Sparse and Optimal Acquisition Design for Diffusion MRI and Beyond

The focus of this paper is on the development of a sparse and optimal acquisition (SOA) design for diffusion MRI multiple-shell acquisition and beyond. A novel optimality criterion is proposed for sparse multiple-shell acquisition and quasi multiple-shell designs in diffusion MRI and a novel and effective semi-stochastic and moderately greedy combinatorial search strategy with simulated annealing to locate the optimum design or configuration. Even though the number of distinct configurations for a given set of diffusion gradient directions is very large in general---e.g., in the order of 10^{232} for a set of 144 diffusion gradient directions, the proposed search strategy was found to be effective in finding the optimum configuration. It was found that the square design is the most robust (i.e., with stable condition numbers and A-optimal measures under varying experimental conditions) among many other possible designs of the same sample size. Under the same performance evaluation, the square design was found to be more robust than the widely used sampling schemes similar to that of 3D radial MRI and of diffusion spectrum imaging (DSI).