# Polar Fourier transform in practice: its efficiency and characteristics in reconstructing radially acquired MRI images

## TL;DR

This paper shows that the Polar Fourier Transform can efficiently reconstruct MRI images from radial scans while preserving image quality in central regions.

## Contribution

The study demonstrates the practical implementation and performance of Polar Fourier Transform for radial MRI reconstruction in a clinical setting.

## Key findings

- PFT was successfully implemented with a runtime of ~6–9× acquisition time.
- PFT preserved image quality in central regions under high acceleration.
- PFT reduced structured streaks and gradient delay artifacts compared to gridding.

## Abstract

The Polar Fourier Transform (PFT) has been proposed as a direct alternative to gridding for reconstructing radially acquired MRI data. This study evaluates the feasibility of inline PFT implementation on a clinical MRI scanner and assesses its computational performance and image quality under acceleration.

PFT was implemented as modular components within the Siemens Image Calculation Environment, using a recursive numerical Hankel transform. Phantom and in vivo brain datasets acquired with 2D radial trajectories were reconstructed using both PFT and vendor-supplied gridding. Reconstruction time, SNR, artifact behavior, and spatial resolution were assessed across multiple undersampling levels (up to 8 ×), using simulations and repeated scans.

PFT was successfully integrated with a runtime of ~ 6–9 × acquisition time. It exhibited spatially variant behavior, concentrating resolution in central region while shifting undersampling-induced blurring outward. Compared to gridding, PFT reduced structured streaks and better preserved image quality under acceleration. Gradient delay artifacts were reduced by alternating spoke polarity. Notably, the pituitary gland and basilar artery remained visible at high acceleration, highlighting preserved central fidelity.

PFT enables effective inline reconstruction for radial MRI and preserves image quality in small central regions of interest under aggressive undersampling—supporting dynamic and ROI-focused applications.