A High-dimensional Sparse Fourier Transform in the Continuous Setting

TL;DR

This paper introduces a novel polynomial-time algorithm for high-dimensional sparse Fourier transform in the continuous setting, effectively addressing the curse of dimensionality in frequency recovery.

Contribution

It proposes a new hashing scheme that enables the first efficient polynomial-time recovery of high-dimensional continuous frequencies.

Findings

Overcomes the curse of dimensionality in Fourier analysis

First polynomial-time algorithm for high-dimensional continuous frequency recovery

Theoretical analysis confirms algorithm efficiency

Abstract

In this paper, we theoretically propose a new hashing scheme to establish the sparse Fourier transform in high-dimensional space. The estimation of the algorithm complexity shows that this sparse Fourier transform can overcome the curse of dimensionality. To the best of our knowledge, this is the first polynomial-time algorithm to recover the high-dimensional continuous frequencies.