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K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging

Artikel i vetenskaplig tidskrift
Författare Mohammad Alipoor
Irene Y.H. Gu
Andrew Mehnert
Stephan E Maier
Göran Starck
Publicerad i Biomed Research International
Sidor Article ID 760230
ISSN 2314-6133
Publiceringsår 2015
Publicerad vid Institutionen för kliniska vetenskaper, Avdelningen för radiofysik
Institutionen för kliniska vetenskaper, Avdelningen för radiologi
Sidor Article ID 760230
Språk en
Länkar dx.doi.org/10.1155/2015/760230
https://gup.ub.gu.se/file/173235
Ämnesord condition number, acquisition schemes, mri, directions, anisotropy, design, Biotechnology & Applied Microbiology, Research & Experimental Medicine
Ämneskategorier Medicinsk bioteknologi

Sammanfattning

The design of an optimal gradient encoding scheme (GES) is a fundamental problem in diffusion MRI. It is well studied for the case of second-order tensor imaging (Gaussian diffusion). However, it has not been investigated for the wide range of non-Gaussian diffusion models. The optimal GES is the one that minimizes the variance of the 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 convex relaxation, we reformulate it as a tractable semidefinite programming problem. Solving this problem leads to several theoretical properties of K-optimal design: (i) the odd moments of the K-optimal design must be zero; (ii) the even moments of the K-optimal design are proportional to the total number of measurements; (iii) the K-optimal design is not unique, in general; and (iv) the proposed method can be used to compute the K-optimal design for an arbitrary number of measurements. Our Monte Carlo simulations support the theoretical results and show that, in comparison with existing designs, the K-optimal design leads to the minimum signal deviation.

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