K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging
Artikel i vetenskaplig tidskrift, 2015

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.



condition number

Biotechnology & Applied Microbiology


Research & Experimental Medicine


acquisition schemes


Mohammad Alipoor

Chalmers, Signaler och system, Signalbehandling och medicinsk teknik

Irene Yu-Hua Gu

Chalmers, Signaler och system, Signalbehandling och medicinsk teknik

Andrew Mehnert

University of Western Australia

Stephan E Maier

Göteborgs universitet

Göran Starck

Göteborgs universitet

BioMed Research International

2314-6133 (ISSN) 2314-6141 (eISSN)

Vol. 2015 Article ID 760230- 760230



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