A 4D Basis and Sampling Scheme for the Tensor Encoded Multi-Dimensional Diffusion MRI Signal

Abstract

We propose a 4-dimensional (4D) basis and sampling scheme, along with a corresponding reconstruction algorithm, for the measurement and reconstruction of the $\mathbf {b}$ -tensor encoded diffusion signal in diffusion magnetic resonance imaging (MRI). This is only the second basis proposed for representing the $\mathbf {b}$ -tensor encoded diffusion signal and the first to allow for planar tensor measurements. We design a sampling scheme that attains an efficient number of samples, equal to the degrees of freedom required to represent the diffusion signal in the proposed 4D basis. The properties of the diffusion signal are studied to provide recommendations on how many $\mathbf {b}$ -tensor measurements to use. Evaluation of the proposed scheme using Monte Carlo simulations of the diffusion signal is done to show that the proposed scheme gives accurate interpolation of the signal.