K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging. (14th September 2015)

• Record Type: Journal Article
• Authors: Alipoor, Mohammad; Gu, Irene Yu-Hua; Mehnert, Andrew; Maier, Stephan E.; Starck, Göran
• Other Names: Murgia Sergio Academic Editor.
• Is Part Of: BioMed research international. Volume 2015(2015)
• Publication Date: 2015-09-14
• Subjects: Medicine -- Periodicals; Biology -- Periodicals; Biotechnology -- Periodicals; Life sciences -- Periodicals; 610.5
• DOI: 10.1155/2015/760230
• Languages: English
• ISSNs: 2314-6133

Abstract

Abstract : 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.