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A Mixed Precision FFT with applications in MRI

Nikhil Deveshwar, Abhejit Rajagopal, Peder E. Z. Larson

TL;DR

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.

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.

A Mixed Precision FFT with applications in MRI

TL;DR

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.

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.

Paper Structure

This paper contains 11 sections, 1 equation, 4 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methods
  3. Global Prescale
  4. MX-scaled Complex Butterfly Operations
  5. Evaluation
  6. Results
  7. Discussion
  8. Mantissa limits accuracy under MX
  9. Block size trade-offs
  10. MRI evaluation
  11. Conclusion

Figures (4)

  • Figure 1: A: Forward/Round-trip FFT for MRI, B: Butterfly Operations, C: Floating point formats; E=exponent, M=mantissa bits
  • Figure 2: Forward MXFFT in low precision MX variants
  • Figure 3: Round-trip MXFFT for both FP8 variants for both datasets
  • Figure 4: A) Forward FP16 and MXFFT performance across formats. B) Round-trip FP16 and MXFFT quality across formats. Error bars show mean±std over 10 images. MXFFT suffers from higher quantization noise compared to FP16.