FFCz: Fast Fourier Correction for Spectrum-Preserving Lossy Compression of Scientific Data

2026-01-04

arXiv.org

AI Summary

This work addresses the limitation of existing lossy compression methods, which typically prioritize spatial-domain accuracy while failing to preserve spectral fidelity—critical for scientific applications such as cosmology and turbulent combustion. The authors propose a fast Fourier correction algorithm that, for the first time, establishes a joint spatial–spectral error constraint model built upon outputs from compressors like SZ3 and ZFP. By iteratively projecting reconstruction errors into the intersection of allowable error bounds in both domains and leveraging GPU acceleration, the method achieves efficient dual-domain fidelity preservation. Experiments demonstrate that the approach significantly retains essential spatial structures and spectral characteristics across diverse datasets, including cosmological simulations, X-ray diffraction data, combustion models, and electroencephalography signals, thereby balancing high accuracy with practical usability.

Technology Category

• Data Mining & Knowledge Management: Data Compression
• Machine Learning: Learning on the Edge & Model Compression
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Security and Privacy: Large-scale security measurements

Abstract

This paper introduces a novel technique to preserve spectral features in lossy compression based on a novel fast Fourier correction algorithm\added{ for regular-grid data}. Preserving both spatial and frequency representations of data is crucial for applications such as cosmology, turbulent combustion, and X-ray diffraction, where spatial and frequency views provide complementary scientific insights. In particular, many analysis tasks rely on frequency-domain representations to capture key features, including the power spectrum of cosmology simulations, the turbulent energy spectrum in combustion, and diffraction patterns in reciprocal space for ptychography. However, existing compression methods guarantee accuracy only in the spatial domain while disregarding the frequency domain. To address this limitation, we propose an algorithm that corrects the errors produced by off-the-shelf ``base''compressors such as SZ3, ZFP, and SPERR, thereby preserving both spatial and frequency representations by bounding errors in both domains. By expressing frequency-domain errors as linear combinations of spatial-domain errors, we derive a region that jointly bounds errors in both domains. Given as input the spatial errors from a base compressor and user-defined error bounds in the spatial and frequency domains, we iteratively project the spatial error vector onto the regions defined by the spatial and frequency constraints until it lies within their intersection. We further accelerate the algorithm using GPU parallelism to achieve practical performance. We validate our approach with datasets from cosmology simulations, X-ray diffraction, combustion simulation, and electroencephalography demonstrating its effectiveness in preserving critical scientific information in both spatial and frequency domains.

Problem

• lossy compression
• spectral preservation
• frequency domain
• scientific data
• error bounding

Innovation

• spectrum-preserving compression
• Fourier-domain error correction
• dual-domain error bounding
• lossy scientific data compression
• GPU-accelerated projection