A note on the high-dimensional sparse Fourier transform in the continuous setting*Supported in part by National Natural Science Foundation of China under Grant 11971490, and by Natural Science Foundation of Guangdong Province under Grant 2018A030313841. (1st March 2022) - Chen, Liang
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.