K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging
Joint Authors
Alipoor, Mohammad
Maier, Stephan E.
Gu, Irene Yu-Hua
Mehnert, Andrew
Starck, Göran
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-09-14
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
The design of an optimal gradient encoding scheme (GES) is a fundamental problem in diffusion MRI.
It iswell studied for the case of second-order tensor imaging (Gaussian diffusion).
However, it has not been investigatedfor the wide range of non-Gaussian diffusion models.
The optimal GES is the one that minimizes the variance ofthe estimated parameters.
Such a GES can be realized by minimizing the condition number of the design matrix(K-optimal design).
In this paper, we propose a new approach to solve the K-optimal GES design problem for fourth-order tensor-based diffusion profile imaging.
The problem is a nonconvex experiment design problem.
Using convexrelaxation, we reformulate it as a tractable semidefinite programming problem.
Solving this problem leads to severaltheoretical properties of K-optimal design: (i) the odd moments of the K-optimal design must be zero; (ii) the evenmoments of the K-optimal design are proportional to the total number of measurements; (iii) the K-optimal design isnot unique, in general; and (iv) the proposed method can be used to compute the K-optimal design for an arbitrarynumber of measurements.
Our Monte Carlo simulations support the theoretical results and show that, in comparisonwith existing designs, the K-optimal design leads to the minimum signal deviation.
American Psychological Association (APA)
Alipoor, Mohammad& Gu, Irene Yu-Hua& Mehnert, Andrew& Maier, Stephan E.& Starck, Göran. 2015. K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging. BioMed Research International،Vol. 2015, no. 2015, pp.1-10.
https://search.emarefa.net/detail/BIM-1056655
Modern Language Association (MLA)
Alipoor, Mohammad…[et al.]. K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging. BioMed Research International No. 2015 (2015), pp.1-10.
https://search.emarefa.net/detail/BIM-1056655
American Medical Association (AMA)
Alipoor, Mohammad& Gu, Irene Yu-Hua& Mehnert, Andrew& Maier, Stephan E.& Starck, Göran. K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging. BioMed Research International. 2015. Vol. 2015, no. 2015, pp.1-10.
https://search.emarefa.net/detail/BIM-1056655
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1056655