title: K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging.
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.
authors.affiliation: Department of Signals and Systems, Chalmers University of Technology, 41296 Gothenburg, Sweden.
authors.forename: Mohammad
authors.initials: M
authors.lastname: Alipoor
authors.affiliation: Department of Signals and Systems, Chalmers University of Technology, 41296 Gothenburg, Sweden.
authors.forename: Irene Yu-Hua
authors.initials: IY
authors.lastname: Gu
authors.affiliation: Centre for Microscopy, Characterisation and Analysis, The University of Western Australia, Perth, WA 6009, Australia.
authors.forename: Andrew
authors.initials: A
authors.lastname: Mehnert
authors.affiliation: Department of Radiology, Sahlgrenska University Hospital, Gothenburg University, 41345 Gothenburg, Sweden.
authors.forename: Stephan E
authors.initials: SE
authors.lastname: Maier
authors.affiliation: Department of Radiation Physics, Institute of Clinical Sciences, University of Gothenburg, 41345 Gothenburg, Sweden ; Department of Medical Physics and Biomedical Engineering, Sahlgrenska University Hospital, 41345 Gothenburg, Sweden.
authors.forename: Göran
authors.initials: G
authors.lastname: Starck
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D015233:Models, Statistical; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity