, Angelos Barmpoutis, Stella M AtkinsAbstract:A novel method for estimating a field of fiber orientation distribution (FOD) based on signal de-convolution from a given set of diffusion weighted magnetic resonance (DW-MR) images is presented. We model the FOD by higher order Cartesian Tensor basis using a parametrization that explicitly enforces the positive semi-definite property to the computed FOD. The computed Cartesian Tensors, dubbed Cartesian TensorFOD (CT-FOD), are symmetric positive semi-definite Tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Next, we show how to use our method for converting higher-order diffusion Tensors to CT-FODs, which is an essential task since the maxima of higher-order Tensors do not correspond to the underlying fiber orientations. Finally, we propose a diffusion anisotropy index computed directly from CT-FODs using higher order Tensor distance measures thus consolidating the whole analysis pipeline of diffusion imaging solely using CT-FODs. We evaluate our method qualitatively and quantitatively using simulated DW-MR images, phantom images, and human brain real dataset. The results conclusively demonstrate the superiority of the proposed technique over several existing multi-fiber reconstruction methods.
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symmetric positive definite Cartesian Tensor orientation distribution functions ct odf
Medical Image Computing and Computer-Assisted Intervention, 2010Co-Authors: Yonas T Weldeselassie, Angelos Barmpoutis, Stella M AtkinsAbstract:A novel method for estimating a field of orientation distribution functions (ODF) from a given set of DW-MR images is presented. We model the ODF by Cartesian Tensor basis using a parametrization that explicitly enforces the positive definite property to the computed ODF. The computed Cartesian Tensors, dubbed Cartesian Tensor-ODF (CT-ODF), are symmetric positive definite Tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Furthermore, we show how to use our method for converting higher-order diffusion Tensors to CT-ODFs, which is an essential task since the maxima of higher-order Tensors do not correspond to the underlying fiber orientations. We quantitatively evaluate our method using simulated DW-MR images as well as a real brain dataset from a post-mortem porcine brain. The results conclusively demonstrate the superiority of the proposed technique over several existing multifiber reconstruction methods.
Dennis G Mcgavin - One of the best experts on this subject based on the ideXlab platform.
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higher order zeeman and spin terms in the electron paramagnetic resonance spin hamiltonian their description in irreducible form using Cartesian tesseral spherical Tensor and stevens operator expressions
Journal of Physics: Condensed Matter, 2009Co-Authors: Dennis G Mcgavin, Craighead W TennantAbstract:In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical Tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian Tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS3 and BS5. Starting from the well-known decomposition of the general Cartesian Tensor of second rank to three irreducible Tensors of ranks 0, 1 and 2, the decomposition of Cartesian Tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical Tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.
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Higher-order Zeeman and spin terms in the electron paramagnetic resonance spin Hamiltonian; their description in irreducible form using Cartesian, tesseral spherical Tensor and Stevens' operator expressions
Journal of Physics: Condensed Matter, 2009Co-Authors: Dennis G Mcgavin, W. Craighead TennantAbstract:In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical Tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian Tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS(3) and BS(5). Starting from the well-known decomposition of the general Cartesian Tensor of second rank to three irreducible Tensors of ranks 0, 1 and 2, the decomposition of Cartesian Tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical Tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, [Formula: see text] Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.
Angelos Barmpoutis - One of the best experts on this subject based on the ideXlab platform.
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symmetric positive semi definite Cartesian Tensor fiber orientation distributions ct fod
Medical Image Analysis, 2012Co-Authors: Yonas T Weldeselassie, Angelos Barmpoutis, Stella M AtkinsAbstract:A novel method for estimating a field of fiber orientation distribution (FOD) based on signal de-convolution from a given set of diffusion weighted magnetic resonance (DW-MR) images is presented. We model the FOD by higher order Cartesian Tensor basis using a parametrization that explicitly enforces the positive semi-definite property to the computed FOD. The computed Cartesian Tensors, dubbed Cartesian TensorFOD (CT-FOD), are symmetric positive semi-definite Tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Next, we show how to use our method for converting higher-order diffusion Tensors to CT-FODs, which is an essential task since the maxima of higher-order Tensors do not correspond to the underlying fiber orientations. Finally, we propose a diffusion anisotropy index computed directly from CT-FODs using higher order Tensor distance measures thus consolidating the whole analysis pipeline of diffusion imaging solely using CT-FODs. We evaluate our method qualitatively and quantitatively using simulated DW-MR images, phantom images, and human brain real dataset. The results conclusively demonstrate the superiority of the proposed technique over several existing multi-fiber reconstruction methods.
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symmetric positive definite Cartesian Tensor orientation distribution functions ct odf
Medical Image Computing and Computer-Assisted Intervention, 2010Co-Authors: Yonas T Weldeselassie, Angelos Barmpoutis, Stella M AtkinsAbstract:A novel method for estimating a field of orientation distribution functions (ODF) from a given set of DW-MR images is presented. We model the ODF by Cartesian Tensor basis using a parametrization that explicitly enforces the positive definite property to the computed ODF. The computed Cartesian Tensors, dubbed Cartesian Tensor-ODF (CT-ODF), are symmetric positive definite Tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Furthermore, we show how to use our method for converting higher-order diffusion Tensors to CT-ODFs, which is an essential task since the maxima of higher-order Tensors do not correspond to the underlying fiber orientations. We quantitatively evaluate our method using simulated DW-MR images as well as a real brain dataset from a post-mortem porcine brain. The results conclusively demonstrate the superiority of the proposed technique over several existing multifiber reconstruction methods.
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MICCAI (1) - Symmetric positive-definite Cartesian Tensor orientation distribution functions (CT-ODF)
Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Inte, 2010Co-Authors: Yonas T Weldeselassie, Angelos Barmpoutis, M. Stella AtkinsAbstract:A novel method for estimating a field of orientation distribution functions (ODF) from a given set of DW-MR images is presented. We model the ODF by Cartesian Tensor basis using a parametrization that explicitly enforces the positive definite property to the computed ODF. The computed Cartesian Tensors, dubbed Cartesian Tensor-ODF (CT-ODF), are symmetric positive definite Tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Furthermore, we show how to use our method for converting higher-order diffusion Tensors to CT-ODFs, which is an essential task since the maxima of higher-order Tensors do not correspond to the underlying fiber orientations. We quantitatively evaluate our method using simulated DW-MR images as well as a real brain dataset from a post-mortem porcine brain. The results conclusively demonstrate the superiority of the proposed technique over several existing multifiber reconstruction methods.