Magnetic Resonance Arbitrary Density Compensation Function (MRArbDcf, MAD)

Introduction

This is the code repository for paper "Sampling Density Compensation using Fast Fourier Deconvolution" [1]. To fill the gap that the previous iterative DCF methods are slow (especially in 3D), this package provides a non-iterative method based on fast Fourier deconvolution. This package supports both CPU and GPU and can derive DCF for a trajectory designed for a 256³ matrix size in 20 seconds on a multi-core CPU or 10 seconds on a GPU.

Installation

You can install this package either via pip:

$ pip install mrarbdcf

or offline

$ bash install.bash

Optionally, to enable CUDA acceleration in this package, you need to install cufinufft and cupy. It's recommended to read their official installation guides before installing - pip is not the best source for installation because some dependencies are only available from conda.

Usage

For tutorials, you can find examples in the example folder. Most functions are well-commented in the Google style. We plan to release the documents on readthedocs.org in the future.

Acknowledgement

FINUFFT [2,3] and CUFINUFFT [4] are used as NUFFT operators in this package. We thank the authors for their contributions to create such fast NUFFT libraries.

Reference

[1] Luo R, Hu P, Qi H. Sampling Density Compensation using Fast Fourier Deconvolution [Internet]. arXiv; 2025 [cited 2025 Oct 17]. Available from: http://arxiv.org/abs/2510.14873

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

[4] 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.