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

## TL;DR

This paper introduces a multi-shell sampling scheme and precise transforms for diffusion MRI, enabling accurate reconstruction of diffusion signals with optimal sampling and near-perfect angular accuracy.

## Contribution

It presents a novel multi-shell sampling grid and exact spherical polar Fourier transforms for improved diffusion MRI signal reconstruction.

## Key findings

- Transform is exact radially and highly accurate angularly
- Sampling scheme uses minimal samples matching degrees of freedom
- Achieves near machine precision in angular reconstruction

## Abstract

We propose a multi-shell sampling grid and develop corresponding transforms for the accurate reconstruction of the diffusion signal in diffusion MRI by expansion in the spherical polar Fourier (SPF) basis. The transform is exact in the radial direction and accurate, on the order of machine precision, in the angular direction. The sampling scheme uses an optimal number of samples equal to the degrees of freedom of the diffusion signal in the SPF domain.