Python Non-Uniform Fast Fourier Transform (PyNUFFT): multi-dimensional non-Cartesian image reconstruction package for heterogeneous platforms and applications to MRI

This paper reports the development of a Python Non-Uniform Fast Fourier Transform (PyNUFFT) package, which accelerates non-Cartesian image reconstruction on heterogeneous platforms. Scientific computing with Python encompasses a mature and integrated environment. The NUFFT algorithm has been extensively used for non-Cartesian image reconstruction but previously there was no native Python NUFFT library. The current PyNUFFT software enables multi-dimensional NUFFT on heterogeneous platforms. The PyNUFFT also provides several solvers, including the conjugate gradient method, $\ell$1 total-variation regularized ordinary least square (L1TV-OLS) and $\ell$1 total-variation regularized least absolute deviation (L1TV-LAD). Metaprogramming libraries were employed to accelerate PyNUFFT. The PyNUFFT package has been tested on multi-core CPU and GPU, with acceleration factors of 6.3 - 9.5$\times$ on a 32 thread CPU platform and 5.4 - 13$\times$ on the GPU.