A Mixed Precision FFT with applications in MRI

TL;DR

This paper introduces a mixed precision FFT method optimized for MRI applications, demonstrating how precision and block size choices impact image quality and numerical accuracy.

Contribution

It presents a novel mixed precision FFT approach with per-block microscaling and prequantized twiddles, improving efficiency for MRI data processing.

Findings

Mantissa precision limits FFT fidelity under MX scaling

Larger block sizes improve numerical performance

Weak dependence of image size on FFT quality

Abstract

A mixed precision Fast Fourier transform (FFT) implementation is presented. The procedure uses per-block microscaling (MX), a global power-of-two prescale, and prequantized low bit twiddles. We evaluate forward and round-trip FFT fidelity on two public MRI datasets and compare the effect of various low precision formats, image sizes, and MX block sizes on image quality. Results show that mantissa precision is the primary limiter under MX scaling while ablations suggest weak dependence on image size but a clear block-size trade-off with larger block sizes resulting in better numerical performance.