A PARALLEL NONUNIFORM FAST FOURIER TRANSFORM LIBRARY BASED ON AN 'EXPONENTIAL OF SEMICIRCLE' KERNEL

摘要

The nonuniform fast Fourier transform (NUFFT) generalizes the FFT to off-grid data. Its many applications include image reconstruction, data analysis, and the numerical solution of differential equations. We present FINUFFT, an efficient parallel library for type 1 (nonuniform to uniform), type 2 (uniform to nonuniform), or type 3 (nonuniform to nonuniform) transforms, in dimensions 1, 2, or 3. It uses minimal RAM, requires no precomputation or plan steps, and has a simple interface to several languages. We perform the expensive spreading/interpolation between nonuniform points and the fine grid via a simple new kernel-the "exponential of semicircle" e(beta root 1-x2) in x is an element of [-1, 1]-in a cache-aware load-balanced multithreaded implementation. The deconvolution step requires the Fourier transform of the kernel, for which we propose efficient numerical quadrature. For types 1 and 2, rigorous error bounds asymptotic in the kernel width approach the fastest known exponential rate, namely that of the Kaiser-Bessel kernel. We benchmark against several popular CPU-based libraries, showing favorable speed and memory footprint, especially in three dimensions when high accuracy and/or clustered point distributions are desired.