NUFFT module for PyTorch

Introduction

There is no built-in NUFFT function in PyTorch, neither is Toeplitz MSE loss module, which is important for non-Cartesian MRI reconstruction works. To fill this gap, this package provides:

1. A high performance NUFFT torch.nn module wrapping cufinufft [3] and finufft [1,2] - they are the fastest NUFFT backends to the best of my knowledge.
2. Another elegant MSE loss (mean square of l2 loss) module for non-Cartesian reconstruction with DCF preconditioning boosted by Toeplitz operator. Basically, this is done by replacing the two-pass NUFFTs with a Cartesian fast Fourier convolution. This method is also fast but slightly slower than cufinufft in practice. Use as you need.

Both CPU and GPU are supported. Benchmark indicates a 2ms (NUFFT module) or a 3ms (Toeplitz MSE loss module) time cost per iteration in a 256×256 inverse NUFFT problem using a RTX3090 GPU.

Install

For offline installing:

$ bash install.bash

To install with pip:

$ pip install torchfinufft-ryan

Optionally, to enable CUDA computation, cufinufft>=2.5.0 has to be installed. To solve for the density compensation function, I recommend my mrarbdcf package [4].

Usage

Please refer to the exmaple folder - there are minimal example(s) for tutorial.

References

[1] Barnett AH. Aliasing error of the kerne exp(β√(1-z²)) in the nonuniform fast Fourier transform. Applied and Computational Harmonic Analysis. 2021 Mar 1;51:1–16.

[2] Barnett AH, Magland J, af Klinteberg L. A Parallel Nonuniform Fast Fourier Transform Library Based on an “Exponential of Semicircle" Kernel. SIAM J Sci Comput. 2019 Jan;41(5):C479–504.

[3] Shih Y hsuan, Wright G, Anden J, Blaschke J, Barnett AH. cuFINUFFT: a load-balanced GPU library for general-purpose nonuniform FFTs. 2021 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW). 2021 June;688–97.

[4] Luo R, Hu P, Qi H. Sampling Density Compensation using Fast Fourier Deconvolution. In: Proceedings of the Cape Town - 2026 ISMRM-ISMRT Annual Meeting and Exhibition, Cape Town, South Africa. Program #461-03-015.