# An Optimal Dimensionality Multi-shell Sampling Scheme with Accurate and Efficient Transforms for Diffusion MRI

## TL;DR

This paper introduces an optimal multi-shell sampling scheme for diffusion MRI that enables accurate, efficient signal reconstruction with improved angular discrimination and rotational invariance compared to existing methods.

## Contribution

It presents a novel sampling scheme aligned with the SPF basis, optimizing sample number for precise diffusion signal reconstruction in MRI.

## Key findings

- Greater reconstruction accuracy than gEEM schemes
- Enhanced angular discrimination in diffusion signal
- Improved rotational invariance of reconstruction

## Abstract

This paper proposes a multi-shell sampling scheme and corresponding transforms for the accurate reconstruction of the diffusion signal in diffusion MRI by expansion in the spherical polar Fourier (SPF) basis. The sampling scheme uses an optimal number of samples, equal to the degrees of freedom of the band-limited diffusion signal in the SPF domain, and allows for computationally efficient reconstruction. We use synthetic data sets to demonstrate that the proposed scheme allows for greater reconstruction accuracy of the diffusion signal than the multi-shell sampling schemes obtained using the generalised electrostatic energy minimisation (gEEM) method used in the Human Connectome Project. We also demonstrate that the proposed sampling scheme allows for increased angular discrimination and improved rotational invariance of reconstruction accuracy than the gEEM schemes.