# PyNUFFT: Python non-uniform fast Fourier transform
![](g5738.jpeg)


A minimal "getting start" tutorial is available at http://jyhmiinlin.github.io/pynufft/ . This package reimplements the min-max interpolator (Fessler, Jeffrey A., and Bradley P. Sutton. "Nonuniform fast Fourier transforms using min-max interpolation." IEEE transactions on signal processing 51.2 (2003): 560-574.) for Python.


### Latest work

Please cite our latest work:

Chen HC, Yang HC, Chen CC, Harrevelt S, Chao YC, Lin JM, Yu WH, Chang HC, Chang CK, Hwang FN. 
Improved Image Quality for Static BLADE Magnetic Resonance Imaging Using the Total-Variation Regularized Least Absolute Deviation Solver. 
Tomography. 2021 Oct 8;7(4):555-572. doi: 10.3390/tomography7040048. PMID: 34698286; PMCID: PMC8544655.
(https://pubmed.ncbi.nlm.nih.gov/34698286/) (We used pynufft to perform BLADE MRI reconstruction. No singularity in the coil sensitivity profiles)

![](nosingularity.png)


### Some recent research works using PyNUFFT (Thank you!)

https://iopscience.iop.org/article/10.1088/1361-6560/ab9358/meta (deep learning)

https://arxiv.org/abs/2103.09203 (deep learning)

https://aapm.onlinelibrary.wiley.com/doi/10.1002/mp.14809 (deep learning)

https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8579232 (deep learning)

https://joss.theoj.org/papers/10.21105/joss.02825 (gravitational lens)

https://pubmed.ncbi.nlm.nih.gov/33906008/ (tomographic imaging)

https://joss.theoj.org/papers/10.21105/joss.02578 (Off-resonance CorrecTion OPen soUrce Software)

Please remind us if there are other publications.

### Recent NUFFT functions available in Python

You can also find other very useful Python nufft/nfft functions at: 

1. SigPy (Ong, F., and M. Lustig. "SigPy: a python package for high performance iterative reconstruction." Proceedings of the ISMRM 27th Annual Meeting, Montreal, Quebec, Canada. Vol. 4819. 2019. Note the order starts from the last axis), https://sigpy.readthedocs.io/en/latest/generated/sigpy.nufft.html?highlight=nufft
2. gpuNUFFT: (Knoll, Florian, et al. "gpuNUFFT-an open source GPU library for 3D regridding with direct Matlab interface." Proceedings of the 22nd annual meeting of ISMRM, Milan, Italy. 2014.): https://github.com/andyschwarzl/gpuNUFFT/tree/master/python
3. mrrt.nufft (mrrt.mri demos for the ISMRM 2020 Data Sampling Workshop in Sedona, AZ with raw cuda kernels): https://github.com/mritools/mrrt.nufft
4. pyNFFT (Keiner, J., Kunis, S., and Potts, D. ''Using NFFT 3 - a software library for various nonequispaced fast Fourier transforms'' ACM Trans. Math. Software,36, Article 19, 1-30, 2009. The python wrapper of NFFT): https://pythonhosted.org/pyNFFT/tutorial.html
5. python-NUFFT: Please see: https://github.com/dfm/python-nufft, "Python bindings by Dan Foreman-Mackey, Thomas Arildsen, and Marc T. Henry de Frahan but the code that actually does the work is from the Greengard lab at NYU (see the website). " 
6. finufft (Barnett, Alexander H., Jeremy Magland, and Ludvig af Klinteberg. "A Parallel Nonuniform Fast Fourier Transform Library Based on an “Exponential of Semicircle" Kernel." SIAM Journal on Scientific Computing 41.5 (2019): C479-C504., exponential semicircle kernel): https://finufft.readthedocs.io/en/latest/python.html. Recently providing a new cuda implementation with the python wrapper. 
7. torchkbnufft (M. J. Muckley, R. Stern, T. Murrell, F. Knoll, TorchKbNufft: A High-Level, Hardware-Agnostic Non-Uniform Fast Fourier Transform, 2020 ISMRM Workshop on Data Sampling and Image Reconstruction): https://github.com/mmuckley/torchkbnufft
8. tfkbnufft (adapt torchkbnufft for TensorFlow): https://github.com/zaccharieramzi/tfkbnufft
9. TFNUFFT (adapt the min-max interpolator in PyNUFFT for tensorflow): https://github.com/yf0726/TFNUFFT
10. tensorflow-nufft: https://github.com/mrphys/tensorflow-nufft

## Installation

$ pip3 install pynufft --user


### Using Numpy/Scipy

```
$ python
Python 3.6.11 (default, Aug 23 2020, 18:05:39) 
[GCC 7.5.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> from pynufft import NUFFT
>>> import numpy
>>> A = NUFFT()
>>> om = numpy.random.randn(10,2)
>>> Nd = (64,64)
>>> Kd = (128,128)
>>> Jd = (6,6)
>>> A.plan(om, Nd, Kd, Jd)
0
>>> x=numpy.random.randn(*Nd)
>>> y = A.forward(x)
```

### Using PyCUDA

```
>>> from pynufft import NUFFT, helper
>>> import numpy
>>> A2= NUFFT(helper.device_list()[0])
>>> A2.device
<reikna.cluda.cuda.Device object at 0x7f9ad99923b0>
>>> om = numpy.random.randn(10,2)
>>> Nd = (64,64)
>>> Kd = (128,128)
>>> Jd = (6,6)
>>> A2.plan(om, Nd, Kd, Jd)
0
>>> x=numpy.random.randn(*Nd)
>>> y = A2.forward(x)
```

### Using NUDFT (double precision)

Some users ask for double precision. 
NUDFT is offered.

```
>>> from pynufft import  NUDFT
>>> import numpy
>>> x=numpy.random.randn(*Nd)
>>> om = numpy.random.randn(10,2)
>>> Nd = (64,64)
>>> A = NUDFT()
>>> A.plan(om, Nd)
>>> y_cpu = A.forward(x)

```


## Testing GPU acceleration

```
Python 3.6.11 (default, Aug 23 2020, 18:05:39) 
[GCC 7.5.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> from pynufft import tests
>>> tests.test_init(0)
device name =  <reikna.cluda.cuda.Device object at 0x7f41d4098688>
0.06576069355010987
0.006289639472961426
error gx2= 2.0638987e-07
error gy= 1.0912560261408778e-07
acceleration= 10.455399523742015
17.97926664352417 2.710083246231079
acceleration in solver= 6.634211944790991
```
### Comparisons

![](comparison.png)

The comparison may not imply the clinical quality of third-party packages.

### Contact information
If you have professional requests related to the project, please contact
email: pynufft@gmail.com