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

Abstract EN

The design of an optimal gradient encoding scheme (GES) is a fundamental problem in diffusion MRI.

It iswell studied for the case of second-order tensor imaging (Gaussian diffusion).

However, it has not been investigatedfor the wide range of non-Gaussian diffusion models.

The optimal GES is the one that minimizes the variance ofthe 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 convexrelaxation, we reformulate it as a tractable semidefinite programming problem.

Solving this problem leads to severaltheoretical properties of K-optimal design: (i) the odd moments of the K-optimal design must be zero; (ii) the evenmoments of the K-optimal design are proportional to the total number of measurements; (iii) the K-optimal design isnot unique, in general; and (iv) the proposed method can be used to compute the K-optimal design for an arbitrarynumber of measurements.

Our Monte Carlo simulations support the theoretical results and show that, in comparisonwith existing designs, the K-optimal design leads to the minimum signal deviation.