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

Mohammad Alipoor (Institutionen för signaler och system, Signalbehandling) ; Irene Y.H. Gu (Institutionen för signaler och system, Signalbehandling) ; Andrew Mehnert ; Stephan E Maier ; Göran Starck
Biomed Research International (2314-6133). p. Article ID 760230. (2015)
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: condition number, acquisition schemes, mri, directions, anisotropy, design, Biotechnology & Applied Microbiology, Research & Experimental Medicine



Denna post skapades 2015-10-27. Senast ändrad 2015-12-03.
CPL Pubid: 224870

 

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Institutioner (Chalmers)

Institutionen för signaler och system, Signalbehandling (1900-2017)
Institutionen för kliniska vetenskaper, sektionen för onkologi, radiofysik, radiologi och urologi (GU)
Institutionen för kliniska vetenskaper, sektionen för onkologi, radiofysik, radiologi och urologi, Avdelningen för radiofysik (GU)

Ämnesområden

Medicinsk bioteknologi

Chalmers infrastruktur